Behavioral Mistakes Support Cooperation in an N-Person Repeated Public Goods Game

TL;DR

This paper demonstrates that behavioral mistakes can unexpectedly promote the stability of cooperative strategies in repeated public goods games, challenging the common view of mistakes as purely detrimental.

Contribution

It reveals that behavioral mistakes can make all conditional cooperative strategies evolutionarily stable, providing new insights into cooperation dynamics.

Findings

Behavioral mistakes stabilize cooperative equilibria.

Mistakes prevent defectors from gaining advantages.

Mistakes serve as a criterion for equilibrium selection.

Abstract

This study investigates the effect of behavioral mistakes on the evolutionary stability of the cooperative equilibrium in a repeated public goods game. Many studies show that behavioral mistakes have detrimental effects on cooperation because they reduce the expected length of mutual cooperation by triggering the conditional retaliation of the cooperators. However, this study shows that behavioral mistakes could have positive effects. Conditional cooperative strategies are either neutrally stable or are unstable in a mistake-free environment, but we show that behavioral mistakes can make \textit{all} of the conditional cooperative strategies evolutionarily stable. We show that behavioral mistakes stabilize the cooperative equilibrium based on the most intolerant cooperative strategy by eliminating the behavioral indistinguishability between conditional cooperators in the cooperative equilibrium. We also show that mistakes make the tolerant conditional cooperative strategies evolutionarily stable by preventing the defectors from accumulating the free-rider's advantages. Lastly, we show that the behavioral mistakes could serve as a criterion for the equilibrium selection among cooperative equilibria.