A Strategic Theory of Markets

Abstract

This paper investigates the asymptotic behavior of a Bayesian Nash equilibrium in uniform price double auctions among buyers and sellers with a unit demand and supply who receive private signals independently and identically distributed conditional on the unknown state with the monotone likelihood ratio condition and have interdependent values with a strictly private value element. Every nontrivial mixed strategy Bayesian Nash equilibrium converges to the fully revealing rational expectation equilibrium as the number of buyers and sellers increases and the bid step size goes to zero. A monotone pure strategy Bayesian Nash equilibrium exists in sufficiently large finite economies, and provides a consistent and asymptotically normal estimator of the unknown value when the set of possible bids is continuous.