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

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

Finite Memory Distributed Systems

A distributed system model is studied, where individual agents play repeatedly against each other and change their strategies based upon previous play. It is shown how to model this environment in terms of continuous population densities of agent types. A complication arises because the population densities of different strategies depend upon each other not only through game payoffs, but also through the strategy distributions themselves. In spite of this, it is shown that when an agent imitates the strategy of his previous opponent at a sufficiently high rate, the system of equations which governs the dynamical evolution of agent populations can be reduced to one equation for the total population. In a sense, the dynamics 'collapse' to the dynamics of the entire system taken as a whole, which describes the behavior of all types of agents. We explore the implications of this model, and present both analytical and simulation results.Fixed strategy, Prisoner's dilemma, Fokker-Plank, Distributed system

Cocaine use disorder in females is associated with altered social decision-making: a study with the prisoner's dilemma and the ultimatum game

BACKGROUND Chronic cocaine use is associated with cognitive deficits, including poor performance on neuropsychological tasks of memory, executive functions, theory of mind and decision-making. However, the relationship between cocaine use disorder and social decision-making remains unclear. This is particularly relevant given the fact that many cocaine abusers present impairments in social functioning. In this sense, game theory paradigms have been helping to comprehend the behavior of psychiatric patients when they directly engage in social situations, which may better approximate many of their real-life choices. METHODS The present study investigated social decision-making in individuals with or without cocaine use disorder, examining their behavior in the Prisoner's Dilemma and in the Ultimatum Game. Thus, 129 females diagnosed with cocaine use disorder and 55 females with no history of substance abuse were recruited and performed both social decision-making tasks. Additional assessments included information about demographics, patterns of substance consumption and executive function performance. RESULTS Females with cocaine use disorder opted more often to not defect in the Prisoner's Dilemma, while in the Ultimatum Game they frequently chose to accept the first and unfair offer as responders. These effects were more pronounced within females with long-term history of cocaine use. Associations between cocaine use disorder and altered social decision-making were independent from demographic and executive function variables. CONCLUSIONS The influence of cocaine use disorder on social decision-making was detected in both game paradigms, resulting in more cooperative behavior in the Prisoner's Dilemma and higher acceptance rate of unfair offers in the Ultimatum Game. Further studies should focus on investigating these associations to shed light on the putative biopsychosocial factors underlying the observed effects

The Evolution of Cooperation in Spatially Heterogeneous Populations

A challenging problem in sociobiology is to understand the emergence of cooperation in a nonsocial world. Recent models of the iterated Prisoner's Dilemma (IPD) game conclude that population mixing due to individual mobility limits cooperation; however, these models represent space only implicitly. Here we develop a dynamical IPD model where temporal and spatial variations in the population are explicitly considered. Our model accounts for the stochastic motion of individuals and the inherent nonrandomness of local interactions. By deriving a spatial version of Hamilton's rule, we find that a threshold level of mobility in selfish always-defect (AD) players is required to beget invasion by social 'tit for tat'(TFT) players. Furthermore, the level of mobility of successful TFT newcomers must be approximately equal to or somewhat higher than that of resident defectors. Significant mobility promotes the assortment of TFT pioneers on the front of invasion and of AD intruders in the core of a cooperative cluster. It also maximizes the likelihood of TFT retaliation. Once this first step whereby TFT takes over AD is completed, more generous and perhaps more suspicious strategies may outperform and displace TFT. We derive the conditions under which this continued evolution of more robust cooperative strategies occurs

A simple model of cognitive processing in repeated games

In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a lot and they are seldom completely symmetric. The purpose of this paper is to discuss a simple model of cognitive processing in the context of a repeated interaction with varying payoffs. The interaction between players is modelled by a repeated game with random observable payoffs. Cooperation is not simply associated with a certain action but needs to be understood as a phenomenon of the behaviour in the repeated game. The players are thus faced with a more complex situation, compared to the Prisoner's Dilemma that has been widely used for investigating the conditions for cooperation in evolving populations. Still, there are robust cooperating strategies that usually evolve in a population of players. In the cooperative mode, these strategies select an action that allows for maximizing the sum of the payoff of the two players in each round, regardless of the own payoff. Two such players maximise the expected total long-term payoff. If the opponent deviates from this scheme, the strategy invokes a punishment action, which aims at lowering the opponent's score for the rest of the (possibly infinitely) repeated game. The introduction of mistakes to the game actually pushes evolution towards more cooperative strategies even though the game becomes more difficult.Comment: Accepted for publication in the conference proceedings of ECCS'0

Reply to Will and Hegselmann

[No abstract]Replication, Social Dilemmas, Simulation Methodology, Cooperation, Trust, Agent-Based Modelling