Equilibrium in the two-player, k-double auction with affiliated private values

The opinions expressed in this paper do not necessarily reflect the position of Summary We prove the existence of an increasing equilibrium, and study the comparative statics of correlation in the k-double auction with affiliated private values. This is supposedly the simplest bilateral trading mechanism that allows for dependence in valuations between buyers and sellers. In the case k ∈{0 ,1} there exists a unique equilibrium in non-dominated strategies. Using this equilibrium we show that correlation has a dual effect on strategic bidding. It might impose bidders to become more or less aggressive depending on their private valuation, and on the level of correlation. In the case k ∈ (0 ,1), we prove the existence of a family of strictly increasing equilibria, and demonstrate them using examples. Moreover, we show that equilibria in the case of independent private values are pointwise limits of equilibria with strictly affiliated private values.