On the Repeated Volunteer's Dilemma with Equal Cost Sharing

Abstract

We study the symmetric volunteer’s dilemma with binary actions and cost sharing, where the volunteering cost is split equally among volunteers. In the one-shot game, all pure-strategy Nash equilibria involve a single volunteer, while Pareto optimality allows any non-zero number. In the infinitely repeated game, all Pareto optima can be sustained in a subgame-perfect Nash equilibrium based on a grim-trigger strategy: trivially under undiscounted payoffs, and provided the discount factor exceeds a threshold under discounted payoffs. This threshold is non-monotonic in the number of volunteers; it is zero with one volunteer, highest with two, and decreases with both more volunteers beyond two and more players. Thus, the scope for tacit cooperation is universal with one volunteer, minimal with two, then improving as more join in, all the way to universal again only in the limit with more and more players and volunteers. Considering both equity and scope for cooperation as criteria, the grand coalition as volunteers emerges as the best cooperation scenario.