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Efficiency of Large Double Auctions

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  • Martin W Cripps
  • Jeroen M Swinkels

Abstract

We consider large double auctions with private values. Values need be neither symmetric nor independent. Multiple units may be owned or desired. Participation may be stochastic. We introduce a very mild notion of "a little independence." We prove that all nontrivial equilibria of auctions that satisfy this notion are asymptotically efficient. For any alpha>0, inefficiency disappears at rate (1/n)^(2 alpha). Copyright The Econometric Society 2006.
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  • Martin W Cripps & Jeroen M Swinkels, 2003. "Efficiency of Large Double Auctions," Levine's Working Paper Archive 666156000000000329, David K. Levine.
  • Handle: RePEc:cla:levarc:666156000000000329
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    References listed on IDEAS

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    1. 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.
    2. George J. Mailath & Andrew Postlewaite, 1990. "Asymmetric Information Bargaining Problems with Many Agents," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 351-367.
    3. Swinkels, Jeroen M, 2001. "Efficiency of Large Private Value Auctions," Econometrica, Econometric Society, vol. 69(1), pages 37-68, January.
    4. Milgrom, Paul R, 1979. "A Convergence Theorem for Competitive Bidding with Differential Information," Econometrica, Econometric Society, vol. 47(3), pages 679-688, May.
    5. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
    6. Robert Wilson, 1977. "A Bidding Model of Perfect Competition," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 511-518.
    7. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    8. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    9. Wolfgang Pesendorfer & Jeroen M. Swinkels, 1997. "The Loser's Curse and Information Aggregation in Common Value Auctions," Econometrica, Econometric Society, vol. 65(6), pages 1247-1282, November.
    10. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    11. Mark A. Satterthwaite & Steven R. Williams, 2002. "The Optimality of a Simple Market Mechanism," Econometrica, Econometric Society, vol. 70(5), pages 1841-1863, September.
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    Cited by:

    1. 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.
    2. Michael Peters & Sergei Severinov, 2008. "An ascending double auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 281-306, November.
    3. Gresik, Thomas A., 2011. "The effects of statistically dependent values on equilibrium strategies of bilateral k-double auctions," Games and Economic Behavior, Elsevier, vol. 72(1), pages 139-148, May.
    4. Piero Gottardi & Roberto Serrano, 2005. "Market Power And Information Revelation In Dynamic Trading," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1279-1317, December.
    5. Kovalenkov, Alexander & Vives, Xavier, 2014. "Competitive rational expectations equilibria without apology," Journal of Economic Theory, Elsevier, vol. 149(C), pages 211-235.
    6. Xavier Vives, 2011. "Strategic Supply Function Competition With Private Information," Econometrica, Econometric Society, vol. 79(6), pages 1919-1966, November.
    7. 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.
    8. Eaves, James & Williams, Jeffrey & Power, Gabriel J., 2016. "Do traders strategically time their pledges during real-world Walrasian auctions?," Journal of Banking & Finance, Elsevier, vol. 71(C), pages 109-118.
    9. Aaron Bodoh-Creed & Brent Hickman, 2016. "College Assignment as a Large Contest," Working Papers 2016-27, Becker Friedman Institute for Research In Economics.
    10. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    11. 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.
    12. McAdams, David, 2007. "On the failure of monotonicity in uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 137(1), pages 729-732, November.
    13. Shirata, Yasuhiro, 2017. "First price package auction with many traders," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 71-83.
    14. 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.
    15. Art Shneyerov, 2006. "Dynamic Matching with Two-sided Incomplete Information and Participation Costs," Theory workshop papers 815595000000000009, UCLA Department of Economics.
    16. Araujo, Luis & Camargo, Braz & Minetti, Raoul & Puzzello, Daniela, 2012. "The essentiality of money in environments with centralized trade," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 612-621.
    17. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    18. In-Koo Cho, 2004. "Monotonicity and Rationalizability in Large Uniform Price and Double Auctions," Theory workshop papers 658612000000000076, UCLA Department of Economics.
    19. Zhan, Wenjie & Friedman, Daniel, 2007. "Markups in double auction markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 2984-3005, September.
    20. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    21. Bodoh-Creed, Aaron, 2013. "Efficiency and information aggregation in large uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2436-2466.
    22. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2007. "The efficiency of competitive mechanisms under private information," Journal of Economic Theory, Elsevier, vol. 137(1), pages 383-403, November.
    23. repec:eee:gamebe:v:105:y:2017:i:c:p:59-83 is not listed on IDEAS
    24. Yoon, Kiho, 2008. "The participatory Vickrey-Clarke-Groves mechanism," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 324-336, February.
    25. 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.

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