Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price

The existence and uniqueness of equilibrium for a general class of two-player bidding games are proved and the uniqueness results hold in the class of nondecreasing strategy equilibria.

Abstract

We prove existence and uniqueness of equilibrium for a general class of two-player bidding games. We apply our results to the first price auction, the combination of first and second price auctions, the war of attrition, the all pay auction, as well as combinations of the latter two auction forms. We also treat the first price auction without risk neutrality. Our results deal with the asymmetric, affiliated common values environment. In the case where signals are independent our results apply to all equilibria. When signals are not independent, our uniqueness results hold in the class of nondecreasing strategy equilibria. Journal of Economic Literature Classification Number: D44.