Strategy-Proof Compromises

We study strategy-proof decision rules in the variant of the canonical public good model proposed by Borgers and Postl (2009). In this setup, we fully characterize the set of budget-balanced strategy-proof deterministic mechanisms, which are simple threshold rules. For smooth probabilistic mechanisms, we provide a necessary and sufficient condition for dominant strategy implementation. When allowing for discontinuities in the mechanism, our necessary condition remains valid, but additional conditions must hold for sufficiency. We also show that, among ex post efficient decision rules, only dictatorial ones are strategy-proof. While familiar in spirit, this result is not the consequence of any known result in the literature.