Optional participation only provides a narrow scope for sustaining cooperation

TL;DR

This paper explores how optional participation influences cooperation in public goods games, revealing that its effectiveness is limited and depends on the strategic motives of non-participants, with cooperation thriving mainly under specific motivations.

Contribution

It generalizes the understanding of optional participation by incorporating non-participants' payoffs and their influence, revealing the conditions under which cooperation is sustained.

Findings

Cooperation thrives when non-participants are motivated by individualistic or prosocial values.

Optimal cooperation occurs with individualistic motivations for non-participants.

Robustness to mutation slightly expands the conditions for cooperation through cyclic dominance.

Abstract

Understanding how cooperation emerges in public goods games is crucial for addressing societal challenges. While optional participation can establish cooperation without identifying cooperators, it relies on specific assumptions -- that individuals abstain and receive a non-negative payoff, or that non-participants cause damage to public goods -- which limits our understanding of its broader role. We generalize this mechanism by considering non-participants' payoffs and their potential direct influence on public goods, allowing us to examine how various strategic motives for non-participation affect cooperation. Using replicator dynamics, we find that cooperation thrives only when non-participants are motivated by individualistic or prosocial values, with individualistic motivations yielding optimal cooperation. These findings are robust to mutation, which slightly enlarges the region where cooperation can be maintained through cyclic dominance among strategies. Our results suggest that while optional participation can benefit cooperation, its effectiveness is limited and highlights the limitations of bottom-up schemes in supporting public goods.