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On the relationship between robustness to incomplete information and noise-independent selection in global games

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  • Oyama, Daisuke
  • Takahashi, Satoru

Abstract

This note demonstrates that a symmetric 3×3 supermodular game may fail to have any equilibrium robust to incomplete information. Since the global game solution in symmetric 3×3 supermodular games is known to be independent of the noise structure, this result implies that a noise-independent selection in global games may not be a robust equilibrium. Our proof reveals that the assumption in global games that the noise errors are independent of the state imposes a non-trivial restriction on incomplete information perturbations.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:683-688
    DOI: 10.1016/j.jmateco.2011.09.001
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    References listed on IDEAS

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    1. UNO, Hiroshi, 2011. "Nested potentials and robust equilibria," CORE Discussion Papers 2011009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. Honda, Jun, 2011. "Noise-independent selection in global games and monotone potential maximizer: A symmetric 3×3 example," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 663-669.
    5. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    6. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
    7. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    8. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    9. Basteck, Christian & Daniëls, Tijmen R. & Heinemann, Frank, 2013. "Characterising equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2620-2637.
    10. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
    11. Galesloot, Bob M. & Goyal, Sanjeev, 1997. "Costs of flexibility and equilibrium selection," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 249-264, October.
    12. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    13. Goyal, Sanjeev & Janssen, Maarten C. W., 1997. "Non-Exclusive Conventions and Social Coordination," Journal of Economic Theory, Elsevier, vol. 77(1), pages 34-57, November.
    14. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
    15. Oyama, Daisuke & Takahashi, Satoru, 2015. "Contagion and uninvadability in local interaction games: The bilingual game and general supermodular games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 100-127.
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    Citations

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    Cited by:

    1. Ori Haimanko & Atsushi Kajii, 2012. "On Continuity of Robust Equilibria," KIER Working Papers 818, Kyoto University, Institute of Economic Research.
    2. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
    3. Harrison, Rodrigo & Jara-Moroni, Pedro, 2015. "A dominance solvable global game with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 1-11.
    4. Ori Haimanko & Atsushi Kajii, 2016. "Approximate robustness of equilibrium to incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 839-857, November.
    5. Marion Oury, 2012. "Noise-Independent Selection in Multidimensional Global Games," THEMA Working Papers 2012-28, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. Honda, Jun, 2011. "Noise-independent selection in global games and monotone potential maximizer: A symmetric 3×3 example," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 663-669.
    7. Oyama, Daisuke & Takahashi, Satoru, 2015. "Contagion and uninvadability in local interaction games: The bilingual game and general supermodular games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 100-127.
    8. Basteck, Christian & Daniëls, Tijmen R. & Heinemann, Frank, 2013. "Characterising equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2620-2637.
    9. Grafenhofer, Dominik & Kuhle, Wolfgang, 2016. "Observing each other’s observations in a Bayesian coordination game," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 10-17.
    10. Oury, Marion, 2013. "Noise-independent selection in multidimensional global games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2638-2665.

    More about this item

    Keywords

    Equilibrium selection; Supermodular game; Incomplete information; Robustness; Contagion; Global game;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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