Asymmetric auctions: perturbations, \(\varepsilon\)-equilibrium, and equilibrium (Q6634099)

In this article, the authors consider first-price auctions with independent and private valuations that have asymmetric valuation distributions and supports. The topic relates to classical problems related to the study of dynamic models with asymmetric potential. Probabilistic construction for control over the oscillations is given.\N\NThe authors 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. They then characterize this BNE and show that the \(\epsilon\)-equilibrium (\(\epsilon\)-BNE) of the auction with asymmetric supports is a BNE of ``close'' auctions with common supports.\N\NNumerical examples are also given. Section 2 introduces the model and the perturbation approach. Section 3 presents the existence and characterization of the BNE and relates BNE to \(\epsilon\)-BNE. Subsection 3.1 provides the results, discussions, and proof strategies. Subsection 3.2 contains the proofs of Theorems 1 and 2.