Equilibrium in the Two Player, K-Double Auction with Affiliated Private Values

Abstract

We present sufficient conditions for the existence of an increasing equilibrium in the two player k-double auction with affiliated private values. In the case k ∈ {0, 1} there exists a unique equilibrium in non-dominated strategies. Applying this equilibrium, we provide a detailed example illustrating how dependence level affects strategic bidding. In the case k ∈ (0, 1) we prove existence of a continuum of strictly increasing equilibria, and illustrate them using an example. Furthermore, we show that equilibria in the case of independent private values are pointwise limits of equilibria with strictly affiliated private values.

Keywords: Double Auction, Affiliation, Single Crossing

JEL Classification: C72, D44