Dynamic Matching,Two-sided Incomplete Information, and Participation Costs: Existence and Convergence to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and each unit of time continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady-state equilibria that satisfy a subgame perfection criterion. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show existence of equilibria for δ sufficiently small. ∗Kellogg School of Management, Northwestern University and Department of Economics, University of British Columbia respectively. †We owe special thanks to Zvika Neeman who originally devised a proof showing the strict monotonicity of strategies. We also thank Hector Chade, Patrick Francois, Paul Milgrom, Dale Mortensen, Peter Norman, Mike Peters, Jeroen Swinkels, Asher Wolinsky, Jianjun Wu, Okan Yilankaya, and two very perceptive anonymous referees; the participants at the “Electronic Market Design Meeting” (June 2002, Schloss Dagstuhl), the 13th Annual International Conference on Game Theory at Stony Brook, the 2003 NSF Decentralization Conference held at Purdue University, the 2003 General Equilibrium Conference held at Washington University, the 2003 Summer Econometric Society Meeting held at Northwestern University, the 2004 Canadian Economic Theory Conference held in Montreal, and Games 2004 held at Luminy in Marseille; seminar participants at Carnegie-Mellon, Washington University, Northwestern University, University of Michigan, Harvard and MIT, UBC, and Stanford; and the members of the collaborative research group on “Foundations of Electronic Marketplaces” for their constructive comments. Adam Wong provided excellent research assistance. Finally, both of us acknowledge gratefully that this material is based on work supported by the National Science Foundation under Grant IIS-0121541. Artyom Shneyerov also acknowledges support from the Canadian SSHRC Grant 410-2003-1366.