Simulating Evolutionary Games: A Python-Based Introduction

This paper is an introduction to agent-based simulation using the Python programming language. The core objective of the paper is to enable students, teachers, and researchers immediately to begin social-science simulation projects in a general purpose programming language. This objective is facilitated by design features of the Python programming language, which we very briefly discuss. The paper has a 'tutorial' component, in that it is enablement-focused and therefore strongly application-oriented. As our illustrative application, we choose a classic agent-based simulation model: the evolutionary iterated prisoner's dilemma. We show how to simulate the iterated prisoner's dilemma with code that is simple and readable yet flexible and easily extensible. Despite the simplicity of the code, it constitutes a useful and easily extended simulation toolkit. We offer three examples of this extensibility: we explore the classic result that topology matters for evolutionary outcomes, we show how player type evolution is affected by payoff cardinality, and we show that strategy evaluation procedures can affect strategy persistence. Social science students and instructors should find that this paper provides adequate background to immediately begin their own simulation projects. Social science researchers will additionally be able to compare the simplicity, readability, and extensibility of the Python code with comparable simulations in other languages.Agent-Based Simulation, Python, Prisoner's Dilemma

Evolutionary Game Theory

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Iterated Prisoner\u27s Dilemma for Species

The Iterated Prisoner\u27s Dilemma (IPD) is widely used to study the evolution of cooperation between self-interested agents. Existing work asks how genes that code for cooperation arise and spread through a single-species population of IPD playing agents. In this paper, we focus on competition between different species of agents. Making this distinction allows us to separate and examine macroevolutionary phenomena. We illustrate with some species-level simulation experiments with agents that use well-known strategies, and with species of agents that use team strategies

Critical dynamics in the evolution of stochastic strategies for the iterated Prisoner's Dilemma

The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of conditional probabilities that represent the response of decision pathways given previous plays. We find that if these stochastic strategies are encoded as genes that undergo Darwinian evolution, the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory, which could be either cooperation or defection. A transition between cooperative and defective attractors occurs as a function of different parameters such a mutation rate, replacement rate, and memory, all of which affect a player's ability to predict an opponent's behavior.Comment: 27 pages, including supplementary information. 5 figures, 4 suppl. figures. Version accepted for publication in PLoS Comp. Bio

A hyperheuristic methodology to generate adaptive strategies for games

Hyperheuristics have been successfully applied in solving a variety of computational search problems. In this study, we investigate a hyper-heuristic methodology to generate adaptive strategies for games. Based on a set of low-level heuristics (or strategies), a hyper-heuristic game player can generate strategies which adapt to both the behaviour of the co-players and the game dynamics. By using a simple heuristic selection mechanism, a number of existing heuristics for specialised games can be integrated into an automated game player. As examples, we develop hyperheuristic game players for three games: iterated prisoner's dilemma, repeated Goofspiel and the competitive traveling salesmen problem. The results demonstrate that a hyperheuristic game player outperforms the low-level heuristics, when used individually in game playing and it can generate adaptive strategies even if the low-level heuristics are deterministic. This methodology provides an efficient way to develop new strategies for games based on existing strategies

Parasites may help stabilize cooperative relationships

Background: The persistence of cooperative relationships is an evolutionary paradox; selection should favor those individuals that exploit their partners (cheating), resulting in the breakdown of cooperation over evolutionary time. Our current understanding of the evolutionary stability of mutualisms (cooperation between species) is strongly shaped by the view that they are often maintained by partners having mechanisms to avoid or retaliate against exploitation by cheaters. In contrast, we empirically and theoretically examine how additional symbionts, specifically specialized parasites, potentially influence the stability of bipartite mutualistic associations. In our empirical work we focus on the obligate mutualism between fungus-growing ants and the fungi they cultivate for food. This mutualism is exploited by specialized microfungal parasites (genus Escovopsis) that infect the ant's fungal gardens. Using sub-colonies of fungus-growing ants, we investigate the interactions between the fungus garden parasite and cooperative and experimentally-enforced uncooperative ("cheating") pairs of ants and fungi. To further examine if parasites have the potential to help stabilize some mutualisms we conduct Iterative Prisoner's Dilemma (IPD) simulations, a common framework for predicting the outcomes of cooperative/non-cooperative interactions, which incorporate parasitism as an additional factor. Results: In our empirical work employing sub-colonies of fungus-growing ants, we found that Escovopsis-infected sub-colonies composed of cheating populations of ants or fungi lost significantly more garden biomass than sub-colonies subjected to infection or cheating (ants or fungi) alone. Since the loss of fungus garden compromises the fitness of both mutualists, our findings suggest that the potential benefit received by the ants or fungi for cheating is outweighed by the increased concomitant cost of parasitism engendered by non-cooperation (cheating). IPD simulations support our empirical results by confirming that a purely cooperative strategy, which is unsuccessful in the classic IPD model, becomes stable when parasites are included. Conclusion: Here we suggest, and provide evidence for, parasitism being an external force that has the potential to help stabilize cooperation by aligning the selfish interests of cooperative partners in opposition to a common enemy. Specifically, our empirical results and IPD simulations suggest that when two mutualists share a common enemy selection can favor cooperation over cheating, which may help explain the evolutionary stability of some mutualisms

Influence of Supply Chain Network Topology on the Evolution of Firm Strategies

This study investigates the influence of the topological structure of a supply chain network (SCN) on the evolution of cooperative and defective strategies adopted by the individual firms. First, a range of topologies representative of SCNs was generated using a fitness-based network growth model, which enabled cross comparisons by parameterising the network topologies with the power law exponent of their respective degree distributions. Then, the inter-firm links in each SCN were considered as repeated strategic interactions and were modelled by the Prisoner’s Dilemma game to represent the self-interested nature of the individual firms. This model is considered an agent-based model, where the agents are bound to their local neighbourhood by the network topology. A novel strategy update rule was then introduced to mimic the behaviour of firms. In particular, the heterogeneously distributed nature of the firm rationality was considered when they update their strategies at the end of each game round. Additionally, the payoff comparison against the neighbours was modelled to be strategy specific as opposed to accumulated payoff comparison analysis adopted in past work. It was found that the SCN topology, the level of rationality of firms and the relative strategy payoff differences are all essential elements in the evolution of cooperation. In summary, a tipping point was found in terms of the power law exponent of the SCN degree distribution, for achieving the highest number of co- operators. When the connection distribution of an SCN is highly unbalanced (such as in hub and spoke topologies) or well balanced (such as in random topologies), more difficult it is to achieve higher levels of co-operation among the firms. It was concluded that the scale-free topologies provide the best balance of hubs firms and lesser connected firms. Therefore, scale-free topologies are capable of achieving the highest proportion of co- operators in the firm population compared to other network topologies