Optimal Trading Mechanisms with Ex Ante Unidentified Traders

Abstract

We analyze optimal trading mechanisms in an exchange economy where each trader owns some units of a good to be traded and may be either a seller or a buyer, depending on the realization of the privately observed valuations. The concept of virtual valuation is extended to ex ante unidentified traders. The traders' virtual valuations now depend on the choice of the trading mechanism and are generally nonmonotonic. We show that the trading mechanisms that maximize a broker's expected profit or expected total gains from trade are generalized double auctions which maximize the gains from trade measured in some modified monotonic virtual valuations for the traders. The bunching phenomena will be a general feature in these mechanisms. We also show that the optimal mechanisms converge towards simple bid-ask price mechanisms as the number of participants in the market increases. Journal of Economic Literature Classification Numbers: D44, D82.