Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations

TL;DR

This study reveals how a complex interplay of strategies, including defection and extortion, can unexpectedly promote unconditional cooperation in structured populations through specific evolutionary dynamics.

Contribution

It demonstrates that myopic updating enables the coexistence of five strategies, including cooperation and extortion, via a novel chain of invasions in structured populations.

Findings

Unconditional cooperation and extortion are sustained through strategy invasions.

Myopic updating fosters coexistence of five strategies in the prisoner's dilemma.

Stable five-strategy phase emerges regardless of network size and structure.

Abstract

We study the evolution of cooperation in the spatial prisoner's dilemma game, where besides unconditional cooperation and defection, tit-for-tat, win-stay-lose-shift and extortion are the five competing strategies. While pairwise imitation fails to sustain unconditional cooperation and extortion regardless of game parametrization, myopic updating gives rise to the coexistence of all five strategies if the temptation to defect is sufficiently large or if the degree distribution of the interaction network is heterogeneous. This counterintuitive evolutionary outcome emerges as a result of an unexpected chain of strategy invasions. Firstly, defectors emerge and coarsen spontaneously among players adopting win-stay-lose-shift. Secondly, extortioners and players adopting tit-for-tat emerge and spread via neutral drift among the emerged defectors. And lastly, among the extortioners, cooperators become viable too. These recurrent evolutionary invasions yield a five-strategy phase that is stable irrespective of the system size and the structure of the interaction network, and they reveal the most unexpected mechanism that stabilizes extortion and cooperation in an evolutionary setting.