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Existence and Convergence of Equilibria in the Buyer's Bid Double Auction

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  • Steven R. Williams

Abstract

This paper concerns a Bayesian game model of the Buyer's Bid Double Auction, which is a procedure for organizing trade that selects a market-clearing price from a list of offers/bids. Strategic misrepresentation by traders may make the outcome of trade inefficient. Satterthwaite and Williams (1989) showed that misrepresentation and inefficiency quickly converge to zero as the number of traders on each side of the market increases. This is extended here to cases in which the number of buyers may differ from the number of sellers. The existence of equilibria in a generic instance of the model is also proven.

Suggested Citation

  • Steven R. Williams, 1991. "Existence and Convergence of Equilibria in the Buyer's Bid Double Auction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 351-374.
    • Handle: RePEc:oup:restud:v:58:y:1991:i:2:p:351-374.
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    Citations

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    Cited by:

    1. Zacharias, Eleftherios & Williams, Steven R., 2001. "Ex Post Efficiency in the Buyer's Bid Double Auction When Demand Can Be Arbitrarily Larger Than Supply," Journal of Economic Theory, Elsevier, vol. 97(1), pages 175-190, March.
    2. Song, Yangwei, 2023. "Approximate Bayesian implementation and exact maxmin implementation: An equivalence," Games and Economic Behavior, Elsevier, vol. 139(C), pages 56-87.
    3. Sarkar, Soumendu, 2018. "Convergence of VCG mechanism to ex-post budget balance in a model of land acquisition," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 37-46.
    4. Ohad Kadan, 2004. "Equilibrium in the Two Player, k-Double Auction with Affiliate Private Values," Working Papers 2004.12, Fondazione Eni Enrico Mattei.
    5. Claudia Neri, 2015. "Quantal response equilibrium in a double auction," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 79-90, April.
    6. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "The rate of convergence to perfect competition of matching and bargaining mechanisms," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1164-1187, May.
    7. Kadan, Ohad, 2006. "So who gains from a small tick size?," Journal of Financial Intermediation, Elsevier, vol. 15(1), pages 32-66, January.
    8. Kadan, Ohad, 2007. "Equilibrium in the two-player, k-double auction with affiliated private values," Journal of Economic Theory, Elsevier, vol. 135(1), pages 495-513, July.
    9. Fudenberg, Drew & Mobius, Markus & Szeidl, Adam, 2007. "Existence of equilibrium in large double auctions," Journal of Economic Theory, Elsevier, vol. 133(1), pages 550-567, March.
    10. Art Shneyerov, 2006. "Dynamic Matching with Two-sided Incomplete Information and Participation Costs," Theory workshop papers 815595000000000009, UCLA Department of Economics.
    11. Azrieli Yaron & Levin Dan, 2012. "Dominance Solvability of Large k-Price Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-11, May.
    12. Satterthwaite, Mark A. & Williams, Steven R. & Zachariadis, Konstantinos E., 2022. "Price discovery using a double auction," Games and Economic Behavior, Elsevier, vol. 131(C), pages 57-83.
    13. Ángel Hernando Veciana, 2001. "Competition Among Auctioneers," Working Papers. Serie AD 2001-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    14. Moreira, Humberto Ataíde & Araújo, Aloísio Pessoa de & Castro Filho, Luciano I. de, 2004. "Pure strategy equilibria of multidimensional and non-monotonic auctions," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 571, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    15. Araujo, Aloisio & de Castro, Luciano I., 2009. "Pure strategy equilibria of single and double auctions with interdependent values," Games and Economic Behavior, Elsevier, vol. 65(1), pages 25-48, January.
    16. Hu Lu & Jacques Robert, 1997. "Optimal Trading Mechanisms with Ex Ante Unidentified Traders," CIRANO Working Papers 97s-29, CIRANO.
    17. Mark A. Satterthwaite & Steven R. Williams, 1991. "The Double Auction Market: Institutions," Discussion Papers 971, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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