Implementation in Weakly Undominated Strategies, with Applications to Auctions and Bilateral Trade

We study the mechanism-design problem of guaranteeing desirable performances whenever agents are rational in the sense of not playing weakly dominated strategies. We first provide an upper bound for the best performance we can guarantee among all feasible mechanisms. We then prove the bound to be tight under certain conditions in auction and bilateral-trade applications. In particular, we find that a second-price auction is optimal in revenue with interdependent values, which is neither dominant-strategy nor ex post incentive compatible, but satisfies the novel incentive compatibility introduced in this analysis.