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Convergence of a Dynamic Matching and Bargaining Market with Two-sided Incomplete Information to Perfect Competition

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  • Mark Satterthwaite
  • Artyom Shneyerov

Abstract

Consider a decentralized, dynamic market with an infinite horizon in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length ?, and each unit of time a large number of new buyers and sellers enter the market to trade. Within a period each buyer is matched 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 either continue in the market to be rematched or become discouraged with probability ?? (? is the discouragement rate) and exit with zero utility. We characterize the steady-state, perfect Bayesian equilibria as ? becomes small and the market–in effect– becomes large. We show that, as ? converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation.

Suggested Citation

  • Mark Satterthwaite & Artyom Shneyerov, 2003. "Convergence of a Dynamic Matching and Bargaining Market with Two-sided Incomplete Information to Perfect Competition," Discussion Papers 1384, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1384
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    1. Mark Satterthwaite & Artyom Shneyerov, 2007. "Dynamic Matching, Two-Sided Incomplete Information, and Participation Costs: Existence and Convergence to Perfect Competition," Econometrica, Econometric Society, vol. 75(1), pages 155-200, January.
    2. Art Shneyerov, 2006. "Dynamic Matching with Two-sided Incomplete Information and Participation Costs," Theory workshop papers 815595000000000009, UCLA Department of Economics.
    3. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
    4. Sjaak Hurkens & Nir Vulkan, 2006. "Dynamic Matching and Bargaining: The Role of Deadlines," UFAE and IAE Working Papers 660.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 19 Apr 2006.

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