Econ Papers Daily / 期刊论文
关于成本均摊下的重复志愿者困境
On the repeated volunteer’s dilemma with equal cost sharing
摘要
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 efficiency, scope for cooperation and equity/focality as criteria, the grand coalition of volunteers emerges as the best cooperation scenario.
中文摘要
我们研究了具有二元行动和成本分担的对称志愿者困境，其中志愿者成本由所有志愿者平均分担。在一次性博弈中，所有纯策略纳什均衡都只涉及一名志愿者，而帕累托最优则允许任意非零数量的志愿者。在无限重复博弈中，所有帕累托最优状态都可以通过基于冷酷触发策略的子博弈完美纳什均衡得以维持：在无折现收益下显然成立，而在有折现收益下，需满足折现因子超过某一阈值。该阈值随志愿者数量呈非单调变化：当只有一名志愿者时为零，两名志愿者时最高，随后随着志愿者数量超过两人以及玩家数量增加而下降。因此，隐性合作的范围在只有一名志愿者时具有普遍性，在两名志愿者时最小，随着更多人加入而改善，直到在玩家和志愿者数量趋于极限时再次达到普遍性。综合考虑效率、合作范围以及公平性/焦点性等标准，志愿者的大联盟成为最佳合作情景。