Evolved resource sharing behaviour in disaster situations

by Peter R Lewis

Evolved Resource Sharing Behaviour in Disaster Situations Peter R. Lewis MSc Project Report Supervised by Dr. Jonathan Rowe School of Computer Science University of Birmingham September 2006 Abstract It is accepted knowledge that during times of strife human beings come together and act selﬂessly for the common good. But why is this the case? Is the tendency to share resources with those less fortunate than ourselves motivated purely psychologically or is there an economic or social beneﬁt to this behaviour? A multi-agent based social and economic model is developed and used for exploration of such behaviour. An investigation into the dynamics of the model is conducted in order to inform the interpretation of results. The eﬀect of both resource density and rate of availability on the carrying capacity of an environment are shown. The model is extended to include natural and other resource shortage causing disasters and the eﬀect of such disasters on the population is explored. The model is then further extended to include the option for agents to engage in resource sharing behaviour according to an individual generosity characteristic. An evolutionary preference for certain forms of resource sharing is identiﬁed and its subsequent eﬀect on population dynamics are described. Further investigation shows a causal link between the severity of disaster faced by a population and its preference for resource sharing, and a complex though loosely proportional relationship is exposed. Conclusions are presented with reference to economic theories of altruism and behaviour in adversity. Finally, the results are evaluated and potential alternative theoretical approaches are discussed. Keywords: agent based modelling, artiﬁcial society, disaster, economic behaviour, population dynamics, resource sharing. I would like to extend my thanks to my supervisor Dr. Jonathan Rowe for his inspiration, support and guidance throughout this project, to David Siﬀord for introducing me to agent based social modelling, to Pieter Buzing for the use of his JAWAS system. I would also like to thank my girlfriend Marla Reyzer for keeping me going when my motivation faded and for indulging my endless will to discuss the ideas in this project. Finally, I would like to thank my parents for their seemingly limitless support, especially my mother for continually challenging my scientiﬁc approach to society. This project extends a previous mini-project, also completed in partial fulﬁlment of an MSc Natural Computation at the University of Birmingham. In order to distinguish between this and previous related work, ideas developed during that mini-project are referenced where used. In addition, sections 2.1, 2.2, 2.3 and 2.5 are heavily based on the mini-project report, as are some parts of sections 2.4, 2.6 and 3.2. 1 Contents 1 Introduction 2 History and Examples of Agent Based 2.1 Modelling Segregation . . . . . . . . . 2.2 Axelrod . . . . . . . . . . . . . . . . . 2.3 Simple, Methodical, Relevant . . . . . 2.4 Sugarscape . . . . . . . . . . . . . . . 2.4.1 Vision . . . . . . . . . . . . . . 2.4.2 Metabolism . . . . . . . . . . . 2.4.3 Old Age and Reproduction . . 2.4.4 Experiments and Results . . . 2.4.5 Carrying Capacity . . . . . . . 2.4.6 Wealth . . . . . . . . . . . . . 2.4.7 Conclusion . . . . . . . . . . . 2.5 Communication and Cooperation . . . 2.6 Other Examples . . . . . . . . . . . . Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 6 6 7 9 10 11 11 12 12 14 14 15 17 3 Altruism, Sharing and Selﬁshness 18 3.1 The Economics of Altruism . . . . . . . . . . . . . . . . . . . . . 18 3.2 Examples of Altruism in Agent Based Modelling . . . . . . . . . 20 3.3 Sharing in Disaster Situations . . . . . . . . . . . . . . . . . . . . 21 4 A Multi-Agent Society 4.1 Experimental Set-Up . . . . . . 4.2 Population Dynamics . . . . . . 4.2.1 The Generational Eﬀect 4.2.2 Resource Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 24 25 25 27 5 Resource Sharing 30 5.1 A Deﬁnition of Sharing . . . . . . . . . . . . . . . . . . . . . . . 30 5.2 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6 Disasters 35 6.1 A Deﬁnition of Disaster . . . . . . . . . . . . . . . . . . . . . . . 35 6.2 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2 7 Introducing Sharing in Disaster Situations 39 7.1 Theory and Hypothesis . . . . . . . . . . . . . . . . . . . . . . . 39 7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 8 A Relationship Between Severity and Generosity? 43 8.1 Adapting the Model . . . . . . . . . . . . . . . . . . . . . . . . . 43 8.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 9 Conclusions 10 Evaluation and Future Work 10.1 Extensions to this Work . . . . . . . . . . . . . . . . 10.1.1 Alternative Theoretical Approaches . . . . . 10.1.2 Diﬀerent Models of Sharing . . . . . . . . . . 10.2 Investigating Other Social and Economic Behaviour 10.3 Alternative Modelling Methods . . . . . . . . . . . . A Project Proposal B Full Model Speciﬁcation B.1 Objects . . . . . . . . B.1.1 Environment . B.1.2 Cell . . . . . . B.1.3 Agent . . . . . B.2 Rules . . . . . . . . . . B.2.1 Cell Rules . . . B.2.2 Agent Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 50 50 50 51 51 51 54 56 56 56 56 56 57 57 58 3 List of Figures 2.1 2.2 2.3 2.4 2.5 4.1 4.2 4.3 5.1 5.2 5.3 6.1 6.2 7.1 7.2 7.3 8.1 8.2 Sugar mountains on the Sugarscape . . . . . . . . . . . . . . . . Agents on the Sugarscape . . . . . . . . . . . . . . . . . . . . . . An agent’s range of vision in Sugarscape . . . . . . . . . . . . . . Oscillation of the population size around the carrying capacity in Sugarscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distribution of wealth in Sugarscape . . . . . . . . . . . . . . . . Population size with and without reproductive restrictions . . . . Eﬀect of diﬀerent sugar densities on population size . . . . . . . Eﬀect of diﬀerent sugar growback rates on population size . . . . Normalised distribution of wealth across the population in control model . . . . . . . . . . . . . . . . . . . . . . . . . . Evolution of generosity when sharing is added . . . . . . . . Population size when sharing is added . . . . . . . . . . . . the . . . . . . . . . 9 10 11 13 15 26 27 28 32 33 34 37 38 Population size with and without random disasters . . . . . . . . Wealthiest individual with and without random disasters . . . . Comparison of evolved generosity with and without random disasters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Comparison of population size with and without random disasters 42 Wealth of the richest individual with and without disasters and sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Evolved generosity under diﬀerent severities of resource shortage Relationship between severity and evolved generosity . . . . . . . 45 46 4 Chapter 1 Introduction It is accepted knowledge that during times of strife human beings come together and act selﬂessly for the common good. But why is this the case? Is the tendency to share resources with those less fortunate than ourselves motivated purely psychologically or is there an economic or social beneﬁt to this behaviour? The primary aim of this project is to investigate how a population’s preference for the sharing or hoarding of resources develops under varying environmental conditions, in particular, natural disasters and other causes of resource shortage. A secondary aim is to investigate how this preference aﬀects the demographics and particularly dynamics of the population. Artiﬁcial agent-based societies provide us with the tools with which to investigate such population wide social and economic behaviour. Using a bottom-up approach, we may specify the way in which individual agents interact, according to rules derived from human behaviour, and observe the eﬀect of these interactions at the population level. This project makes use of and extends a model developed for a previous mini-project (Lewis 2006). Speciﬁc objectives include: • To complete a survey and review of work relating to resource sharing in agent-based social modelling, and theories of altruism and sharing in disaster situations. • To formally extend the model used in the mini-project to include the behaviour and environments to be investigated, using theoretical bases. • To describe experiments to be carried out based on theoretical hypotheses. • To perform the experiments and draw conclusions. 5 Chapter 2 History and Examples of Agent Based Modelling 2.1 Modelling Segregation The ﬁrst published example of agent-based social modelling is commonly acknowledged to be Schelling’s work on segregation (Schelling 1978). A grid world was populated with agents and each agent was either one colour or another. Agents of each colour were initially distributed randomly across the grid. The agents followed one simple rule; if the number of neighbouring agents of its own colour is greater than a certain preference threshold, then it is satisﬁed and does nothing. If on the other hand it is not, then the agent moves to the nearest available location on the grid which does satisfy the threshold condition. This rule is run for each agent in turn, and the process iterated. Schelling found that from an initial random distribution of each colour, the agents quickly clustered together into coloured blocks, forming ‘segregated neighbourhoods’. Schelling also found that this eﬀect was remarkably robust. Even when most of the agents on the scape were ‘colour-blind’ and did not follow the rule laid out above, the eﬀect was still reproduced (Schelling 1978). This shows how a preference to be near similar individuals as onesself present in just a small section of society can have an overwhelming impact on the emergent spacial structure of the population. 2.2 Axelrod Though Schelling had shown how agent-based modelling could be applied to a speciﬁc problem, much of the theory of agent-based modelling was explored by Axelrod (1997). Building upon the Prisoner’s Dilemma, as explored in his previous book (Axelrod 1984), Axelrod increases the size and scope of the game, by adding multiple actors and types of interaction to the original idea. Using computer simulation as a tool investigate the dilemmas presented, local interactions between playing agents give rise to emergent behaviours which may then 6 be observed directly. Many of Axelrod’s extended Prisoner’s Dilemma-style problems were concerned with alliances and conﬂicts between organisations such as nations and companies. One speciﬁc example is that of the alignment of European nations during the second world war. Nations were represented as agents in the system, which obeyed simple local rules to put themselves into one of two alliances, similarly to the classical conform or defect decision in the Prisoner’s Dilemma. Using this system, Axelrod hoped to reproduce the historical alliances of Europe in the 1930’s. Local rules were developed based upon the assumption that a nation chooses to group itself with other ‘similar’ nations in the hope of resisting a perceived threat from another nation. Similarities and diﬀerences between nations were calculated in terms of ”ethnic, religious, territorial, ideological, economical and historical concerns” (Axelrod 1997, pp 83-84), and the potential threat posed by a nation was determined according to its size. Using this model, a surprisingly accurate picture of historical alliances was reproduced (Axelrod 1997). Other investigations include alliances formed by companies to promote technical standards and the emergence of social norms. Though much of the detail of Axelrod’s examples is not particularly relevant to this paper, his work opened up the door to a wide range of possible applications of emergent agent-based modelling. 2.3 Simple, Methodical, Relevant What we are interested in here is the emergence of complex global behaviour through the widespread repeated application of simple local rules. Complexity theory describes to us the distinct paradigms of looking at a system at micro and macro levels (Axelrod 1997). At the micro level, the local rules determine interactions between the agents, but at the macro-level, our observations are made. Throughout his examples, Axelrod argues for the principle of keeping the model as simple as possible at the micro level. It is important to realise, as Axelrod states, that the aim of agent-based modelling is not to make the simulation as realistic as possible (Axelrod 1997). Quite the opposite, as the ‘keeping it simple’ principle suggests, we want to create the simplest possible model with which we can reproduce our desired phenomenon. Then, the complex behaviour patterns may be observed at the macro level, and we may reasonably be expected to explain what changes at a micro level brought about the diﬀerent macro-behaviours. For this reason, it is therefore important to ensure that we begin any investigation with the simplest possible micro-behaviour and that all changes made at the micro level are incremental. In doing this kind of science by simulation, Axelrod argues that we are departing from the traditional scientiﬁc methods of induction and deduction (Axelrod 1997), and instead moving toward a ”third way of doing science” (Axelrod 1997, p3). Induction, commonly used in the social sciences, biology and in some branches of physics, involves collecting and analysing large amounts of data. This analysis then provides us with observed behaviour, which we can be conﬁdent (to a certain degree) of being reproduced in a given set of circumstances. 