Indirect exclusion can promote cooperation in repeated group interactions

TL;DR

This paper explores how indirect social exclusion, implemented via probabilistic selection of cooperators in repeated public goods games, can promote cooperation in both infinite and finite populations, revealing nonlinear effects and the importance of interaction rounds.

Contribution

It introduces a novel indirect exclusion mechanism into public goods games and analyzes its impact on cooperation evolution from a theoretical perspective.

Findings

Indirect exclusion induces stable coexistence or dominance of cooperators.

Higher identifying probability maintains high cooperation levels.

More rounds of interaction promote cooperation.

Abstract

Social exclusion has been regarded as one of the most effective measures to promote the evolution of cooperation. In real society, the way in which social exclusion works can be direct or indirect. However, thus far there is no related work to explore how indirect exclusion influences the evolution of cooperation from a theoretical perspective. Here, we introduce indirect exclusion into the repeated public goods game where the game organizer probabilistically selects cooperators after the first game round to participate in the following possible game interactions. We then investigate the evolutionary dynamics of cooperation both in infinite and finite well-mixed populations. Through theoretical analysis and numerical calculations, we find that the introduction of indirect exclusion can induce the stable coexistence of cooperators and defectors or the dominance of cooperators, which thus effectively promotes the evolution of cooperation. Besides, we show that the identifying probability of the organizer has a nonlinear effect on public cooperation when its value is lower than an intermediate value, while the higher identifying probability can maintain a high level of cooperation. Furthermore, our results show that increasing the average rounds of game interactions can effectively promote the evolution of cooperation.