Rate of Convergence to Full Efficiency in the Buyers' Bid Double Auction as the Market Becomes Large

Abstract

This chapter discusses the rate of convergence to full efficiency in the buyer's bid double auction as the market becomes large. A market with m sellers is considered, each having a single item to sell and m buyers, each desiring to buy at most one item. Each trader has a reservation value for an item independently drawn from the unit interval; seller's value is drawn from the distribution F1 and a buyer's value is drawn from the distribution F2. Sellers and buyers simultaneously submit offers and bids. These offer and bids determine a closed interval in which a market clearing price may be selected. In the buyer's bid double auction (BBDA), the price selected is the upper endpoint of the interval. Trade then occurs at this price. Bayesian Nash equilibria is considered in which all sellers use one strategy and all buyers use a second strategy. Each seller in the BBDA has a dominant strategy to set his/her offer equal to his/her reservation value. In response to these dominant strategies, each buyer has an incentive to bid less than his reservation value. The camount of misrepresentation by buyers must be small when the market is large.