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

The analysis of equilibrium in double auctions is complicated, with almost no closed-form examples and with formal results limited to bounds on bidding behavior. We consider the buyer’s bid double auction in a correlated, private values model. Sellers have the incentive to submit their costs as their asks while buyers strategically underbid. We determine (i) the asymptotic distribution of the equilibrium market price and (ii) the asymptotic limits of terms in the first order condition for a buyer’s selection of his bid. Part (i) reveals the properties of the strategically determined market price as an estimator of the rational expectations equilibrium price. Part (ii) provides a simple formula for a buyer’s bid that is shown numerically to closely approximate his equilibrium bid even in relatively small markets. This formula reveals how equilibrium varies with the numbers of buyers and sellers and the distribution of their values/costs. JEL Classification: C63, C72, D44, D82