Comparing the Robustness of Trading Systems to Higher Order Uncertainty*

This paper compares the performance of a decentralized market with that of a dealership market when traders have differential information. Trade occurs as a result of equilibrium actions in a Bayesian game, where uncertainty is captured by a finite state space and information is represented by partitions on this space. In the benchmark case of trade with common knowledge of endowments, the two mechanisms deliver virtually identical outcomes. However, with differential information, the dealership market has strictly higher trading volume, and yields an efficient post-trade allocation in most states. In contrast, the decentralized market suffers from suboptimal trading volume. The reason for this poor performance is the vulnerability of the decentralized market to higher order uncertainty concerning the fundamentals of the market. Traders may know that mutually beneficial trade is feasible, and perhaps know that they know, and yet a failure of common knowledge that this is so precludes efficient trade. The dealership market is robust to this type of uncertainty. * I would like to record my debt to Stephen Morris for shaping my views on the issues raised here. Ian Jewitt, as managing editor, and three referees guided this paper through several revisions, and I am grateful to them for their perseverance. I am especially grateful to one of the referees for pointing to the importance of limit orders in modifying the results reported here. I have gained from the comments of Helmut Bester, Katie Graddy, Ruben Lee, Ailsa Roell, Daniel Seidmann, Peter Sinclair, John Vickers and seminar participants at ̈ Tilburg, Newcastle, CORE, Cambridge, IFS, Southampton and the 1994 European Summer Symposium in Financial Markets at the Studienzentrum Gerzensee. An earlier version of this paper was circulated under the title, “The Volume of Trade in Auction and Dealership Markets with Differential Information".