Win-stay-lose-learn promotes cooperation in the spatial prisoner's dilemma game

TL;DR

This paper introduces an aspiration-based win-stay-lose-learn strategy updating rule in the spatial prisoner's dilemma game, which promotes cooperation robustly even from minimal initial cooperation, challenging traditional strategy change assumptions.

Contribution

It proposes a simple, intuitive strategy update rule based on aspiration, demonstrating its effectiveness in fostering cooperation in spatial prisoner's dilemma games.

Findings

Win-stay-lose-learn rule promotes cooperation.

Even minimal initial cooperation can lead to highly cooperative states.

Results are supported by simulations and pair approximation analysis.

Abstract

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed win-stay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related win-stay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.