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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 6 ()
Pages: 683-688

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Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:683-688

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Web page: http://www.elsevier.com/locate/jmateco

Related research

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

References

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  1. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  2. Galesloot, Bob M. & Goyal, Sanjeev, 1997. "Costs of flexibility and equilibrium selection," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 28(3), pages 249-264, October.
  3. Christian Basteck & Tijmen R. Daniëls & Frank Heinemann, 2010. "Characterising Equilibrium Selection in Global Games with Strategic Complementarities," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Carlsson, H. & Damme, E.E.C. van, 1990. "Global games and equilibrium selection," Discussion Paper, Tilburg University, Center for Economic Research 1990-52, Tilburg University, Center for Economic Research.
  5. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1394, Cowles Foundation for Research in Economics, Yale University.
  6. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers, Iowa State University, Department of Economics 11920, Iowa State University, Department of Economics.
  7. Christian Basteck & Tijmen R. Daniëls, 2010. "Every Symmetric 3 x 3 Global Game of Strategic Complementarities Is Noise Independent," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany.
  9. UNO, Hiroshi, 2011. "Nested potentials and robust equilibria," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, Econometric Society, vol. 69(5), pages 1373-80, September.
  11. Goyal, Sanjeev & Janssen, Maarten C. W., 1997. "Non-Exclusive Conventions and Social Coordination," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 34-57, November.
  12. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, American Economic Association, vol. 79(3), pages 385-91, June.
  13. Honda, Jun, 2011. "Noise-independent selection in global games and monotone potential maximizer: A symmetric 3×3 example," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 47(6), pages 663-669.
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Cited by:
  1. Ori Haimanko & Atsushi Kajii, 2012. "Approximate Robustness Of Equilibrium To Incomplete Information," Working Papers, Ben-Gurion University of the Negev, Department of Economics 1209, Ben-Gurion University of the Negev, Department of Economics.
  2. Oury, Marion, 2013. "Noise-independent selection in multidimensional global games," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(6), pages 2638-2665.
  3. Marion Oury, 2012. "Noise-Independent Selection in Multidimensional Global Games," THEMA Working Papers, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise 2012-28, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  4. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 47(6), pages 749-754.
  5. Christian Basteck & Tijmen R. Daniëls & Frank Heinemann, 2010. "Characterising Equilibrium Selection in Global Games with Strategic Complementarities," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Honda, Jun, 2011. "Noise-independent selection in global games and monotone potential maximizer: A symmetric 3×3 example," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 47(6), pages 663-669.
  7. Ori Haimanko & Atsushi Kajii, 2012. "On Continuity of Robust Equilibria," KIER Working Papers, Kyoto University, Institute of Economic Research 818, Kyoto University, Institute of Economic Research.

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