N-Person Prisoners' Dilemmas

Abstract

This review is an attempt to systematically present the problem of various N-person Prisoners' Dilemma games and some of their possible solutions. Thirteen characteristics of the game are discussed. The role of payoff curves, personalities, and neighborhood is investigated. We report computer simulation experiments based on our new agent-based simulation tool to model social situations for the case of large numbers of not necessarily rational decision-makers. Our model has a number of user-defined parameters such as the size and shape of the simulation environment, the definition of neighborhood, the payoff (reward/penalty) functions, the learning rules, the agents' personalities, and the initial conditlons. We have performed a series of simulation experiments with various combinations of these parameters. lnvestigations of realistic (non-dyadic) situations in which agents have various personalities show interesting new results. For the case of Pavlovian agents the game has two non-trivial but remarkably regular solutions. For a wide range of initial conditions, the number of cooperators oscillates around a relatively small value. When the initial aggregate cooperation probability is above a certain value, the solutions tend to reach well-defined constant values that are dependent on the initial values. For other types of agents the solutions show interesting chaos-like behavior. Examples of non-uniform distributions and mixed personalities are also presented. All solutions strongly depend on the choice of parameter values. The paper provides some insight into the conditions of decentralized cooperation in spatially distributed populations of agents.