7 Conversely, deduction is concerned with identifying and setting basic principles, from which we can derive more complex behaviours. This method will be more familiar to computer scientists. Rather than seeing agent-based modelling as a separate scientiﬁc method however, we have previously argued that in doing this type of research we are in fact employing both induction and deduction on our problem (Lewis 2006). In agent-based modelling, we ﬁrst specify our basic principles; our assumptions about the environment, the agents and their interactions. In this case however, the deduction from these basic principles is deemed too complex to be done with a pencil and paper. The computer simulation is therefore run to perform the deduction of complex behaviour for us. The patterns of this behaviour are observed by the computer and recorded in some useful way, as determined by the scientist. We then employ an inductive scientiﬁc method to analyse these data in order to produce some useful statement about the properties of our model. Axelrod correctly notes that we depart from traditional induction during the inductive step, as our data do not come from the real world. It does not appear though that such a bound on induction need exist; this is still induction. Similarly, the deductive step extends the idea of traditional deduction, as we are now not merely dealing with the science of what is, we are making deductions based on the science of what might be. Nevertheless, this is still deduction and therefore agent-based modelling makes use of a serialisation of induction and deduction and does not depart from these time-honoured methods. It is also important to realise that in simplifying the real world into a model of this type, we necessarily make many assumptions. For example, the agents used in all the models described in this paper are deterministic, following set rules. Many advocates of free-will will ﬁnd this a diﬃcult assumption to make. If however we remove the constraint of seeing agents as one-to-one representations of humans in society, it may be argued that our ﬁxed agent rules actually represent an aggregate of decisions made by several people in the real world. In this context, the free-will question becomes irrelevant, as we are simply modelling observed behaviour. Similarly, we often make the simpliﬁcation of a spatially discrete environment, which places signiﬁcant bounds on the movement and spacial interaction of the agents on the scape. In each model, there are many more assumptions than could reasonably be described here, though the key point is to ensure that we are mindful that these assumptions exist nonetheless. In doing this, when we draw conclusions from the model, we must ask ourselves whether these assumptions are unduly aﬀecting our results in unrealistic ways. This is no trivial task, especially considering that many of the more diﬃcult to identify assumptions will have been introduced subconsciously by the scientist or programmer based on their own perspective of the world. This leads to a complex debate on the applicability or truth of such simulations. See Schmid (2005), Frank and Troitzsch (2005) and David, Sichman, and Coelho (2005) for an interesting discussion of this. Nevertheless, as this chapter will show, agent-based modelling can be a useful tool in the social sciences. It is however important to be mindful of the context in which its conclusions must be considered. 8 2.4 Sugarscape The economists Epstein and Axtell took the idea of agent-based modelling and applied it to the study of society as a whole (Epstein and Axtell 1996). People living in the world were represented as agents occupying space on a scape. The scape was a toroidal lattice of cells, each containing a certain quantity of a generalised resource, known as sugar. The sugar was arranged in two ‘sugar mountains’ with high concentrations of sugar in the centre of each, lower concentrations around the edges and barren patches between them (see ﬁgure 2.1). As agents move from one cell to another, they harvest the sugar, adding it to their own personal stash. The sugar on the cell then grows back over time (according to a growback rate) and the agent moves on. Each agent metabolises a certain amount of sugar on each move, and if an agent’s stash ever becomes empty it ‘dies’ and is removed from the scape. This requires the agents to continue to harvest sugar in order to survive. As in Axelrod’s work, each agent was subject only to local rules based on limited local information. The simulation proceeds on a turnwise basis, executing of all agents’ rules. The full execution of all the agents’ rules once, plus rules pertaining to the scape itself, such as the regeneration of sugar, is called an iteration or cycle of the Sugarscape. When one iteration is complete, the process begins again. Through the use of only very simple local rules, some surprisingly complex emergent behaviours were observed. Figure 2.1: Sugar mountains on the scape, with the highest concentration of sugar at the centre of each mountain. Source: Epstein and Axtell (1996) Each of the Epstein and Axtell’s agents occupied exactly one cell on the 50x50 cell scape. Agents were not permitted to share their cell with another agent. The agent population was also heterogeneous as each agent possessed a number 9 of individual characteristics. Figure 2.2: Agents on the scape. Source: Epstein and Axtell (1996) 2.4.1 Vision In order to decide which cell to move to next, an agent ﬁrst looks at the nearby cells, noting how much sugar is available on each cell. It then moves to that cell. How far an agent can ‘see’ when deciding where to move next is determined by its vision. For example, an agent with a range of vision of one cell, will be able to see all cells in its Von Neumann neighbourhood; one cell in each direction, but not diagonally, in order to ﬁnd the most sugar-rich cell. Figure 2.3 illustrates this. An agent with a vision of two, by extension, has twice as many cells to choose from when deciding where to move, as it can not only see each adjacent cell, but also the one beyond that. Note that if an agent selects a cell which is not directly adjacent to it, it may still move directly there. It is not required to move through the intermediate cell, nor does the agent use up more than one move to reach the new cell. Having a higher vision would therefore seem to be a signiﬁcant advantage to survival, as not only does the agent have more cells to choose from when making a move, but it may also move further. Each agent was given a vision value between 1 and 6 inclusive, which remained ﬁxed for its lifetime. 10 Figure 2.3: An agent’s range of vision in Sugarscape. Source: Epstein and Axtell (1996) 2.4.2 Metabolism An agent’s metabolism is the amount of sugar it consumes (i.e. is removed from its private stash) per iteration. This may also vary from agent to agent. Clearly, a lower metabolism is a signiﬁcant advantage to survival, since an agent will be able to make more moves for a ﬁxed amount of harvested sugar than an agent with a higher metabolism. The pressure to ﬁnd more sugar is therefore greater for those agents with higher metabolisms. Each agent was give a metabolism between 1 and 4 inclusive, which remained ﬁxed for its lifetime. 2.4.3 Old Age and Reproduction Two additional possibilities were added to the model; death by old age and reproduction. To achieve this, the following rules were introduced. • Death from old age. Each agent is given a maximum age of between 60 and 100. When the agent reaches this age it dies of natural causes and is removed from the scape. • Reproduction. Agents are given a male/female tag at random. When two agents of opposite genders are in adjacent cells, they have the opportunity to reproduce. Whether they do so is determined by a number of factors such as whether there is space available on the scape for a new agent to occupy and whether the agents are of fertile age (loosely between 15 and 50, with some random variation). When sex occurs, a new agent is placed on the scape adjacent to the parents. Each of the new agent’s characteristics (such as vision and metabolism) are inherited with some probability from one or other of the parents. Each parent then gives half of its current sugar to the oﬀspring, and the new agent proceeds to go about its business following the rules as the other agents do. The addition of these simple rules has a profound eﬀect on the behaviour of the Sugarscape. As agents move about harvesting sugar, reproducing and dying, we 11 see the growth of a whole society of agents, spread over generations. As stated earlier, it was expected it to be an advantage to survival on the Sugarscape to have high vision and low metabolism. Since those agents which survive longer will have more opportunity to reproduce and hence have more oﬀspring, as the simulation proceeds we will see the optimisation of the agents’ characteristics to life on the Sugarscape. This optimisation is evolution in its simplest form; the adaptation over generations of characteristics to an environment. 2.4.4 Experiments and Results Epstein and Axtell’s Sugarscape model provided them with signiﬁcant experimental opportunities and some interesting results. Emergent spatial eﬀects such as terracing on the sugar mountains, diagonal migration towards areas of high sugar concentration even though the agents have no diagonal vision and migration wave patterns were phenomena of particular interest (Epstein and Axtell 1996). Our previous work gives a review of these experiments and eﬀects (Lewis 2006). Epstein and Axtell also experimented with the evolution of the vision and metabolism characteristics (Epstein and Axtell 1996). They found that after a few hundred iterations the metabolism of all the agents on the scape had reached the minimum value of 1. The vision parameter however did not as expected always reach the maximum allowed. Epstein and Axtell point out that it is not necessarily desirable for the entire population to have the highest vision possible, as this may lead to overgrazing and an explosion in population size, both of which might contribute to the extinction of the population. In our previous work (Lewis 2006), further investigation of the evolution of both vision and metabolism reveals that there is indeed a balance to be struck. The evolutionary patterns are investigated in detail and results indicate a tendency for the evolutionary process to direct the population’s characteristics away from a bad conﬁguration rather than towards a good one. When a conﬁguration which is good enough is reached, the evolutionary pressure subsides (Lewis 2006). 2.4.5 Carrying Capacity “One of the most fundamental ideas in ecology and environmental studies” (Epstein and Axtell 1996, p30) is that of the carrying capacity of an environment. Each member of any species will have a certain minimum resource requirement, in food, space and other areas. If its available supply of any of these resources dips below this tolerated minimum, then the creature will die. Across a whole population sharing an environment, resources must be shared or otherwise divided up between the population members. It therefore follows, that there exists a maximum size which a population may reach and that this may indeed be less than that determined by the space available in the environment. This is known as the environment’s carrying capacity (Cohen 1997). A Sugarscape-like model, in which agents move about in search of food, reproducing and dying either of starvation or old-age, provides us with one of 12 the simplest spacial representations of population dynamics over time. Indeed, Epstein and Axtell (1996) show that this model is capable of identifying the carrying capacity of the environment. In the Sugarscape model, where each agent occupies exactly one cell each, clearly there is a maximum permitted population, equal to the number of cells on the scape. In Sugarscape, the population could not be expected to reach this level however, as there was not enough sugar available to support such a high number of agents. Due to a generational eﬀect however, rather than settle exactly on one particular ﬁgure, Epstein and Axtell (1996) found that the population size oscillated around the carrying capacity (see ﬁgure 2.4). No investigations were performed however into the relationship of the carrying capacity to the properties of the environment itself. Indeed, Epstein and Axtell intentionally always began their simulations with an initial population size close to the expected carrying capacity. Figure 2.4: Oscillation of the population size around the carrying capacity in Sugarscape. Source: Epstein and Axtell (1996) In Lewis (2006) we showed how by allowing multiple occupation of a cell by agents, the physical size of the scape need not limit the number of agents present. Indeed on a scape with suﬃcient resources and fast resource growback rates, the number of agents can easily exceed the number of cells. This may appear at ﬁrst to be an unrealistic extension to the model, as in the real world people occupy a minimum amount of space. This is unfounded however, as human population densities frequently exceed the level at which each person has enough space to produce suﬃcient resources for his or her survival. Indeed this is present in virtually all industrialised societies. 13 We also showed that for a given stable environment, so long as there is suﬃcient resource for the population not to become extinct, it will always stabilise, though not always to the carrying capacity. Indeed, when the simulation was begun with a particularly small initial population, the stabilised population size was somewhat lower than the carrying capacity (Lewis 2006). Furthermore, we showed that when resources (the metaphorical sugar) are distributed with a ﬁxed density and even distribution rather than sugar mountains, the carrying capacity grows in direct proportion to the size of the scape (Lewis 2006). It was not determined however whether this proportionality is in full due to a directly proportional relationship with the amount of resource on the scape, or if the physical properties of the scape are also in part responsible. This is investigated more fully in section 4.2. 