# On the Existence of Equilibria in a Class of Bayesian Allocation-Mechanisms (with Paulo Barelli and Robert Wilson)

Srihari Govindan | University of Rochester

## Abstract

We study the question of equilibrium-existence in the following class of Nplayer Bayesian games. Each player n ∈ {1, ..., N} has a general type space Ωn, and there’s a prior p on Ω = QN n=1 Ωn that is absolutely continuous with respect to the product of its marginals. The action space An of player n is compact Hausdorff. The outcome space, denoted ∆(Z), is the set of probability distributions over a finite set Z. The outcome function is given by λ : A → ∆(Z), where A = QN n=1 An. Transfers are denoted by tn and payoffs by un : Ω × Z × R → R, so un(ω, z, tn) is the payoff to n when the type profile is ω, the outcome is z and the payment he makes is tn. We assume that the game is “mildly discontinuous” in the sense that λ is continuous almost everywhere. The model subsumes standard auction models. We provide sufficient conditions for the existence of Nash and ε-Nash equilibria in these games and explore the implications of these results for auctions.

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