A dynamic analysis of the repeated prisoner's dilemma game
Inspired by Smale's analysis of the repeated prisoner's dilemma game, this paper studies a quite different approach to a dynamic description of the evolution of the repeated game. Assuming an infinite number of potential players the dynamics is defined by changes in the distribution of players over strategies, and a continuous dynamical system, describing the evolution of the distribution over strategies is obtained. Basic questions such as existence of solutions, ''good'' strategies leading to ''good'' solutions, and the stability of solutions are given exact affirmative answers. Further we obtain the results to be structurally stable. That is, small perturbations of the basic payoff matrix in the one shot game do not change the qualitative picture of the evolution. The obtained results give one possible explanation of how the basically non-cooperative behaviour of the players may lead to a cooperative outcome of the repeated game. Finally an example illustrates the applicability of the results to a duopoly model.
evolution of the distribution over strategies
scientific article; zbMATH DE number 3948037