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The Rate of Convergence to Perfect Competition of Matching and Bargaining Mechanisms

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  • Artyom Shneyerov
  • Adam Chi Leung Won

Abstract

We study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information. We first consider generalized random-proposer take-it-or-leave-it offer games (GRP TIOLI games). This class of games includes a simple random-proposer TIOLI game, but also many other interesting bargaining games. A friction parameter is tau, the length of the time period until the next meeting. We find that as tau (right arrow) 0, all market equilibria converge to the Walrasian limit, at the fastest possible rate Omicron (tau) among all bargaining mechanisms. Some important bargaining games not in this class may have non-convergent market equilibria. This is the case for the k-double auction: we find that there are equilibria that converge at a linear rate, those that converge at a slower rate or even not converge at all.

Suggested Citation

  • Artyom Shneyerov & Adam Chi Leung Won, 2008. "The Rate of Convergence to Perfect Competition of Matching and Bargaining Mechanisms," Discussion Papers 1467, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1467
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    1. Peters, Michael, 2000. "Limits of Exact Equilibria for Capacity Constrained Sellers with Costly Search," Journal of Economic Theory, Elsevier, vol. 95(2), pages 139-168, December.
    2. 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.
    3. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "Bilateral matching and bargaining with private information," Games and Economic Behavior, Elsevier, vol. 68(2), pages 748-762, March.
    4. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
    5. Ausubel, Lawrence M. & Cramton, Peter & Deneckere, Raymond J., 2002. "Bargaining with incomplete information," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 50, pages 1897-1945 Elsevier.
    6. Serrano, Roberto, 2002. "Decentralized information and the Walrasian outcome: a pairwise meetings market with private values," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 65-89, September.
    7. Martin W. Cripps & Jeroen M. Swinkels, 2006. "Efficiency of Large Double Auctions," Econometrica, Econometric Society, vol. 74(1), pages 47-92, January.
    8. Gianni De Fraja & Jozsef Sakovics, 2001. "Walras Retrouve: Decentralized Trading Mechanisms and the Competitive Price," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 842-863, August.
    9. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 267-289.
    10. Dale T. Mortensen & Randall Wright, 2002. "Competitive Pricing and Efficiency in Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(1), pages 1-20, February.
    11. Alp E. Atakan, 2006. "Competitive Equilibria in Decentralized Matching with Incomplete Information," Discussion Papers 1437, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Nir Dagan & Roberto Serrano & Oscar Volij, 2000. "Bargaining, coalitions and competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 279-296, March.
    13. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
    14. Moreno, Diego & Wooders, John, 2002. "Prices, Delay, and the Dynamics of Trade," Journal of Economic Theory, Elsevier, vol. 104(2), pages 304-339, June.
    15. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
    16. Max R. Blouin & Roberto Serrano, 2001. "A Decentralized Market with Common Values Uncertainty: Non-Steady States," Review of Economic Studies, Oxford University Press, vol. 68(2), pages 323-346.
    17. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    18. Mark A. Satterthwaite & Steven R. Williams, 1989. "The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 477-498.
    19. Thomas A. Gresik & Mark A. Satterthwaite, 1985. "The Rate At Which a Simple Market Becomes Efficient as the Number of Traders Increases: An Asymptotic Result for Optimal Trading Mechanisms," Discussion Papers 708, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. Wolinsky, Asher, 1990. "Information Revelation in a Market with Pairwise Meetings," Econometrica, Econometric Society, vol. 58(1), pages 1-23, January.
    21. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    22. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
    23. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
    24. Gale, Douglas, 1987. "Limit theorems for markets with sequential bargaining," Journal of Economic Theory, Elsevier, vol. 43(1), pages 20-54, October.
    25. Philip J Reny & Motty Perry, 2006. "Toward a Strategic Foundation for Rational Expectations Equilibrium," Econometrica, Econometric Society, vol. 74(5), pages 1231-1269, September.
    26. Steven R. Williams, 1991. "Existence and Convergence of Equilibria in the Buyer's Bid Double Auction," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 351-374.
    27. Ariel Rubinstein & Asher Wolinsky, 1990. "Decentralized Trading, Strategic Behaviour and the Walrasian Outcome," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 63-78.
    28. Satterthwaite, Mark & Shneyerov, Artyom, 2008. "Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate," Games and Economic Behavior, Elsevier, vol. 63(2), pages 435-467, July.
    29. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-1063, September.
    30. Asher Wolinsky, 1988. "Dynamic Markets with Competitive Bidding," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 71-84.
    31. Leininger, W. & Linhart, P. B. & Radner, R., 1989. "Equilibria of the sealed-bid mechanism for bargaining with incomplete information," Journal of Economic Theory, Elsevier, vol. 48(1), pages 63-106, June.
    32. Mark A. Satterthwaite & Steven R. Williams, 2002. "The Optimality of a Simple Market Mechanism," Econometrica, Econometric Society, vol. 70(5), pages 1841-1863, September.
    33. Tymon Tatur, 2005. "On the Trade off Between Deficit and Inefficiency and the Double Auction with a Fixed Transaction Fee," Econometrica, Econometric Society, vol. 73(2), pages 517-570, March.
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    Cited by:

    1. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "Bilateral matching and bargaining with private information," Games and Economic Behavior, Elsevier, vol. 68(2), pages 748-762, March.
    2. Dipjyoti Majumdar & Artyom Shneyerov & Huan Xie, 2010. "How Optimism Leads to Price Discovery and Efficiency in a Dynamic Matching Market," Working Papers 10004, Concordia University, 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. Dipjyoti Majumdar & Artyom Shneyerov & Huan Xie, 2016. "An optimistic search equilibrium," Review of Economic Design, Springer;Society for Economic Design, vol. 20(2), pages 89-114, June.
    5. Lauermann, Stephan, 2012. "Asymmetric information in bilateral trade and in markets: An inversion result," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1969-1997.
    6. Satterthwaite, Mark A. & Williams, Steven R. & Zachariadis, Konstantinos E., 2014. "Optimality versus practicality in market design: A comparison of two double auctions," Games and Economic Behavior, Elsevier, vol. 86(C), pages 248-263.
    7. repec:eee:indorg:v:58:y:2018:i:c:p:214-235 is not listed on IDEAS
    8. Shneyerov, Artyom, 2014. "A Walrasian Rubinstein and Wolinsky model," Economics Letters, Elsevier, vol. 124(2), pages 314-317.
    9. Shneyerov, Artyom & Wong, Adam Chi Leung, 2011. "The role of private information in dynamic matching and bargaining: Can it be good for efficiency?," Economics Letters, Elsevier, vol. 112(1), pages 128-131, July.
    10. Klaus Kultti, 2010. "Inefficiency caused by random matching and heterogeneity," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 9(1), pages 19-28, April.

    More about this item

    Keywords

    Matching and Bargaining; Search; Double Auctions; Foundations for Perfect Competition; Rate of Convergence;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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