Cooperation among behaviorally heterogeneous players in social dilemma with stay or leave decisions

Given the substantial evidence of behavioral heterogeneity in social dilemma experiments, in this study we consider how to achieve cooperation in n-player prisoner's dilemma situations where each player has one behavioral type, either selfish or conditionally cooperative. We introduce a two-stage game form called the stay-leave mechanism, where each cooperator has the chance to revise his choice when players' choices are not unanimous. For homogeneous behavioral type cases, theory predicts that the unique outcome is cooperative under the stay-leave mechanism, regardless of the benefit derived from cooperation. For heterogeneous behavioral type cases, we show that the benefits of cooperation shrink such that the unique outcome is cooperative under the stay-leave mechanism if the number of conditionally cooperative players increases. The average cooperation rate in the stay-leave mechanism experiment is 86.6% across 15 periods, which increases to 96.0% after period 5. We also provide evidence that selfish and conditionally cooperative types coexist throughout the sessions, in the proportion that the equilibrium outcome is cooperative. Our results corroborate the importance of incorporating behavioral heterogeneity into institutional design.