PERCEPTRON VERSUS AUTOMATON∗

We study the finitely repeated prisoner’s dilemma in which the players are restricted to choosing strategies which are implementable by a machine with a bound on its complexity. One player must use a finite automaton while the other player must use a finite perceptron. Some examples illustrate that the sets of strategies which are induced by these two types of machines are different and not ordered by set inclusion. The main result establishes that a cooperation in almost all stages of the game is an equilibrium outcome if the complexity of the machines players may use is limited enough. This result persists when there are more than T states in the player’s automaton, where T is the duration of the repeated game. We further consider the finitely repeated prisoner’s dilemma in which the two players are restricted to choosing strategies which are implementable by perceptrons and prove that players can cooperate in most of the stages provided that the complexity of their perceptrons is sufficiently reduced.

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

Evolutionary Markovian Strategies in 2 x 2 Spatial Games

Evolutionary spatial 2 x 2 games between heterogeneous agents are analyzed using different variants of cellular automata (CA). Agents play repeatedly against their nearest neighbors 2 x 2 games specified by a rescaled payoff matrix with two parameteres. Each agent is governed by a binary Markovian strategy (BMS) specified by 4 conditional probabilities [p_R, p_S, p_T, p_P] that take values 0 or 1. The initial configuration consists in a random assignment of "strategists" among the 2^4= 16 possible BMS. The system then evolves within strategy space according to the simple standard rule: each agent copies the strategy of the neighbor who got the highest payoff. Besides on the payoff matrix, the dominant strategy -and the degree of cooperation- depend on i) the type of the neighborhood (von Neumann or Moore); ii) the way the cooperation state is actualized (deterministically or stochastichally); and iii) the amount of noise measured by a parameter epsilon. However a robust winner strategy is [1,0,1,1].Comment: 18 pages, 8 figures (7 of these figures contain 4 encapsulapted poscript files each

Trust is bound to emerge (In the repeated Trust Game)

This paper addresses the emergence of cooperation in asymmetric pris- oners' dilemmas in which one player chooses after having observed the other player's choice (Trust Game). We use the finite automata approach with complexity costs to study the equilibria of the repeated version of this game. We show that there is a small set of automata that form the unique Closed Under Rational Behavior (CURB) set for this game. This set contains two non-strict Nash equilibria, a cooperative and a non- cooperative one. We show that the cooperative equilibrium is the only (cyclically) stable set under the so called Best Response Dynamics.

Learning and innovative elements of strategy adoption rules expand cooperative network topologies

Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying the reinforcement learning strategy adoption rule, Q-learning on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent Prisoners Dilemma and Hawk-Dove games. Furthermore, we found that using the above model systems other long-term learning strategy adoption rules also promote cooperation, while introducing a low level of noise (as a model of innovation) to the strategy adoption rules makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and random elements in the strategy adoption rules, when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during the re-organization of real-world networks, and may play a prominent role in the evolution of self-organizing, complex systems.Comment: 14 pages, 3 Figures + a Supplementary Material with 25 pages, 3 Tables, 12 Figures and 116 reference

Cooperative Strategies in Groups of Strangers: An Experiment

We study cooperation in four-person economies of indefinite duration. Subjects interact anonymously playing a prisoner’s dilemma. We identify and characterize the strategies employed at the aggregate and at the individual level. We find that (i) grim trigger well describes aggregate play, but not individual play; (ii) individual behavior is persistently heterogeneous; (iii) coordination on cooperative strategies does not improve with experience; (iv) systematic defection does not crowd-out systematic cooperation.repeated games, equilibrium selection, prisoners’ dilemma, random matching