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Equilibrium selection in interdependent value auctions

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  • Bajoori, Elnaz
  • Vermeulen, Dries

Abstract

In second-price auctions with interdependent values, bidders do not necessarily have dominant strategies. Moreover, such auctions may have many equilibria. In order to rule out the less intuitive equilibria, we define the notion of distributional strictly perfect equilibrium (DSPE) for Bayesian games with infinite type and action spaces. This equilibrium is robust against arbitrary small perturbations of strategies. We apply DSPE to a class of symmetric second-price auctions with interdependent values. We show that the efficient equilibrium defined by Milgrom (1981) is a DSPE, while a class of less intuitive, inefficient, equilibria introduced by Birulin (2003) is not.

Suggested Citation

  • Bajoori, Elnaz & Vermeulen, Dries, 2019. "Equilibrium selection in interdependent value auctions," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 47-56.
    • Handle: RePEc:eee:matsoc:v:98:y:2019:i:c:p:47-56
    DOI: 10.1016/j.mathsocsci.2019.01.003
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    1. Meirowitz, Adam, 2003. "On the existence of equilibria to Bayesian games with non-finite type and action spaces," Economics Letters, Elsevier, vol. 78(2), pages 213-218, February.
    2. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    3. Kim, Taesung & Yannelis, Nicholas C., 1997. "Existence of Equilibrium in Bayesian Games with Infinitely Many Players," Journal of Economic Theory, Elsevier, vol. 77(2), pages 330-353, December.
    4. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2013. "Perfect equilibrium in games with compact action spaces," Games and Economic Behavior, Elsevier, vol. 82(C), pages 490-502.
    5. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    6. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    7. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-943, June.
    8. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2004. "Corrigendum to "Communication and Equilibrium in Discontinuous Games of Incomplete Information"," Econometrica, Econometric Society, vol. 72(6), pages 1927-1929, November.
    9. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
    10. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    11. Liu, Heng, 2014. "Equilibrium selection in common-value second-price auctions," Games and Economic Behavior, Elsevier, vol. 84(C), pages 1-6.
    12. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Oleksii Birulin, 2003. "Inefficient ex-post equilibria in efficient auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 675-683, October.
    14. Wolfstetter, Elmar, 1996. "Auctions: An Introduction," Journal of Economic Surveys, Wiley Blackwell, vol. 10(4), pages 367-420, December.
    15. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    16. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    17. Parreiras Sergio O., 2006. "Affiliated Common Value Auctions with Differential Information: The Two Bidder Case," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-21, December.
    18. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    19. Larson, Nathan, 2009. "Private value perturbations and informational advantage in common value auctions," Games and Economic Behavior, Elsevier, vol. 65(2), pages 430-460, March.
    20. 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.
    21. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2016. "Behavioral perfect equilibrium in Bayesian games," Games and Economic Behavior, Elsevier, vol. 98(C), pages 78-109.
    22. 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.
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