2.4.6 Wealth Another useful tool which Sugarscape gives us is the ability to observe the distribution of wealth in a population. By taking a snapshot of the amount of sugar in each agent’s personal stash at a given iteration, Epstein and Axtell produced histograms displaying how wealth was distributed across the population. They found that although the distribution of sugar was initially relatively evenly spread, it quickly became highly skewed (see ﬁgure 2.5). No speciﬁc information was given regarding the time intervals between each of these histograms. The emergence of this type of wealth distribution has long been recognised as a common occurrence in human societies (Pareto 1897), and debate continues about the exact nature of the distribution (Hogan 2005). Further experimentation with wealth distributions revealed that the development of this highly skewed distribution of wealth is both highly robust and extremely quick to emerge (Lewis 2006). 2.4.7 Conclusion A summary of those ideas developed by Axtell and Epstein which are relevant to this paper has been presented here. In addition, extensions and contradictions revealed by our own work with Sugarscape-like environments has been summarised. It should be noted that the model used in this work is not identical to Axtell and Epstein’s and full details of the diﬀerences are explained in that paper (Lewis 2006). Axtell and Epstein have continued to investigate various social, ecological and economical eﬀects in the Sugarscape framework, such as pollution, trade and inheritance. They hoped that the ideas presented would inspire a new form of “generative social science” (Epstein and Axtell 1996). Indeed, the framework they presented has been used and adapted to perform research into other areas of social science. A full review of this work is contained in Lewis (2006), but is 14 Figure 2.5: Distribution of wealth in Sugarscape. Source: Epstein and Axtell (1996) not relevant to this paper. 2.5 Communication and Cooperation The Sugarscape model is extremely versatile and may be used to investigate all manner of ecological and evolutionary phenomena. Its generic nature and modularity, easily implemented in an object-oriented programming language, enables researchers to add in or remove particular environmental scenarios and agent characteristics and behaviours. Harnessing the extendability and modularity, a recent re-implementation and extension of the Sugarscape model was done by Buzing et al. (2003) to investigate the evolution of communication preferences in a cooperative situation. Their model, VUScape (later extended into the more general JAWAS framework), is methodologically very similar to the original Sugarscape, though with 15 the following diﬀerences: • Exploratory behaviour: if an agent does not detect any sugar within its vision, it will move to a random cell within its vision in the hope of discovering more sugar. • Multiple occupancy of cells: more than one agent may occupy the same cell; there is no limit to this. • Random sugar locations: sugar is distributed randomly across the scape in a uniform distribution (instead of the sugar mountains present in Sugarscape). • Random age initialisation: at the beginning of the simulation, agents are given a random age rather than zero. This is to reduce the generational eﬀect observed by Epstein and Axtell (1996) as the whole population reaches death at a similar time. In addition to these methodological diﬀerences from Sugarscape, agents also follow communication rules. A limit on the amount of sugar an individual agent can harvest was created. If an agent arrives on a cell with an amount of sugar greater than this threshold, it must cooperate with another agent in order to harvest the sugar. It may achieve this through communication. An agent in this situation will (with some probability proportional to a talk-preference parameter) broadcast a signal indicating that it is in need of help and how much sugar is available at its location. Agents also have a listen-preference parameter, and with some probability proportional to this, will listen for broadcasts and move to the location of the broadcasting agent. When more than one agent is present on the cell with a high level of sugar, the sugar is harvested and the agents share it equally. Both the talk-preference and listen-preference parameters are similar to the vision and metabolism parameters of the original Sugarscape model in that they are ﬁxed for the lifetime of the agent, though vary from agent to agent and are inherited by oﬀspring. In this way, the agents are expected to evolve a higher preference for talking and listening as the simulation proceeds. Buzing et al ran the simulation both with the communication rules on and oﬀ. They found that enabling the communication led to a higher chance of survival of the population as a whole. With communication, all 10 runs of the simulation reached iteration 500 without the population becoming extinct through starvation. This was not always the case without communication, though details of the likelihood of extinction are not given. Buzing et al notably did not ﬁnd any increase in the carrying capacity of the scape when communication was added. As expected, the talk-preference and listen-preference characteristics were optimised by the evolutionary process. Interestingly however, the listen-preference was found to increase more quickly than did the talk-preference (Buzing et al. 2005). We must be careful however with results such as this, not to infer too much from the apparent behaviour of the agents. This study itself must not be seen to support the idea that communicating species have a higher chance of survival in the same environment per se. It is clear that by enabling communication (and 16 therefore cooperation), a greater level of sugar was available on the scape for the agents to harvest. The evolutionary process then discovered the best parameter settings to optimise the amount of sugar available; high listen and talk preferences. Clearly, under a pressure to cooperate brought about by a high individual harvest threshold, cooperation was maximised by the population. But the communication rules present were merely methods for this to occur, and do not imply any further usefulness of communication by a species. 2.6 Other Examples A number of other large and small research projects have also emerged, applying the paradigms of agent-based spatial modelling to a wide range of areas. The Artiﬁcial Anasazi project (Littler 1998; Axtell, Epstein, Dean, Gumerman, Swedlund, Harburger, Chakravarty, Hammond, Parker, and Parker 2002) uses agent-based modelling to attempt to understand the history of the now-extinct Anasazi tribe of ancient Arizona. A dynamic scape-style lattice was created to model the real landscape as geological surveys show it to have existed between 400 and 1450 AD. The simulation is designed to discover how the civilisation could have spontaneously died out in the absence of any external pressures. Research is ongoing. Jager et al. (2001) were surprised by the realism generated by the use of agentbased modelling to investigate the dynamics of crowd formation and movement. Focusing on the causes of mob violence, they were able to investigate a number of diﬀerent group types and dynamics. Most recently, the New Ties project (NEW TIES Consortium 2005) is a large European Union funded research project which aims to use a multi-agent simulation ...to realize an evolving artiﬁcial society capable of exploring the environment and developing its own image of this environment and the society through cooperation and interaction. (NEW TIES Consortium 2004) This ambitious project demonstrates the sheer scale of computing resources necessary to realise all but the simplest of multi-agent simulations. As part of the project, Craenen and Paechte (2005) show how peer-to-peer networks may be used as an architecture for the distributed computation of such large scale simulations. Helpfully, they describe a number of key pitfalls for which one must be mindful in designing such distributed computational models and propose strategies to maximise the eﬃciency and consistency of such systems. Publications so far relate particularly to the evolution of language perception (Divina and Vogt 2005), and describe the current direction of the project (Vogt and Divina 2005). 17 Chapter 3 Altruism, Sharing and Selﬁshness A number of researchers have taken the ideas developed by Axtell and Epstein and extended them to investigate sharing behaviour. Using such agent-based modelling techniques, we are able to investigate the development of altruism and sharing in a variety of environmental conditions. 3.1 The Economics of Altruism In order to study the development of altruistic and mutualistic economic behaviour, it is helpful to have an understanding of what we mean by these terms and how they manifest themselves in society. Jaﬀe (2002) provides a modern theoretical approach to the understanding of altruism, based on unidirectional (purely altruistic) and bidirectional (mutual or commercial) transfers of wealth. Firstly, it is important to recognise the distinction between the utility of the transferred wealth, which may well be diﬀerent for donor and receiver, and its monetary value, which will be equivalent for both. To cite Jaﬀe’s example, if a wealthy person donates a blanket to a homeless person, then the utility of the blanket to the homeless person is much higher than for the wealthy person, even though the net wealth of the system remains the same (Jaﬀe 2002). In an agent based system similar to Sugarscape, this distinction is also present. If we have an agent with an accumulated sugar stash of 3 units and a metabolism of 2, it is clear that the agent has one move in order to ﬁnd more sugar. Failure to do this will lead to the agent’s demise. A second agent arrives however, with several hundred units of sugar accumulated and an equivalent metabolism. This agent clearly does not have the immediate pressure faced by the ﬁrst agent. Rather, it may wander carefree about the scape, harvesting sugar when it can and unless there is a change in environmental circumstances, we can expect it to survive to a ripe old age. Clearly 4 units of sugar have signiﬁcantly diﬀerent utility values for each agent. For the ﬁrst agent, it would provide two extra moves with which to ﬁnd its next supply of sugar. For the second agent, it would probably not even be noticed. The second agent donating 4 units of sugar to the ﬁrst may 18 be seen as metaphorically equivalent to the blanket example. To use Jaﬀe’s notation, we may call value of the utility to the donor K, and the value of the utility to the recipient A. In the above example, K < A and this is known as a synergistic transfer (Jaﬀe 2002). Conversely, K > A implies that total utility is reduced and the repeated occurrence of such transfers will lead to the drain of utility from the system. Such activities are clearly not useful. The special case of K = A is therefore an eﬃcient transfer, but is as Jaﬀe (2002) points out, an ideal case and not likely to be found in nature. The second dimension introduces a temporality to the value of the utility and concerns the donor’s motivation. We have deﬁned K to be the utility value of the transfer to the donor at the time at which the transfer occurs. By extension, B is deﬁned as the utility value or beneﬁt to the donor at some point in the future (Jaﬀe 2002). On the surface, it may appear that a wealthy person has given 10,000 to their friend, but this may be on the understanding that the friend uses the money to set up a business, and the donor expects 12,000 back in a year’s time. If K < B, we therefore have not an altruistic act, but an investment (Jaﬀe 2002). Clearly, in the unidirectional cases above, the donor does not expect anything back in the future. In these cases B = 0 and hence (assuming the donation had some value) K > B. The case of K = B is again the eﬃcient ideal and is unlikely to occur in nature. This second dimension gives us a particularly useful insight into the motivations for some apparently altruistic acts, and may aid us in identifying scenarios in which such behaviour may develop. Of course, not all K < B transactions may be as explicit as a formal investment, so it is important to identify the potential sources of any future beneﬁt to the donor in a system. Thirdly, Jaﬀe points out that the donated utility, K may be in eﬀect exchanged for beneﬁts, either immediately or in the future, which are not measurable in economic terms (Jaﬀe 2002). Given examples of such beneﬁts include security, belonging and happiness. An example of such a transaction occurring in the real world could be someone who engages in voluntary work with the church because they believe that they will get into heaven as a result. This third dimension provides us with signiﬁcantly increased insight into the motivations for altruism, but at the expense of a reduced ability to reason about it. If a donor appears, in economic terms, to be performing a unidirectional synergistic transfer, we would class them as a pure altruist. However, if the actor receives a quantitatively unmeasurable beneﬁt in exchange, then they are not in fact engaging in pure altruism. This presents a signiﬁcant dilemma in the application of the theory to real, psychological actors such as humans. Fortunately, in applying Jaﬀe’s theory of altruism to donations in an artiﬁcial society model, this dilemma is not a barrier. However, this diﬀerence does invite further questions regarding the applicability of such simulations based on non-cognitive agents to the real world. It is helpful to remind ourselves however, that agents in Sugarscape-like models do not necessarily represent people on a one-to-one mapping. As was discussed above (see section 2.3), our ﬁxed agent rules may be seen as a metaphor for an aggregate of decisions made in the real 19 world. If desired, individual psychological motivations for acts such as altruism could be included in this model by introducing a rule representing aggregated behaviour, such as has been done for reproduction. 