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Approximate Robustness Of Equilibrium To Incomplete Information


  • Ori Haimanko

    () (BGU)

  • Atsushi Kajii

    (KIER, Kyoto University)


We relax the Kajii and Morris (1997a) notion of equilibrium ro- bustness by allowing approximate equilibria in close incomplete infor- mation games. The new notion is termed "approximate robustness". The approximately robust equilibrium correspondence turns out to be upper hemicontinuous, unlike the (exactly) robust equilibrium corre- spondence. As a corollary of the upper hemicontinuity, it is shown that approximately robust equilibria exist in all two-player zero-sum games and all two-player two-strategy games, whereas (exactly) robust equilibria may fail to exist for some games in these categories.

Suggested Citation

  • Ori Haimanko & Atsushi Kajii, 2012. "Approximate Robustness Of Equilibrium To Incomplete Information," Working Papers 1209, Ben-Gurion University of the Negev, Department of Economics.
  • Handle: RePEc:bgu:wpaper:1209

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    References listed on IDEAS

    1. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
    2. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    3. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    4. 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.
    5. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    6. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
    7. 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.
    8. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
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    Cited by:

    1. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
    2. Lu, Shih En, 2017. "Coordination-free equilibria in cheap talk games," Journal of Economic Theory, Elsevier, vol. 168(C), pages 177-208.
    3. Nora, Vladyslav & Uno, Hiroshi, 2014. "Saddle functions and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 866-877.

    More about this item


    incomplete information; robustness; Bayesian Nash equi- librium; ?-equilibrium; upper hemicontinuity; zero-sum games.;

    JEL classification:

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

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