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Regularity and Stability in Monotone Bayesian Games

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  • Alan Beggs
  • A.W. Beggs

Abstract

This paper defines regular and weakly regular equilibria for monotone Bayesian games with one-dimensional actions and types. It proves an index theorem and provides applications to uniqueness of equilibrium. It also provides analyses of stability with respect to perturbations and dynamic stability.

Suggested Citation

  • Alan Beggs & A.W. Beggs, 2011. "Regularity and Stability in Monotone Bayesian Games," Economics Series Working Papers 587, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:587
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    References listed on IDEAS

    as
    1. Beggs Alan, 2009. "Learning in Bayesian Games with Binary Actions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-30, September.
    2. Faruk Gül & David Pearce & Ennio Stacchetti, 1993. "A Bound on the Proportion of Pure Strategy Equilibria in Generic Games," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 548-552, August.
    3. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
    4. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    5. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    6. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, vol. 45(2), pages 369-374, November.
    7. Mason, Robin & Valentinyi, Ã kos, 2007. "The existence and uniqueness of monotone pure strategy equilibrium in Bayesian games," Discussion Paper Series In Economics And Econometrics 710, Economics Division, School of Social Sciences, University of Southampton.
    8. 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.
    9. Athey, S., 1996. "Characterizing Properties of Stochastic Objective Functions," Working papers 96-1, Massachusetts Institute of Technology (MIT), Department of Economics.
    10. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    11. 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.
    12. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, September.
    13. Kehoe, Timothy J, 1980. "An Index Theorem for General Equilibrium Models with Production," Econometrica, Econometric Society, vol. 48(5), pages 1211-1232, July.
    14. Mclennan, A., 1989. "Selected Topics In The Theory Of Fixed Points," Papers 251, Minnesota - Center for Economic Research.
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    16. Shannon, Chris, 1994. "Regular nonsmooth equations," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 147-165, March.
    17. Alp Simsek & Asuman Ozdaglar & Daron Acemoglu, 2008. "Local Indices for Degenerate Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 291-300, May.
    18. Mason, Robin & Valentinyi, Ã kos, 2007. "The existence and uniqueness of monotone pure strategy equilibrium in Bayesian games," Discussion Paper Series In Economics And Econometrics 0710, Economics Division, School of Social Sciences, University of Southampton.
    19. Hellwig, Christian, 2002. "Public Information, Private Information, and the Multiplicity of Equilibria in Coordination Games," Journal of Economic Theory, Elsevier, vol. 107(2), pages 191-222, December.
    20. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    21. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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    Cited by:

    1. Beggs, A.W., 2015. "Regularity and robustness in monotone Bayesian games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 145-158.
    2. Alan Beggs, 2015. "Learning in Monotone Bayesian Games," Economics Series Working Papers 737, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    Bayesian games; Monotone strategies; Index theory; Stability; Uniequeness; Regularity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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