The Iterated Prisoner's Dilemma: Good Strategies and Their Dynamics

TL;DR

This paper characterizes strategies in the iterated Prisoner's Dilemma that promote stable cooperation through Nash equilibria and analyzes their impact on evolutionary dynamics.

Contribution

It introduces and characterizes 'good strategies' that ensure stable cooperation and explores their role in evolutionary game dynamics.

Findings

Good strategies form Nash equilibria promoting cooperation.

Unilateral deviation reduces both players' payoffs.

These strategies stabilize cooperative behavior in evolutionary contexts.

Abstract

For the iterated Prisoner's Dilemma, there exist Markov strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally any other strategy, i.e. these are Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent's payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these \emph{good strategies} effectively stabilize cooperative behavior. We characterize these good strategies and analyze their role in evolutionary dynamics.