3.2 Examples of Altruism in Agent Based Modelling Jaﬀe went on to use a simple non-evolutionary agent-based model to observe the eﬀects of these diﬀerent types of altruism on the total amount of wealth in a population (Jaﬀe 2002). He found that there were no examples of either dissipative (K > A) or eﬃcient (K = A) altruism being advantageous to either the group or the individual. Regularly occurring synergistic altruism however, was shown to be of economic beneﬁt to the agent society. Younger used a Sugarscape-like agent-based modelling technique to perform a series of studies into egalitarian and ‘gift-giving’ societies such as are found in Polynesia, the South Paciﬁc and remote parts of Australia (Younger 2004; Younger 2005a; Younger 2005b). Agents were placed on a 20x20 cell scape which contained food sources and were given a vision of two cells in each direction. Additionally, the scape contained a home shelter, to which agents could bring food from the food sources. Agents retained a knowledge of the location of the shelter and of the food sources. Critically, agents were also able to share food and to steal from one another, and this information was also stored in an ‘interaction matrix’ which recorded a personal history of agent encounters. Agents were more likely to share food with those agents with whom they had shared food before, creating a situation of ‘mutual obligation’. It was found that if agents then communicated these histories to each other, creating reputations, then the total mutual obligation signiﬁcantly increased (Younger 2004). Younger also found that if agents shared food indiscriminately, as is the case in many hunter-gatherer societies, then a higher total mutual-obligation was also the result. Conversely, if agents restricted sharing to those most likely to reciprocate sooner (according to the agent’s interaction history) then the total mutual obligation reduced (Younger 2005a). Using a similar model, Younger extensively studied the impact of violence and revenge on the mutual obligation of such gift-giving societies. The agent-based approach was able to provide an insight into the eﬀect of increased violence on sharing, the use of revenge violence as a deterrent to theft and the balance between mitigation against the personal threat of violence (i.e. by making agents more likely to ﬂee) and the ‘cohesion’ of society as measured through the amount of sharing which took place. The agents’ interaction matrices recorded membership of a group with whom the agent would share. Stealing agents would often be quickly excluded from the group due to their reputations (Younger 2004). 20 Younger’s indiscriminate sharing model took no account of the utility value of the food to diﬀerent agents, as sharing agents gave food out equally to all other group members in the locality. This model, which does not take account of the wealth of the recipient does not allow us to diﬀerentiate between synergistic, equitative or dissipative altruism. However, this is not a problem in modelling the simple hunter-gatherer societies which Younger studies. The motivation for the sharing behaviour in such societies may be both a division of labour and an inability to store food for long periods (Younger 2004). For example, in an environment where collaborative hunting is necessary every day to provide for the group, each hunter may only realistically participate in a proportion of the hunts. Since food may not stay fresh for more than a day or two and non-participants also need to eat, the gathered food is shared by the entire group. Outside the realms of this particular predicament, Younger’s indiscriminate sharing model is not applicable. 3.3 Sharing in Disaster Situations In times of strife, the sharing of resources takes on a diﬀerent role. It is not news that when faced with adversity, human beings come together, but the motivation for the development of this behaviour is not widely understood. It is commonly known that in Britain during the Second World War - a time of chronic resource shortage - communities came together, people worked long hours for little pay and food was rationed and often grown at home. Economically, in disaster situations, human beings often behave in rather surprising ways. One well documented example is that of the Alaskan earthquake of 1964. Kunreuther and Dacy found that despite the fact that supply lines to the remote communities were cut oﬀ, prices did not increase as would be predicted by traditional supply and demand economics. In fact, many prices remained unchanged for months and in some cases actually fell (Kunreuther and Dacy 1967). They attribute this apparently irrational economic behaviour to a sudden spread of ‘community feeling’, prompted by the disaster. Hirshleifer draws parallels between the behaviour in Alaska and that observed in other disaster situations thoughout the twentieth century, identifying such behaviour as the most common reaction to a disaster. He does not accept however that a purely psychological increase in community spirit can be held completely to account for the phenomenon (Hirshleifer 1987). Hirshleifer proposes instead the development of a rational taste for preserving the alliances present in society. By partaking in apparent altruistic behaviour; giving up ones resources in the short term to those in need, the individual can hope to ensure that the already troubled society of which he is a member will avoid further economic breakdown. Complete economic collapse of course, is of beneﬁt to very few members of society indeed, as Hirshleifer adds, not even to most criminals (Hirshleifer 1987). The avoidance of this breakdown through a set of mutual duties is described by Hirshleifer as alliance preserving behaviour (Hirshleifer 1987). 21 Returning to the earlier example of the homeless person and the blanket (see section 3.1), it quickly becomes apparent that such synergistic altruism is particularly helpful in times of disaster. Let us ﬁrst forgive ourselves of any assumptions that the homeless person was not a useful contributor to society; instead he was the victim of an earthquake which destroyed his house. Rather than being unemployed, the homeless person is in fact a baker, but his bakery was also destroyed. Had the homeless baker not received the blanket from the unaﬀected wealthy donor, he might indeed have died overnight from the cold. His immediate survival could well ensure the supply of bread to more of those aﬀected by the disaster. This is a rather contrived example, but the principle at the macro level is clear. When society faces breakdown due to economic adversity, synergistic donation on the part of those with the ability to perform it can lead to the preservation of the social alliance. It has already been hinted at that the kind of donations described here are not in fact purely altruistic. Since according to the theory, the donor hopes to ensure the future stability of the social alliance, he is in fact making an exchange. The exact nature of what the donor has purchased in initialising the transfer may vary. As in the above example, the expectation may be something quite concrete, such as the future supply of bread or the preservation of low prices. As an aside, given the signiﬁcance of the Far East to the world economy, this explanation may account for a larger proportion of the donations in the wake of the 2004 Asian tsunami than we might have previously expected. Of course, the donor’s purchase may also fall into Jaﬀe’s third category; non-economic beneﬁts. There is no doubt that the preservation of the social alliance provides a sense of solidarity and security which would be sorely missed in its absence. It would perhaps be interesting to compare such transactions with the psychological motivations for donation, such as those described by Kunreuther and Dacy (1967), but this is a discussion for another day. We may therefore describe a model of resource sharing which is representative of behaviour in disaster situations and grounded in economic theory based on real world events. Such a model should allow for the donation of resource from wealthier individuals to poorer ones and should take account of some aspect of the severity of the adversity faced. Possible models will be explored in a later chapter. 22 Chapter 4 A Multi-Agent Society In order to investigate any of the ideas described above using agent based modelling, it is foremostly important to have a full grasp of the nature and dynamics of the system which we are using. To the scientist, this may seem an over-obvious statement; to the social-scientist it may seem an impossible task. Since our work lies between the two, it is important to be mindful of that which we may otherwise assume. In previous work, we described a multi-agent artiﬁcial society, based on the Buzing et al’s JAWAS framework (see section 2.5)(Lewis 2006). In particular, two key drivers were identiﬁed when designing such a model: • Wherever possible, the simplest form of an existing model should be used as a basis for the work, with modiﬁcations only where necessary, though • Investigation of arbitrary characteristics present in existing models may yield preferable variations. The JAWAS framework is a modern, freely available JAVA implementation of the original Sugarscape with some modiﬁcations. The object-oriented design of the framework lends itself well to extension in various directions, as rules can be easily added and removed as are required. The system uses Java’s threading libraries to enable experiments to be implemented across large parallel architectures. Section 2.5 above details the key methodological diﬀerences between SugarScape and JAWAS. Our previous work provides a full discussion of the implications of these diﬀerences and where relevant, justiﬁcation for their continued inclusion (Lewis 2006). In our previous work with multi-agent societies, we tuned the model to enable the investigation of simple evolvable characteristics such as metabolism and vision. As described above (see section 2.4.4), this enabled us to further investigate the initial results described by Epstein and Axtell (1996) and Buzing et al. (2003, Buzing et al. (2005). In order to understand to the greatest degree possible the dynamics of the model which we are employing, it is vital to keep the model in its simplest form. 23 Since, in this work we are no longer interested in the development of the agents’ metabolism and vision characteristics, this is an obvious instance of where such a simpliﬁcation may be made. Whereas in our previous work, both the agents’ metabolism and vision were allowed to vary between 1 and 10, here they may both be ﬁxed to a suitable value. Disallowing the evolution of these characteristics ensures that when faced with the need to adapt their characteristics to suit the environment, the population’s only option is to evolve those characteristics in which we are interested. This ensures that we can be absolutely certain which behaviour at the micro level leads to the observed behaviour at the macro level and is a key practical example of Axelrod’s ‘keep it simple’ approach, described in section 2.3. Other than where changes are speciﬁcally noted, the model employed here is the same as that described by Lewis (2006). A full model speciﬁcation may also be found in appendix B. Additions to the model speciﬁc to the experiments conducted here, are described in the relevant sections below. 