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On Continuity of Robust Equilibria

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  • Ori Haimanko

    ()
    (Department of Economics, Ben-Gurion University)

  • Atsushi Kajii

    ()
    (Institute of Economic Research, Kyoto University)

Abstract

We relax the Kajii and Morris (1997a) notion of equilibrium ro- bustness by allowing approximate equilibria when information in a game becomes incomplete. The new notion is termed "approximate robustness". The approximately robust equilibrium correspondence turns out to be upper hemicontinuous, unlike the (exactly) robust equilibrium correspondence. Another distinction comes to light when we show that, as a corollary of upper hemicontinuity, approximately robust equilibria exist in all zero-sum games. Thus, although approx- imate robustness is only a small variation of the original notion, it is strictly weaker than the latter, and its adoption enriches the domain of games for which robust equilibria exist.

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Bibliographic Info

Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 818.

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Length: 15pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:kyo:wpaper:818

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Related research

Keywords: incomplete information; robustness; Bayesian Nash equi- librium; ε-equilibrium; upper hemicontinuity; zero-sum games;

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  1. Oyama, Daisuke & Takahashi, Satoru, 2011. "On the relationship between robustness to incomplete information and noise-independent selection in global games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 683-688.
  2. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, Econometric Society, vol. 69(5), pages 1373-80, September.
  3. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  4. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Levine's Working Paper Archive 506439000000000325, David K. Levine.
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