Asymmetric auctions: Perturbations, ε- equilibrium, and equilibrium

Abstract

We consider first-price auctions with independent and private valuations that have asymmetric valuation distributions and supports. We first show the existence of equilibrium in these auctions through a perturbation approach, thereby establishing that the limit of Bayesian Nash equilibria (BNE) of such perturbed auctions is indeed the Bayesian Nash equilibrium (BNE) of the limit auction with asymmetric supports. We then characterize this BNE and show that the ε-equilibrium (ε-BNE) of the auction with asymmetric supports is a BNE of “close” auctions with common supports. We then demonstrate some numerical examples.