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Every symmetric 3×3 global game of strategic complementarities has noise-independent selection

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  • Basteck, Christian
  • Daniëls, Tijmen R.

Abstract

We prove that the global game selection in all 3×3 payoff-symmetric supermodular games is independent of the noise structure. As far as we know, all other proofs of noise-independent selection in such games rely on the existence of a so-called monotone potential (MP) maximiser. Our result is more general, since some 3×3 symmetric supermodular games do not admit an MP maximiser. As a corollary, noise-independent selection does not imply the existence of an MP maximiser, nor the existence of an equilibrium robust to incomplete information.

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  • 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.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:749-754
    DOI: 10.1016/j.jmateco.2011.10.004
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    1. 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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    13. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
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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. 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.
    3. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    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. 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.
    6. 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.
    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. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    10. Stephen Morris & Daisuke Oyama & Satoru Takahashi, 2023. "Strict robustness to incomplete information," The Japanese Economic Review, Springer, vol. 74(3), pages 357-376, July.

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