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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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    1. UNO, Hiroshi, 2011. "Nested potentials and robust equilibria," LIDAM Discussion Papers CORE 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.
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    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. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
    10. Basteck, Christian & Daniëls, Tijmen R., 2010. "Every symmetric 3 x 3 global game of strategic complementarities is noise independent," SFB 649 Discussion Papers 2010-061, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    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. 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.
    16. 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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    Cited by:

    1. Jun Honda, 2018. "Games with the total bandwagon property meet the Quint–Shubik conjecture," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 893-912, September.
    2. Ori Haimanko & Atsushi Kajii, 2012. "On Continuity of Robust Equilibria," KIER Working Papers 818, Kyoto University, Institute of Economic Research.
    3. Rodrigo Harrison & Pedro Jara‐Moroni, 2021. "Global Games With Strategic Substitutes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(1), pages 141-173, February.
    4. 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.
    5. Stephen Morris & Daisuke Oyama & Satoru Takahashi, 2023. "Strict robustness to incomplete information," The Japanese Economic Review, Springer, vol. 74(3), pages 357-376, July.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    11. Daisuke Oyama & Satoru Takahashi, 2020. "Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games," Econometrica, Econometric Society, vol. 88(2), pages 693-726, March.
    12. 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.
    13. 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.
    14. Satoru Takahashi, 2020. "Non-equivalence between all and canonical elaborations," The Japanese Economic Review, Springer, vol. 71(1), pages 43-57, January.
    15. Oury, Marion, 2013. "Noise-independent selection in multidimensional global games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2638-2665.
    16. 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.

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    More about this item

    Keywords

    Equilibrium selection; Supermodular game; Incomplete information; Robustness; Contagion; Global game;
    All these keywords.

    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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