<b>p</b>-dominant Implementation

Abstract

We introduce and study a partial implementation notion, which we term p-dominant implementation, where p ∈ [0, 1]^N and N is the number of agents. When agents have interdependent valuation, this notion captures robustness to strategic uncertainty, contrasting with ex-post implementation. The corresponding solution concept generalizes p-dominant equilibrium (Morris et al., 1995) to games with incomplete information so as to be employed in the mechanism design problem. The incentive compatibility (p-DIC) condition requires each agent i find it optimal to truthfully report his/her type as long as the opponents are believed to do so with probability at least pi. In the quasilinear environment with one-dimensional payoff type spaces, we completely characterize p-dominant implementable allocation rules for any p. In the special case of agents with private valuation, we find that p-dominant implementable allocation rule is completely characterized by p-monotonicity of allocation rule. On the other hand, when agents’ valuation is interdependent, the condition is necessary but not sufficient. The complete characterization involves a stronger version of monotonicity of marginal benefit of reporting a higher type) with respect to agent’s true type for any report-indistinguishable reporting strategies of the opponents. Especially, with continuous types and interdependent valuation, the condition requires that any p-dominant implementable allocation rule to be 0-dominant implementable; we show that an allocation rule is p-dominant implementable for p ≪ 1 if and only if it satisfies ex-post monotonicity and additive separability. As an application of our result, we also study constrained efficient allocation that is 0-dominant implementable. We find that when there are two agents, the constrained efficient auction is a discriminatory posted-price mechanism, where the planner determines one and only one agent to whom the planner tries to sell the item.