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On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games

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  • Philip J. Reny

Abstract

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure strategy equilibria in Bayesian games. We allow action spaces to be compact locally-complete metrizable semilattices and type spaces to be partially ordered probability spaces. Our proof is based upon contractibility rather than convexity of best reply sets. Several examples illustrate the scope of the result, including new applications to multi-unit auctions with risk-averse bidders.
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Suggested Citation

  • Philip J. Reny, 2005. "On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games," Levine's Working Paper Archive 784828000000000067, David K. Levine.
  • Handle: RePEc:cla:levarc:784828000000000067
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    References listed on IDEAS

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    1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    2. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    3. Philip J. Reny & Shmuel Zamir, 2004. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Econometric Society, vol. 72(4), pages 1105-1125, July.
    4. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1039-1056.
    5. 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.
    6. 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.
    7. 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.
    8. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    10. David McAdams, 2004. "Monotone Equilibrium in Multi-Unit Auctions," Econometric Society 2004 North American Summer Meetings 211, Econometric Society.
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