The Asymptotics of Price and Strategy in the Buyer's Bid Double Auction

Abstract

In a model with correlated and interdependent values/costs, we identify for the buyer's bid double auction the asymptotic distributions of the price and of two order statistics in the first order conditions for optimal bidding/asking, all of which are normal. The asymptotic distribution of price is used to investigate the shortcomings of the price as an aggregator of information as the common value case is approached. Substitution of the asymptotic distributions into the first order conditions can permit the solution for approximately optimal bids/asks that provide insight into what is "first order" in a trader's strategic decision-making, which has been difficult to obtain through analysis of equilibrium. The accuracy of approximations are then tested using calculated Bayesian-Nash equilibria.

Keywords: double auction, rational expectations equilibrium, interdependent value, common value, central limit theorem

JEL Classification: C63, D44, D82