4.1 Experimental Set-Up Each simulation begins with a population of 500 agents, placed according to a uniform random distribution across the 2500 cell scape. Previous research conducted into the impact of the initial population size showed that the ﬁnal stabilised population size grew with a non-linear proportionality to the size of the initial population (Lewis 2006). It was found that for the size of scape used here, an initial population of at least 500 agents was enough to give the population a good chance of reaching the carrying capacity. Whilst a larger initial population could be used, increasing the initial population size serves also to signiﬁcantly increase simulation run times. The generalised resource referred to as sugar was also distributed according to a uniform random distribution. More speciﬁcally, sugar plants are distributed randomly across the scape, each with a maximum sugar potential beyond which it cannot grow. Each cell may be host to any number of sugar plants, hence each cell also has a maximum sugar potential. An agent will harvest all the sugar on the cell which it occupies and once harvested, the sugar on a cell grows back at a ﬁxed rate up to the cell’s maximum potential. The sugar plant density, and hence maximum total amount of sugar allowable on the scape is determined by a scape-wide richness parameter. Initial experimentation showed that settings such that the maximum sugar density was on average 28 units per cell, with the relatively fast growback rate of 10 units per cycle provided a large, stable population. Though a comprehensive set of experiments was not carried out, initial results suggested that a higher sugar density but lower growback rate led to a smaller, unstable population, whilst a lower sugar density and higher growback rate led to frequent extinctions. Both in previous experiments and in the initial experiments described above, it was observed that following the initial set-up of an experiment, which is necessarily somewhat arbitrary, the population and its characteristics had settled 24 down to stable values after at most 1000 cycles. In order to be sure in any claim relating to the stability of values, each simulation was run for a further 1500 cycles. This allows the identiﬁcation of any patterns such as periodicity or continued growth or decline. The presence of two areas of initial randomness have already been described, and a further one also exists. According to the agents’ rules (see appendix B), an agent selects the cell for its next move based on the amount of sugar present on the cells in its range of vision. It will always select the most sugar rich. However, should an agent be faced with more than one cell containing an identical amount of sugar, one of the candidate cells will be chosen at random. These random elements lead to results which may vary from run to run. For each particular experiment, we are therefore not looking for a particular absolute value for a given metric of the system, but a distribution from which the results come. In order to be able to determine the nature of such distributions, we apply a similar procedure as is commonly used with the comparison of stochastic systems. For each experiment, 20 runs are performed, and the mean and standard deviation of each metric is taken across the runs. Occasionally, due the large amount of data available for each run, a subset of the data are presented, by taking a sample at regular intervals through the simulation. This is indicated on the graphs where appropriate; for example, data where only every tenth point is presented with be annotated with ‘every 10’. In some cases, this signiﬁcantly aids the clarity of the data presented. 4.2 4.2.1 Population Dynamics The Generational Eﬀect The most fundamental dynamic in our model is the population size. As previously discussed, Epstein and Axtell (1996) showed that in a given environment the population would stabilise to within certain bounds and ﬂuctuate as the population went through generational cycles. Buzing et al. (2003) showed how the generational eﬀect may be removed by the introduction of random initial ages for agents and this was borne out in our previous experiments (Lewis 2006). We also showed however, that in a reproduction of Buzing et al’s experiments, virtually all agent deaths were in fact starvations. Further investigation reveals that the large number of starvations in this type of set-up is in fact due to a particularly high birthrate. An overwhelming portion of those agents starving had in fact only just been ‘born’, but did not have the necessary resources to be able to establish themselves on the scape. Recalling that when two agents reproduce they each give half of their sugar to the oﬀspring, assuming that the parents had a healthy amount of sugar, we would expect the oﬀspring to as well. However, if the agents reproduce when they do not have suﬃcient sugar to give their oﬀspring a decent chance of survival, all three will be left with a particularly low amount of sugar. Epstein and Axtell (1996) made use of a ﬁxed minimum reproductive sugar limit, a value above 25 which an agent’s sugar level must be before it is able to reproduce. Buzing et al. (2003) extended the idea to allow for experimentation with such a limit, which may be independently varied from simulation to simulation. The high level of starvations in their experiments however, suggests that they did not set the reproductive sugar limit to a suﬃciently high level. Increasing the reproductive sugar limit, therefore, may reasonably be expected to yield a reduction in the birth rate and the number of starvations. Figure 4.1: Population size with and without reproductive restrictions As ﬁgure 4.1 shows, the population in both instances does stabilise to some extent. However, it is clear that increasing the reproductive sugar limits reintroduced the generational periodicity. This generational noise is not particularly helpful in identifying changes in population dynamics, as any changes must be identiﬁed relative to the wave function. By removing any imposed limits on the reproductive behaviour of the agents, the generational periodicity is removed and the population ﬂattens out. This does lead to the number of infant starvations increasing signiﬁcantly, though this represents an implicit restriction on reproduction rather than the explicit method of an imposed minimum resource level. This is in fact the same approach as was taken by Buzing et al. (2003), and while we are not interested in birth and death rates, this is a safe course of action which simpliﬁes the analysis of future behaviour. We have therefore, a control model with which we may compare future experimentation with resource sharing and disaster situations. 26 4.2.2 Resource Availability In previous work we showed that the stabilised population size grows with direct proportionality to the size of the scape, when sugar is distributed with a ﬁxed density (Lewis 2006). Since there are no explicit physical barriers for the agents, this is most likely related to the availability of resource rather than to the physical size of the scape. Since when sugar is distributed with a ﬁxed density the total amount of available sugar grows in direct proportion to the area of the scape, we may hypothesise that the stabilised population size will grow in direct proportion to the amount of sugar available. As we have previously described, the availability of sugar is determined by two factors; the sugar density and growback rate. We may test the eﬀect of diﬀerent values for each of these on the population. Figure 4.2: Eﬀect of diﬀerent sugar densities on population size Figure 4.2 shows the development of the population’s size for diﬀerent sugar densities between 28 and 40. The ﬁrst observation to be made here is that the carrying capacity of the environment remains the same for each diﬀerent density. In eﬀect, at this level there appears to be no relationship. It is also clear however, that a higher sugar density leads to the population’s growth period occurring much sooner in the simulation. This time diﬀerence is less marked at higher densities, which is probably an eﬀect of the two dimensional ‘square’ nature of the scape. We now turn our attention to the sugar growback rate. Figure 4.3 shows the 27 Figure 4.3: Eﬀect of diﬀerent sugar growback rates on population size eﬀect of varying the rate of sugar growth on the population’s size. Clearly, the growth rate does have an eﬀect on the carrying capacity of the environment and an initial survey of the graph would tend to point us in the direction of the direct proportionality about which we hypothesised. Interestingly, the time at which the population’s period of high growth occurs is also aﬀected by the growback rate. This time however, we see the inverse of the eﬀect created by increasing the sugar density, as a higher growback rate, which implies a higher potential for the availability of resource leads to a later growth period. The relative proximity of the growth periods for the lower growback rates compared with the larger gaps at higher rates identiﬁes a further non-linear relationship. The relationship between growback rate and carrying capacity does appear to be a direct proportionality within the range which we have investigated, whilst the density of resources does not appear to have an eﬀect. This may be explained by recalling that the density parameter acts as a cap on the maximum resource in addition to determining its distribution, and while sugar is growing suﬃciently fast for the agents to multiply and harvest all the sugar this cap is irrelevant. Up to the point at which all sugar is replenished at the end of every cycle it seems unlikely that the density would play a role in determining the carrying capacity, though this remains to be tested. Predicting when the population explosion represented by the steep upward curves will occur appears to be a somewhat more complex matter than ﬁrst thought. In this however, it is clear that the maximum density does play a role. Since in the early stages of the simulation there is more sugar on the scape than 28 is needed by the population it follows that the growback rate should play little part in the expansion of the population. Where it does however, is in controlling the amount of growth in an already heavily populated region of the scape. As yet, we have no explanation for the proportionality between the growback rate and delay in the population’s growth. Indeed, a fuller set of experiments would be needed to completely understand the relationships at work. 29 Chapter 5 Resource Sharing 5.1 A Deﬁnition of Sharing In order to investigate a population’s preference for sharing, we must ﬁrst deﬁne what we mean by sharing and understand the eﬀect of its introduction on the population. We have already presented two models of sharing (Jaﬀe 2002; Younger 2004) which have been used in agent-based social modelling, though neither is suited to the situation which we are modelling. Jaﬀe’s sharing model required the population to engage in either the dissipative, eﬃcient or synergistic donation of resources with the aim of identifying diﬀerent eﬀects between the three. Younger’s model, as was discussed earlier, is only suitable for gift-giving hunter-gatherer societies, and not to disaster situations. It may be widely observed in the real world that some individuals tend to share more than others. In human society, we say that people may be more or less generous. The population in our model may also be heterogeneous with respect to generosity and each agent’s sharing behaviour should be based on its generosity. Of course, since we do not want to assume that generous sharing behaviour is beneﬁcial in disaster situations, we should not place any compulsion or initial preference on the agents to share. We may therefore introduce an evolvable generosity characteristic to each agent, in a similar way that vision and metabolism were evolvable characteristics in the original Sugarscape. This generosity characteristic should determine how much the agent shares in a given situation; it is in eﬀect both a determinant and a measure of its preference for sharing. So as not to assume the beneﬁt of any behaviour which we are trying to prove, all agents should begin the simulation with a generosity characteristic of zero; equivalent to no preference for sharing. In this way any sharing behaviour developed by the population will be the result of mutation between generations and the successful survival of any ‘mutant sharers’. Should sharing not be of conducive to survival, then natural selection will root out the mutants and draw the population away from such futile behaviour, as was seen with the evolution of the metabolism characteristic in inter alia our previous work (Lewis 2006). 30 If we deﬁne an agent’s generosity to be a value between 0 and 10, pseudocode for an additional resource sharing rule for the agents to follow may be thus: while there is another agent on the same or an adjacent cell { let d = my wealth - the other agent’s wealth if (d > 0) { donate (d * my generosity / 10) to the other agent } } Therefore, in line with our requirements, an agent with a generosity characteristic of zero will never share any of its resources and will be purely selﬁsh as in the previous model. An agent with a generosity of 5 will donate half of the diﬀerence in wealth between itself and the other agent, ensuring that both agents walk away from the encounter with equal amounts of sugar. Any generosity characteristic above 5 will lead to the donor walking away with less than the other agent. This may all seem somewhat overkill, as intuition may suggest that a generosity characteristic in excess of 5 would be unlikely to be useful. However, in the interests of reducing any assumptions in the model, the full range of sharing options will be available to the agents. The rules an agent follows may be executed in an order of our choosing. Clearly, there is no merit in altering the established move, harvest, metabolise, reproduce sequence with which we are familiar, though we must be careful not to allow the introduction of the sharing rule to interfere with this and otherwise alter the behaviour of the model. For this reason, the sharing rule is added in a separate subcycle from the other rules. In eﬀect, this means that the entire population must have completed the execution of their original rule-set before any sharing begins. The full cycle is not complete until after all sharing has completed. 