Stress Testing Approval Mechanisms in Public Good Games

We stress test the approval mechanism with the minimum disapproval benchmark (AM) in public good games, extending previous two-player analyses (Masuda et al., 2013, 2014) to a three-player setting. This introduces challenges in vote aggregation, addressed through a comparison of unanimity and majority approval rules. We find that AM is less efficient in the three-player case. While it fully implements optimal contributions in BEWDS for two players (Masuda et al., 2014), implementation in the three-player game depends on the marginal per capita return (MPCR). Only unanimity with low MPCR yields the Pareto optimum; other rule-MPCR combinations result in null contributions, as in the voluntary contribution mechanism (Isaac and Walker, 1988). Nevertheless, this partial implementation remains relevant, as many real-world public goods have low MPCR (Weimann et al., 2012).