Auctions with unique equilibria

We study Bayes-Nash equilibria in a large class of anonymous order-based auctions. These include the generalized first-price auction for allocating positions to bidders, e.g., for sponsored search. We show that when bidders' values are independent and identically distributed the symmetric equilibrium is unique and efficient. Importantly, our proof is simple and structurally revealing. This uniqueness result for the generalized first-price auction is in stark contrast to the generalized second-price auction where there may be no efficient equilibrium. This result suggests, e.g., that first-price payment semantics may have advantages over second-price payment semantics. Our results extend also to certain models of risk aversion.

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