5.2 Hypothesis Having implemented the sharing rule and reproductive behaviour necessary to enable the generosity characteristic to be inherited and hence evolved by the population, we may observe the development of the population’s generosity and any taste for sharing. In order to reason about the expected behaviour in a situation where the option of sharing exists it is useful to examine the distribution of wealth across the population. As has been shown, the wealth distribution found in such simulations bears a striking similarity to those found in real human societies (Epstein and Axtell 1996; Lewis 2006). Indeed, the distribution of wealth in our control model very quickly settles to a highly inequitable distribution (see ﬁgure 5.1), reminiscent of the Pareto curve found in the real world (Pareto 1897). Since the only sharing to be permitted in our model is the donation of resources from wealthy agents to poorer ones (although this relationship may not still 31 Figure 5.1: Normalised distribution of wealth across the population in the control model hold true at the end of the encounter), any amount of sharing will serve to make the distribution of wealth seen in ﬁgure 5.1 more equitable. A more equitable distribution of wealth in eﬀect means that fewer resources are hogged by the wealthiest agents in the population, releasing it for more general consumption. The eﬀect therefore, is an increase in the total amount of resource in circulation in the population. As would be expected in disaster situations, the sharing behaviour in the model favours synergistic transfers. As explained by Jaﬀe’s description of synergistic altruism, the total level of utility is indeed increased across the population. Furthermore, since we have shown that the carrying capacity of the environment grows in proportion to the rate at which resources become available, we may reasonably hypothesise that any amount of sharing behaviour in the population will lead to an increase in stabilised population size. Jaﬀe demonstrated that synergistic altruism did indeed prove to be a useful evolutionary strategy (Jaﬀe 2002), therefore we may indeed expect to see such sharing behaviour, and by extension an increase in the carrying capacity of the environment. We also know that there is a conﬂicting relationship between both the density of resource, the rate of growth and the time at which the population’s period of expansion will occur. A dominance on the part of the density should lead to an earlier expansion when resource sharing is introduced, whereas should the growth rate be of more signiﬁcance, a later expansion should occur. Of course, it is also possible that both eﬀects will cancel each other out and the occurrence 32 of the growth period will remain the same. 5.3 Results The simulation was run according to the experimental set-up described above. The initial population of agents had a generosity characteristic of zero. Firstly, let us observe whether the population did indeed evolve any sharing behaviour. Figure 5.2 shows the mean value of the generosity characteristic across the population and all 20 runs, along with the value of the characteristic for the most generous agent at that point in time; the maximum generosity. The standard deviation is omitted here, as we are not at this stage interested in the distribution of sharers thoughout the population, just the overall level. Figure 5.2: Evolution of generosity when sharing is added to the control model Firstly, it is clear that some sharing did indeed take place. Some of this will have occurred naturally due to the mutation of oﬀspring, though the stability of the most generous agents’ characteristic suggests that there is a real motivation for a certain degree of sharing behaviour. It is also clear that at no point did an agent engage in sharing which would have left the recipient of its donation as well oﬀ as, or in a better position than itself. Having established that there is indeed an evolutionary preference for some degree of resource sharing, we may turn our attention to the eﬀect of this sharing on the carrying capacity of the environment. Figure 5.3 shows the stabilised 33 population size for both the control model and the model with resource sharing added. Both the mean value of, and standard deviation between the runs are present. Figure 5.3: Population size when sharing is added to the control model The results here are also quite clear and show our hypothesis to be valid. The addition of an optional resource sharing rule did increase the carrying capacity of the environment, in this case by around 15%. In addition, we can see that the population’s period of high growth happened earlier when resource sharing was permitted than in the control model. This indicates that the change in resource density brought about by sharing was either more dominant or more signiﬁcant than the change in the rate at which resources became available. Until further investigations of the type outlined in section 4.2.2 have been carried out, we cannot explain this behaviour further. 34 Chapter 6 Disasters 6.1 A Deﬁnition of Disaster We now turn our attention to the modelling of disaster scenarios causing resource shortage. For our purposes, a disaster may be deﬁned as a reduction in the available resource in a particular area for a speciﬁed length of time. This is perhaps most representative of drought and famine in the real world, though similar situations are prompted by wars and natural disasters, when supply lines are severed. In our multi-agent model we may simulate the occurrence of such a disaster by manipulating the levels of sugar in the aﬀected area of the scape. Returning to our control model - without the resource sharing rule added in the previous chapter - we may ﬁrstly observe the eﬀect of disasters on the population. Formally, a disaster may be deﬁned in terms of four parameters; it’s location, the size of the aﬀected area, the length of time for which it remains in eﬀect and its severity. The ﬁrst three are fairly simple parameters. The location consists of co-ordinates on the grid referring to the centre of the disaster area, for simplicity’s sake the area is a square region of the scape and the length of the disaster is measured in cycles of the simulation. The severity of a disaster however, must be deﬁned further. As we have seen, there are two variables governing the availability of sugar on the scape; the density parameter and growback rate. Thinking for a moment about disasters in the real world, it seems likely that a disaster might reasonably aﬀect both variables. The density, a representation of the maximum level of resource permitted in an area, would certainly be aﬀected by a drought, war or natural disaster having an adverse eﬀect on the quality of soil or infrastructure for storing resources. Furthermore, since the growback rate may be seen as a representation of either a literal growth rate of crops or the level of import of resources to the local area, it is reasonable to expect that this parameter should also be aﬀected. The disaster’s severity parameter should therefore have an impact on both the density and growback rate in the aﬄicted area. Using our control model as a baseline, we may therefore deﬁne the severity of disasters in terms of a reduction in the density and growth of resources relative 35 to the control. A cell aﬀected by a disaster with a severity of 20% will therefore represent a 20% reduction in both the maximum sugar density and rate of sugar growth in the cell. Cells outside the disaster’s area will remain unaﬀected. Through the course of a population’s evolution in the real world, it will be exposed to any number of disaster of varying size, severity and length. We have seen how the evolutionary process adapts the population’s characteristics to a given environment, though of course this is rather simplistic. Rather than occurring in a stable environment, evolution in the real world reacts to an environment in a state of constant change. This may be represented in the model through the regular occurrence of unpredictable disasters. We therefore add to the model, a rule for the generation of regular disasters of a random location, size, length and severity. The frequency of these disasters should not be so high as to make it impossible for the population to survive, but high enough to impact upon its behaviour. 6.2 Hypotheses It is expected that regular random disasters will have two main eﬀects on the population. Firstly, since the total amount of resource available on the scape will vary over time, in line with our previous ﬁndings that population size stabilises proportionally to the amount of resource available, we should expect to see ﬂuctuations in the population size. More speciﬁcally, an area of the scape aﬀected by disaster will not be able to support as high a population as the unaffected areas. Secondly, since the total amount of resource on the scape over time will be less than in the control model, we should expect the average population size over time to be lower than in the control model. In order to test these hypotheses, we must ﬁrst specify our bounds for the random disasters. Clearly, disasters should be able to strike at any part of the scape, though limiting the size of the disaster ensures that some areas of the scape will remain unaﬀected. It is also not helpful for individual disasters to last too long. Dominance of a run of the simulation by one particular characterisation of disaster will reduce the eﬀect of the random distribution upon the evolutionary process. After some initial testing of various parameters, it was found that restricting disasters to a size of 1000 cells and a length of 100 cycles provided a suitable balance. Disasters may not occur concurrently and when the scape is currently unaﬀected, a disaster may begin with a probability of 0.02 per cycle. As described above, disasters are categorised in terms of severity, between 0% and 100%, where 0% has no eﬀect and 100% is a total absence of resource or growth in the aﬀected area. 6.3 Results Figure 6.1 illustrates the development of the population’s size for both the control model and for the model with random disasters as described above. Both 36 mean and standard deviation for the 20 runs are shown. Figure 6.1: Population size with and without random disasters As may be seen, our expectations have been met with regard to the population’s size over time. As we already know, in the control model the population becomes remarkably stable after the initial settle-down. In the model with random disasters however, the population does indeed ﬂuctuate. Additionally, the mean population size is lower in the model with random disasters than in the control, thoughout the simulations. An additional observation was also made when comparing the two models. Figure 6.2 shows the level of wealth of the richest agent on the scape at each point in time. As is clear, this maximum individual wealth is higher when random disasters occur. This indicates that at least one agent is proﬁting from the presence of disasters. Further investigation showed that the average level of individual wealth across the population also increased when random disasters were present, however this may well be largely due to the increase in wealth of the richest agents. In fact, the distribution of wealth across the population was found to be less equitable when disasters were present. It is clear that the presence of disasters has led to a less equitable distribution of wealth across the population, with the richest agents being wealthier than in the control model. At this stage, we have no explanation for this phenomenon. 37 Figure 6.2: Wealthiest individual with and without random disasters 38 Chapter 7 Introducing Sharing in Disaster Situations 7.1 Theory and Hypothesis We have seen that when the control model was extended in order to allow the agents the possibility of sharing their resources, they did indeed evolve a preference for doing so. This sharing activity created a more equitable distribution of wealth across the population, leading to a higher carrying capacity for the same total amount of resource available. Given the regular occurrence of random disasters, as described above, is there any reason to suspect that this behaviour will not continue? On the face of it, it seems sensible that when faced with a shortage of resource it will be of beneﬁt to the survival of an agent to be less likely to share what little resource it has. However, Hirshleifer’s theory of alliance preservation may lead us to a diﬀerent conclusion. The theory tells us that in disaster situations, the donations made by wealthy individuals to those in need are not purely altruistic, but instead represent a transaction, whereby the wealthier individual hopes to buy himself a certain social stability. In doing so, he (perhaps unconsciously) recognises that though his own survival may not now be in question, it is more likely to be should the alliance of society break down. For this reason he engages in synergistic altruism, enabling others to survive, in order to preserve the social alliance and increase his survival chances in the long term (Hirshleifer 1987). Are we likely to see such behaviour occur in a model as simple as ours? Firstly, it is quite clear that the economic model employed here is far simpler than the complex economies found in human society. We have, for example, no explicit representation of two-way transactional trade, no division of labour and hence no explicit interdependencies between individual agents. This need not discount the applicability of such a theory, however. The lack of explicit interdependency between agents does mean that an agent, after having made a donation, can have no direct expectation of receiving an equivalent or greater amount in return. It is true that the donating agent may itself receive a donation from an even wealthier agent, but since the wealthiest agents tend to 39 remain so for their entire lifetime, this does not hold true in this case. The exception to this of course, is if a wealthy agent is itself aﬀected by a future disaster. Despite its large savings, when resources fail to renew at a suﬃcient level for the survival of itself and its neighbours, it may ﬁnd itself in need. In this way, it may indeed beneﬁt from the generous behaviour of other agents, perhaps one to whom it has donated money in the past. It would appear that it is indeed in the population’s interest to develop generous behaviour, as an even distribution of wealth means that an agent in need is more likely to encounter a suitable donor. Furthermore, generous behaviour may also be rewarded in a future generation. In addition to the usefulness of widespread generosity in situations where the donor falls on hard times in the future, the preservation of the social alliance also increases the likelihood that other agents will donate to one of the original donor’s descendants, who may not be so wealthy. Thirdly, an agent’s genetic code cannot survive in future generations if there is a shortage of potential mates. It seems sensible to suppose that the development of any behaviour which reduces the chance of this happening - such as large sections of the population dying - would not be favoured by the evolutionary process. In the case of both donations, the transactions are synergistic, as the utility of the sugar to the recipient is greater than to the donor. The only exception to this would be if a donor gave away a signiﬁcant amount of sugar, unaware of a severe imminent disaster. This will only account for a minority of donations however, and may be ignored when taking a view of the behaviour as a whole. Since both donations are synergistic and may be done with an expectation of beneﬁt for either oneself or a future descendant, behaviour of this kind is in fact a synergistic business transaction, the kind of which are common in human society. So, if this is correct, we should expect to see the development of a preference for sharing when disasters are present, in a similar way to when they were not. Furthermore, this should lead to a higher stabilised population size and higher growth rate, as when disasters were not present. 