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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.

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  • 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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    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. Sergey K. Aityan, 2012. "Price-Value Potential for Near-Perfectly Competitive Markets," American Journal of Economics and Business Administration, Science Publications, vol. 3(4), pages 623-635, February.
    4. Andras Niedermayer & Artyom Shneyerov, 2014. "For‐Profit Search Platforms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(3), pages 765-789, August.
    5. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
    6. 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.
    7. 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.
    8. 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.
    9. Shneyerov, Artyom & Wong, Adam C.L., 2020. "Price discovery in a matching and bargaining market with aggregate uncertainty," Games and Economic Behavior, Elsevier, vol. 124(C), pages 183-206.
    10. 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.
    11. Michael Choi & Guillaume Rocheteau, 2024. "Information acquisition and price discrimination in dynamic, decentralized markets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 53, pages 1-46, July.
    12. Niedermayer, Andras & Wang, Chengsi, 2018. "A search model of rental markets: Who should pay the commission?," International Journal of Industrial Organization, Elsevier, vol. 58(C), pages 214-235.
    13. Shneyerov, Artyom, 2014. "A Walrasian Rubinstein and Wolinsky model," Economics Letters, Elsevier, vol. 124(2), pages 314-317.
    14. 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.

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    More about this item

    Keywords

    Matching and Bargaining; Search; Double Auctions; Foundations for Perfect Competition; Rate of Convergence;
    All these keywords.

    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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