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Isotone Equilibrium in Games of Incomplete Information

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  • McAdams, David

Abstract

An isotone pure strategy equilibrium exists in any game of incomplete information in which (1) each player i's action set is a finite sublattice of multi-dimensional Euclidean space, (2) types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "non-primitive conditions" whenever others adopt isotone pure strategies: (3) single-crossing in own action and type and (4) quasisupermodularity in own action. Similarly, given that (134) and (2') types are multi-dimensional (with atoms) an isotone mixed strategy equilibrium exists. Conditions (34) are satisfied in supermodular and log-supermodular games given affiliated types, and in games with independent types in which each player's ex post payoff satisfies (a) supermodularity in own action and (b) non-decreasing differences in own action and type. These results also extend to games with a continuum action space when each player's ex post payoff is also continuous in his and others' actions.

Suggested Citation

  • McAdams, David, 2002. "Isotone Equilibrium in Games of Incomplete Information," Working papers 4248-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  • Handle: RePEc:mit:sloanp:1568
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    File URL: http://hdl.handle.net/1721.1/1568
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    References listed on IDEAS

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    1. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-943, June.
    2. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    4. Athey, S, 1996. "Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity," Working papers 96-22, Massachusetts Institute of Technology (MIT), Department of Economics.
    5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    6. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    Cited by:

    1. 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.
    2. Chade, Hector, 2006. "Matching with noise and the acceptance curse," Journal of Economic Theory, Elsevier, vol. 129(1), pages 81-113, July.

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    Keywords

    Equilibrium; Isotone;

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