7.2 Results The experimental set-up was a combination of the previous two models; sharing as in chapter 5 and random disasters as in chapter 6. Firstly, let us examine the development of the population’s preference for generosity. Figure 7.1 shows a comparison of both the mean and standard deviation of the population’s generosity for the models with and without random disasters. Clearly, there is no signiﬁcant diﬀerence between two remarkably similar distributions; as predicted, the introduction of disasters has not deterred the population from sharing. It should be no surprise therefore that, as ﬁgure 7.2 shows, a behaviour similar to that identiﬁed in 6.3 occurs. As was the case without the presence of disasters, allowing the agents to develop the ability to share increased the carrying capacity of the environment on 40 Figure 7.1: Comparison of evolved generosity with and without random disasters average by around 15%. The ﬂuctuations in population size brought about by the random disasters, identiﬁed in the previous chapter, remain present when sharing occurs, and are of a comparable magnitude. Since the introduction of the sharing rule has been shown to create a more equitable distribution of wealth, we may examine the extent to which this has occurred. Figure 7.3 shows a comparison of the wealth of the richest individuals for all four simulations: control, sharing only, disasters only and sharing with disasters. As we saw in section 6.2, the introduction of random disasters created a greater degree of inequality in the population, as the wealthier agents became wealthier still. As we can see here however, sharing mitigated against this and returned the natural upper limit on individual wealth to one similar to the control model. Whilst some results detailing the distribution of wealth in the various models has been presented here, further work will yield a more complete picture. 41 Figure 7.2: Comparison of population size with and without random disasters Figure 7.3: Wealth of the richest individual with and without disasters and sharing 42 Chapter 8 A Relationship Between Severity and Generosity? So far, it has been shown that evolution has favoured a certain amount of sharing behaviour in the population, in both the control model and when random disasters occur throughout the simulation. If indeed this preference for resource sharing is motivated by alliance preserving behaviour in the face of resource shortage, it would seem sensible to expect that the degree to which sharing behaviour is favoured should be determined to some extent by the severity of the resource shortage being faced. More speciﬁcally, we may hypothesise that higher severities of resource shortage will motivate a higher taste for resource sharing by the population. 8.1 Adapting the Model Hitherto we have seen how a population is aﬀected by regular short disasters of random size and severity, similar in many ways to their occurrence in the real world. In order to understand fully how the population reacts to a speciﬁc severity of disaster, however, we need to know how the population speciﬁcally in the aﬀected area responds. Whilst it is possible to extract metrics about the population in the speciﬁc areas aﬀected at diﬀerent times from the simulation, there is a much simpler way to obtain this information. It is very easy when doing agent-based social modelling to fall into the habit of thinking of agents as individual people, and the scape as a piece of land which is of a suitable size to support a population of the size of our agent population. The cells of the scape simply become a discrete division of this land mass. No such theoretical requirement exists for this narrowing of the metaphor with which we are working. As discussed above (see section 2.3), our agents, being devoid of free will, represent an aggregate of observed behaviour of humans in a particular predicament. In eﬀect, a number of agents in an identical predicament represent a behaviour distribution, based on the likelihood of human being to behave in a certain way in the real world. There is no restriction on the model for agents to map one-to-one to humans, or that an agent should map on to any number 43 of humans, or indeed that the mapping should imply that one agent represents more than one human. We are in fact free to alter our interpretation of the model to represent any scenario where a suﬃciently large number of humans interact over a suﬃciently large area. Indeed, so long as both the number of humans and agents in the interpretation is large enough to ensure a distribution of behaviour approaching a representative sample, our model is applicable. Of course, a full theoretical justiﬁcation for this applicability is required, though we believe the intuition to be correct. Using this ability to scale the model, we may choose to represent only an affected disaster area. By using the deﬁnition of disasters above, we may apply the changes to resource density and growth rate to the entire scape, and observe the evolved behaviour of the population. In doing so, we make two additional assumptions, stemming from the removal of any contact from the outside world. Firstly, we assume no external charitable donations beyond those which may be implicit in the amount of resource available anyway. Secondly, by restricting the evolutionary process to only those other agents who are aﬀected by the disaster, we discount the ability of external actors to inﬂuence the behaviour of those in the aﬀected area. However, we believe that these factors will in fact improve the quality of the results, since we are interested in the behaviour of a population who have been aﬀected by a disaster, not how this behaviour might be altered by inﬂuence from the outside world. In order to test our hypothesis, we use the version of the model with sharing enabled as before, but rather than use random disasters through time, we impose a disaster of a speciﬁc severity to the entire scape, for the duration of the simulation. The evolved generosity of the population may be observed for each severity level. Using the level of resource available in control model as a baseline, we may apply disasters to reduce the available resource, having an eﬀect similar to diﬀerent severities of drought and famine in the real world. 8.2 Results As was done previously, disaster severities are categorised by a percentage reduction from the baseline control model. We do not need to run the simulation to realise that imposing 100% severity on the entire scape is the equivalent of no resource availability, and 0% is the same as the baseline control model. Initially, simulations were run for 20%, 40%, 60% and 80% severity levels. Figure 8.1 shows the mean generosity for the population for each of these. These initial experiments clearly show that there is indeed some causal relationship between the level of severity of resource shortage and the evolved generosity of the population. For 20% severity, only a small reduction from the control model, the generosity follows a similar path of development as in the control model itself, stabilising at slightly above the value of 0.3 which we saw there (see ﬁgure 5.2 for a comparison). With 40% severity however, the population develops a signiﬁcantly higher pref44 Figure 8.1: Evolved generosity under diﬀerent severities of resource shortage erence for sharing, the mean value being around 0.5 by the 2500th cycle, though with a little more noise and a higher variance amongst the population (not shown for clarity). It is not clear, but expected that the shape of this curve will mirror the asymptotic nature of the 20% severity results. Again, at 60% we notice a jump in the mean generosity, though also it is clear that the results for this severity level are signiﬁcantly noisier. The variance amongst the population is higher still. Perhaps most interestingly, when faced with an 80% severity level, the average generosity of the population is actually lower than for 60%, and considerably noiser still. it was initially suspected that this discrepancy may in fact be due to the high level of noise and high variance amongst the population, though a Student’s T-Test, calculated on the two distributions after cycle 1000 (i.e. once they had stabilised) revealed a signiﬁcant diﬀerence between the two distributions to within a 99.99% conﬁdence level. Survival of the population is not guaranteed at 80% severity and it appears that as resource shortage reached such a dangerous level, the average generosity did in fact dip. We have established that there is indeed a link between severity and the population’s preference for generosity. However, in order to have a clearer picture of the relationship, we need a better sample of the behaviour at diﬀerent severity levels. To achieve this, the simulation was run from 5% to 95% severity in 5% intervals. The usual 20 experiments are run and the mean and standard deviation taken. 45 Rather than show the progress of evolution for each experiment, which would provide a rather busy graph, ﬁgure 8.2 shows the mean stabilised generosity for each severity level, providing us with an overall picture of the relationship. Figure 8.2: Relationship between severity and evolved generosity The relationship represented here appears to be a complex one, though following a loose trend of proportionality. The curve may be divided into four distinct sections, as the dashed lines on the graph indicate. At low severity levels, the generosity is largely unaﬀected by the increase in severity. It is not until 25% severity that the shortage kicks in and the preference for sharing increases to adapt. Between 25% and 50%, a roughly linear relationship emerges. By 50%, the average generosity is around double its initial value. 50% to 70% severity sees the generosity rise sharply, only to fall even more sharply by 75%. It is in this range that the variance between the runs is greatest, indicating less predictable behaviour. For the ﬁnal section, above 75%, the generosity remains fairly stable at around three times its value at the lower severities. It is however, signiﬁcantly less than at its peak, between 60% and 70%. Interestingly, 75% is the point above which survival of the population is frequently in question. At 75%, the resource shortage led to 30% of runs terminating with an extinct population, requiring extra runs in order to gather a full set of statistics. It appears that some form of non-linear proportionality exists between severity and generosity, provided that the only issue is comfort, and starvation is not a threat. Once survival cannot be guaranteed, the population returns to a more immeditately selﬁsh strategy, though still retaining a relatively high preference for sharing. 46 Chapter 9 Conclusions In this project we have extended our work investigating the dynamics of a multiagent artiﬁcial society. We have investigated in detail results from our previous work, which showed that the carrying capacity of an environment is directly proportional to the area of the environment when resources are distributed uniformly (Lewis 2006). By conducting a series of experiments investigating the eﬀect of varying the density and the rate of availability of resources independently, on a ﬁxed size scape, it was shown that the carrying capacity was directly proportional to the rate of availability of resource, often referred to as growback rate. Interestingly, it was also observed that a higher growback rate also led to the initial period of growth of the population occurring later than for lower growback rates. It was found that for the range of resource densities tested, varying the density of resource on the scape had no eﬀect on the carrying capacity. However, higher densities led to an earlier period of growth for the population. Our previous results gathered from varying the size of the scape (Lewis 2006), represent a combination of these eﬀects. Intuitively, this behaviour appears to make sense. In the real world, when a population expands to inﬁll a particular region or into a new region, the rate at which it can do so is largely determined by the availability of resource in these hitherto underused or unused areas, and to a lesser extent, by the rate at which new resources may be grown or imported. Once a population has reached carrying capacity in an area, it is entirely dependent on the rate at which new resources may be grown or imported, since any spare capacity indicates that the population is not in fact at its carrying capacity. When the model was extended to include a form of resource sharing which may be expected to take place in disaster situations in modern societies, it was shown how despite there being little obvious immediate advantage to an individual agent for engaging in such behaviour, the population did indeed evolve a certain preference for doing so. This behaviour led to a more equitable distribution of wealth across the population and it was shown how this increased the availability of resource. This in turn led to the environment being able to support a signiﬁcantly larger population for an equivalent amount of resource. The time at which the population’s period of high growth occurred was also aﬀected by resource sharing, due to the eﬀects described above. 