A Spatial Agent-Based Model of N-Person Prisoner's Dilemma Cooperation in a Socio-Geographic Community

The purpose of this paper is to present a spatial agent-based model of N-person prisoner's dilemma that is designed to simulate the collective communication and cooperation within a socio-geographic community. Based on a tight coupling of REPAST and a vector Geographic Information System, the model simulates the emergence of cooperation from the mobility behaviors and interaction strategies of citizen agents. To approximate human behavior, the agents are set as stochastic learning automata with Pavlovian personalities and attitudes. A review of the theory of the standard prisoner's dilemma, the iterated prisoner's dilemma, and the N-person prisoner's dilemma is given as well as an overview of the generic architecture of the agent-based model. The capabilities of the spatial N-person prisoner's dilemma component are demonstrated with several scenario simulation runs for varied initial cooperation percentages and mobility dynamics. Experimental results revealed that agent mobility and context preservation bring qualitatively different effects to the evolution of cooperative behavior in an analyzed spatial environment.Agent Based Modeling, Cooperation, Prisoners Dilemma, Spatial Interaction Model, Spatially Structured Social Dilemma, Geographic Information Systems

Mobility, fitness collection, and the breakdown of cooperation

The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions. DOI: 10.1103/PhysRevE.87.04271

Evolution of Cooperation in a Spatial Prisoner's Dilemma

We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally interacts with his neighbors. Based on a detailed analysis of the local payoff structures we derive critical conditions for the invasion or the spatial coexistence of cooperators and defectors. These results are concluded in a phase diagram that allows to identify five regimes, each characterized by a distinct spatiotemporal dynamics and a corresponding final spatial structure. In addition to the complete invasion of defectors, we find coexistence regimes with either a majority of cooperators in large spatial domains, or a minority of cooperators organized in small non-stationary domains or in small clusters. The analysis further allowed a verification of computer simulation results by Nowak and May (1993). Eventually, we present simulation results of a true 5-person game on a lattice. This modification leads to non-uniform spatial interactions that may even enhance the effect of cooperation. Keywords: Prisoner's dilemma; cooperation; spatial 5-person gameComment: 33 pages, 22 multipart figures, for related papers see http://www.ais.fraunhofer.de/~frank/papers.htm

Statistical Physics of the Spatial Prisoner's Dilemma with Memory-Aware Agents

We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's Dilemma, as it constitutes an emblematic example of a game whose Nash equilibrium is defection. Previous investigations showed that, under opportune conditions, it is possible to reach, in the evolutionary Prisoner's Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms like motion may lead a population to become cooperative. In the proposed model, we map agents to particles of a gas so that, on varying the system temperature, they randomly move. In doing so, we are able to identify a relation between the temperature and the final equilibrium of the population, explaining how it is possible to break the classical Nash equilibrium in the spatial Prisoner's Dilemma when considering agents able to increase their payoff over time. Moreover, we introduce a formalism to study order-disorder phase transitions in these dynamics. As result, we highlight that the proposed model allows to explain analytically how a population, whose interactions are based on the Prisoner's Dilemma, can reach an equilibrium far from the expected one; opening also the way to define a direct link between evolutionary game theory and statistical physics.Comment: 7 pages, 5 figures. Accepted for publication in EPJ-

Spatial population expansion promotes the evolution of cooperation in an experimental Prisoner's Dilemma

Cooperation is ubiquitous in nature, but explaining its existence remains a central interdisciplinary challenge. Cooperation is most difficult to explain in the Prisoner's Dilemma game, where cooperators always lose in direct competition with defectors despite increasing mean fitness. Here we demonstrate how spatial population expansion, a widespread natural phenomenon, promotes the evolution of cooperation. We engineer an experimental Prisoner's Dilemma game in the budding yeast Saccharomyces cerevisiae to show that, despite losing to defectors in nonexpanding conditions, cooperators increase in frequency in spatially expanding populations. Fluorescently labeled colonies show genetic demixing of cooperators and defectors, followed by increase in cooperator frequency as cooperator sectors overtake neighboring defector sectors. Together with lattice-based spatial simulations, our results suggest that spatial population expansion drives the evolution of cooperation by (1) increasing positive genetic assortment at population frontiers and (2) selecting for phenotypes maximizing local deme productivity. Spatial expansion thus creates a selective force whereby cooperator-enriched demes overtake neighboring defector-enriched demes in a "survival of the fastest". We conclude that colony growth alone can promote cooperation and prevent defection in microbes. Our results extend to other species with spatially restricted dispersal undergoing range expansion, including pathogens, invasive species, and humans

Resistance to learning and the evolution of cooperation

In many evolutionary algorithms, crossover is the main operator used in generating new individuals from old ones. However, the usual mechanism for generating offsprings in spatially structured evolutionary games has to date been clonation. Here we study the effect of incorporating crossover on these models. Our framework is the spatial Continuous Prisoner's Dilemma. For this evolutionary game, it has been reported that occasional errors (mutations) in the clonal process can explain the emergence of cooperation from a non-cooperative initial state. First, we show that this only occurs for particular regimes of low costs of cooperation. Then, we display how crossover gets greater the range of scenarios where cooperative mutants can invade selfish populations. In a social context, where crossover involves a general rule of gradual learning, our results show that the less that is learnt in a single step, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one.Evolutionary games, Continuous prisoner's dilemma, Spatially structured, Crossover, Learning

Adaptive long-range migration promotes cooperation under tempting conditions

Migration is a fundamental trait in humans and animals. Recent studies investigated the effect of migration on the evolution of cooperation, showing that contingent migration favors cooperation in spatial structures. In those studies, only local migration to immediate neighbors was considered, while long-range migration has not been considered yet, partly because the long-range migration has been generally regarded as harmful for cooperation as it would bring the population to a well-mixed state that favors defection. Here, we studied the effects of adaptive long-range migration on the evolution of cooperation through agent-based simulations of a spatial Prisoner's Dilemma game where individuals can jump to a farther site if they are surrounded by more defectors. Our results show that adaptive long-range migration strongly promotes cooperation, especially under conditions where the temptation to defect is considerably high. These findings demonstrate the significance of adaptive long-range migration for the evolution of cooperation.Comment: 7 pages, 9 figure

The coevolution of costly heterogeneities and cooperation in the prisoner's dilemma game

This paper discusses the co-evolution of social strategies and an efficiency trait in spatial evolutionary games. The continuous efficiency trait determines how well a player can convert gains from a prisoner's dilemma game into evolutionary fitness. It is assumed to come at a cost proportional to its magnitude and this cost is deducted from payoff. We demonstrate that cost ranges exist such that the regime in which cooperation can persist is strongly extended by the co-evolution of efficiencies and strategies. We find that cooperation typically associates with large efficiencies while defection tends to pair with lower efficiencies. The simulations highlight that social dilemma situations in structured populations can be resolved in a natural way: the nature of the dilemma itself leads to differential pressures for efficiency improvement in cooperator and defector populations. Cooperators benefit by larger improvements which allow them to survive even in the face of inferior performance in the social dilemma. Importantly, the mechanism is possible with and without the presence of noise in the evolutionary replication process