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On Continuity of Robust Equilibria

Author

Listed:
  • 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.

Suggested Citation

  • Ori Haimanko & Atsushi Kajii, 2012. "On Continuity of Robust Equilibria," KIER Working Papers 818, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:818
    as

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP818.pdf
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    References listed on IDEAS

    as
    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, vol. 69(5), pages 1373-1380, September.
    3. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    4. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    incomplete information; robustness; Bayesian Nash equi- librium; ε-equilibrium; upper hemicontinuity; zero-sum games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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