The Evolutionary Robustness of Forgiveness and Cooperation

TL;DR

This paper investigates the evolutionary stability of forgiving and cooperative strategies in repeated prisoners' dilemma games, demonstrating that such strategies can be robust and widely adopted under certain dynamics.

Contribution

It introduces a new analysis of strategy robustness in repeated games considering mistakes and patience, highlighting the importance of forgiveness and cooperation for evolutionary stability.

Findings

Strategies that forgive defections have large basins of attraction.

Forgiving strategies tend to cooperate when symmetric.

Robust strategies are effective regardless of population size.

Abstract

We study the evolutionary robustness of strategies in infinitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator dynamics. We show that there are strategies with a uniformly large basin of attraction independently of the size of the population. Moreover, we show that those strategies forgive defections and, assuming that they are symmetric, they cooperate.