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Every Symmetric 3 x 3 Global Game of Strategic Complementarities Is Noise Independent

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  • Christian Basteck
  • Tijmen R. Daniëls

Abstract

We prove that the global game selection in all 3 x 3 payoff-symmetric supermodular games is independent of the noise structure. As far as we know, all other proofs of noise independence of such games rely on the existence of a so-called monotone potential (MP) maximiser. Our result is more general, since some 3 x 3 symmetric supermodular games do not admit an MP maximiser. Moreover, a corollary is that noise independence does not imply the existence of an MP maximiser.

Suggested Citation

  • Christian Basteck & Tijmen R. Daniëls, 2010. "Every Symmetric 3 x 3 Global Game of Strategic Complementarities Is Noise Independent," SFB 649 Discussion Papers SFB649DP2010-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2010-061
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    Cited by:

    1. 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.
    2. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    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. 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.
    5. Oury, Marion, 2013. "Noise-independent selection in multidimensional global games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2638-2665.
    6. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    7. 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.
    8. Stephen Morris & Daisuke Oyama & Satoru Takahashi, 2023. "Strict robustness to incomplete information," The Japanese Economic Review, Springer, vol. 74(3), pages 357-376, July.
    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. 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.
    11. 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.
    12. 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.

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    Keywords

    global games; noise independence;

    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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