47 Having gleaned a better understanding of the eﬀect of resource availability on the population, we have shown how a multi-agent artiﬁcial society model may be extended to model natural and other disasters which cause resource shortage. It was found that regularly occurring disasters of random size, severity and length led to a ﬂuctuating population size, though did not pose any threat for the overall survival of the population. The introduction of such disasters also prompted a lower average population over time, since the overall rate of resource availability was reduced. Regular disasters did also prompt a less equitable distribution of wealth across the population, with the richer agents appearing to proﬁt signiﬁcantly from the regular disasters. Despite the regular occurrence of disasters, when the option of resource sharing was also added, the population still evolved a certain preference for it. A similar pattern to when no disasters were present was observed; the distribution of wealth was more equitable and the environment could sustain a higher population. In fact, the introduction of sharing acted to bring the distribution of wealth back to a similar level to when disasters were not present, though it was not as equitable as with sharing but no disasters. Through modelling only those areas aﬀected by a disaster, a relationship was discovered between the severity of resource shortage and the population’s preference for resource sharing. Though more data will be required for a full analysis of the relationship, it appears at this stage that: • For a small reduction in the amount of resource available, the population’s taste for sharing is largely unaﬀected, • For moderate resource shortages, the population’s taste for sharing increases at least linearly, and • For very high resource shortages when the population’s survival cannot be guaranteed, less generous behaviour returns. This is well explained by the idea of implicit synergistic business transactions, as described by (Jaﬀe 2002). It is of beneﬁt to the agents for a certain amount of resource sharing to occur, and they are happy to engage in such behaviour, so long as the total amount of utility in the system is at least as high as before the transaction. By extension, this provides a certain safety net to a donating agent, since at some point in the future he or his descendants will probably be a recipient. However, this behaviour breaks down to an extent when the survival of the population as a whole is in question. At this point, the donor can no longer be sure of receiving a donation himself in the future, since his recipient may well die despite his donation. This also ﬁts well with the theory of alliance preservation in disaster situations (Hirshleifer 1987). Despite the apparent rationality behind immediately selﬁsh behaviour when faced with resource shortage, this does not always occur. Spare resource, particularly that with a low utility to oneself, may be better employed in purchasing a little social stability. By making such synergistic donations, the population at large will have a higher likelihood not only of survival, but 48 of being able to reciprocate at a later point in time. Conversely, not engaging in such behaviour will lead to a reduction in the population’s size, and a lower likelihood that potential future donors will exist. 49 Chapter 10 Evaluation and Future Work Since agent-based social and economic modelling remains a relatively young discipline, there are a number of directions in which this work may be taken. 10.1 10.1.1 Extensions to this Work Alternative Theoretical Approaches There are, for example, other potential theoretical explanations for the behaviour observed here. Kin selection theory suggests that a preference for altruism towards ones relatives may well develop in a population (Hamilton 1964). On the face of it, this appears an unlikely explanation here since agents have no way of recognising their oﬀspring. It does appear likely however, that those agents nearest to the donor have a higher chance of being related, so there may be some implicit kin recognition. However, initial experimentation with placing oﬀspring away from their parents at geographically random locations yielded similarly high tastes for sharing. Another alternative explanation for the development for a preference for sharing in some of the examples could be due to diﬀerences in evolutionary pressure across the population. Since there is little evolutionary pressure on the wealthiest individuals with regard to sharing, there is no reason for them to not donate their spare resource. Since the evolutionary pressure will increase along with poverty, some sustained sharing behaviour will be observed. An investigation into any possible relationship between generosity and individual wealth in the above models will shed some light on this possibility, though this additional explanation is not incompatible with the substantive justiﬁcations given. 50 10.1.2 Diﬀerent Models of Sharing In line with Axelrod’s ﬁrm advocacy of the ‘Keep It Simple, Stupid’ approach, we have presented here the simplest model of resource sharing with which the desired behaviour may be reproduced. This has made it somewhat easier to reason about the relationships between the diﬀerent properties of the model. A more realistic model of resource sharing could possibly be used by introducing the concept of an agent’s perception of the severity of any disaster, perhaps through a representation of the media or some other inter-agent communication method. Some initial results were produced comparing models of sharing involving the use of either local or global information to the sharing rule, but until a theoretical basis for this extension can be shown, the value of this information is limited. 10.2 Investigating Other Social and Economic Behaviour One thing which is quite clear is the versatility of a model such as the one employed here. Due to practical or ethical reasons, in social science one does not always have the luxury of a laboratory full of human subjects to observe. Models such as this provide one approach for experimenting with societies in situations where behaviour may be rationalised. The range of the work discussion in chapter 2 illustrates the possibilities. 10.3 Alternative Modelling Methods Models of this kind provide highly complex data and require signiﬁcant amounts of processing time. 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In Proceedings of European Conference on Artiﬁcial Life (ECAL). Epstein, J. M. and R. Axtell (1996). Growing Artiﬁcial Societies. Washington, DC, USA: Brookings Institutional Press. Frank, U. and K. G. Troitzsch (2005). Epistemological perspectives on simulation. Journal of Artiﬁcial Societies and Social Simulation 8 (4). Hamilton, W. D. (1964). The genetical evolution of social behaviour. Journal of Theoretical Biology 7 (1), 1–16. 52 Hirshleifer, J. (1987). Disaster behaviour: Altruism or alliance? In Economic Behaviour in Adversity, pp. 134–141. Brighton, Sussex: Wheatsheaf Books. Hogan, J. (2005, March). Why it’s hard to share the wealth. New Scientist (2490), 6. Jaﬀe, K. (2002). An economic analysis of altruism: who beneﬁts from altruistic acts? Journal of Artiﬁcial Societies and Social Simulation 5 (3). Jager, W., R. Popping, and H. van de Sande (2001). Clustering and ﬁghting in two-party crowds: Simulating the approach-avoidance conﬂict. 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Journal of Artiﬁcial Societies and Social Simulation 8 (4). Vogt, P. and F. Divina (2005). Language evolution in large populations of autonomous agents: issues in scaling. In Proceedings of European Conference on Artiﬁcial Life (ECAL). Younger, S. (2004). Reciprocity, normative reputation, and the development of mutual obligation in gift-giving societies. Journal of Artiﬁcial Societies and Social Simulation 7 (1). Younger, S. (2005a). Reciprocity, sanctions, and the development of mutual obligation in egalitarian societies. Journal of Artiﬁcial Societies and Social Simulation 8 (2). Younger, S. (2005b). Violence and revenge in egalitarian societies. Journal of Artiﬁcial Societies and Social Simulation 8 (4). 53 Appendix A Project Proposal 54 55 Appendix B Full Model Speciﬁcation B.1 Objects A simulation is described, consisting of a set of objects which interact. The simulation proceeds in discrete time steps, called cycles. We deﬁne the following objects. B.1.1 Environment A 50x50 lattice (2-dimensional array) of cells, with wrap around. B.1.2 Cell A discrete space in the environment, which may contain sugar and any number of agents. Each cell has the following properties: • Current amount of sugar, • Initial amount of sugar, • Maximum amount of sugar (density). • Sugar growback rate. • Severity of disaster [0-10]. B.1.3 Agent An autonomous entity, which occupies one cell (and may share it with other agents). Each agent has the following ﬁxed properties: • Gender [M/F]. • Metabolism [4]; the amount of sugar used per cycle.. 56 • Vision [4]; the number of cells in each direction which the agent can see when determining its action. • Begin child bearing age [12-15]; the age at which an agent can begin reproducing. • End child bearing age [40-60]; the age after which an agent can no longer reproduce. • Natural death age [60-100]; the age at which the agent will naturally die. • Reproductive sugar threshold; the minimum amount of sugar an agent must possess in order to reproduce. • Generosity; a determinant of the amount of sugar an agent will share. Integer values such as generosity will be stored as ﬂoating point values in order that crossover and mutation may have suitable eﬀects. Values will then be rounded to the nearest integer when used. The above properties, though ﬁxed for the lifetime of the agent, may vary between agents and may be the subject of evolutionary selection as oﬀspring inherit those properties from their parents (see reproduction section below). This may not always be the case however, as in many experiments we ﬁx vision, metabolism and reproductive sugar threshold levels. Each agent has the following properties which vary through its lifetime: • Age [0-100]; increments one per cycle. • Current sugar [0-inﬁnity]; the current amount of sugar which the agent has stored. If this reaches zero, the agent dies. B.2 Rules Each object in the simulation (except the environment itself) has a set of rules, which are executed once per cycle. B.2.1 Cell Rules The cell object only has one rule. 1. Sugar growback rule. Once harvested by an agent, the amount of sugar on a cell will be less than its maximum. A cell’s sugar will then grow back over time, at a ﬁgure equal to its growback rate per cycle until the maximum is reached. The growback rate is 10, unless otherwise speciﬁed. If a cell is currently aﬀected by a disaster, then both the growback rate and maximum sugar capacity will be reduced by the severity of the disaster. For example, a 20% severity disaster on the cell implies the reduction of both the growback rate and maximum sugar capacity by 20%. 57 B.2.2 Agent Rules Loosely speaking, each agent looks for sugar, moves to the sugar, harvests it, possibly reproduces and then metabolises during one cycle. Each agent has a set of rules which should be executed in strict order. 1. Death. • If the agent’s current level of sugar is zero, the agent dies and is removed from the environment. 2. Movement. • Examine each cell within the agent’s vision range, and identify the cell containing the most sugar. If there is more than one with the same amount of sugar, select one at random. • Move to the identiﬁed cell. 3. Harvest. • If there is sugar on the current cell, increment the current sugar level by the amount on the cell and decrease the cell’s sugar by the same amount. 4. Reproduce. • If there is an agent in this or an adjacent cell of the opposite gender, and both potential partners have reached their reproductive sugar threshold and are of suitable age, then reproduce. See next section for details of this rule. 5. Metabolise. • Decrease the agents current amount of sugar by its metabolic rate. 6. Share. • Share resources according to the following pseudocode: while there is another agent on the same or an adjacent cell { let d = my wealth - the other agent’s wealth if (d > 0) { donate (d * my generosity / 10) to the other agent } } Reproductive rule • With some probability, create a new agent in the same cell with age 0 and each other characteristics determined as follows: 58 – ﬁxed characteristic integer properties (vision, metabolism etc) are set to the mid-point of the parents’ values, plus a random (possibly negative) mutation factor, – each parent gives half its current sugar to the child, Note that if there is more than one possible reproductive partner, sex will only occur more than once if the agent is still above its reproductive sugar threshold after giving half its sugar to the oﬀspring. 59

Evolved resource sharing behaviour in disaster situations

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