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Monotone and local potential maximizers in symmetric 3x3 supermodular games

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  • Daisuke Oyama

    ()
    (Graduate School of Economics, Hitotsubashi University)

  • Satoru Takahashi

    ()
    (Department of Economics, Princeton University)

Abstract

Generalized notions of potential maximizer, monotone potential maximizer (MP-maximizer) and local potential maximizer (LP-maximizer), are studied. It is known that 2x2 coordination games generically have a potential maximizer, while symmetric 4x4 supermodular games may have no MP- or LP-maximizer. This note considers the case inbetween, namely the class of (generic) symmetric 3x3 supermodular coordination games. This class of games are shown to always have a unique MP-maximizer, and its complete characterization is given. A nondegenerate example demonstrates that own-action quasiconcave supermodular games may have more than one LP-maximizers.

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Bibliographic Info

Article provided by AccessEcon in its journal Economics Bulletin.

Volume (Year): 29 (2009)
Issue (Month): 3 ()
Pages: 2123-2135

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Handle: RePEc:ebl:ecbull:eb-09-00406

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Keywords: equilibrium selection; supermodular game; monotone potential; MP-maximizer; local potential; LP-maximizer;

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  1. Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," MPRA Paper 6721, University Library of Munich, Germany.
  2. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1283-1310, November.
  3. 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.
  4. David M. Frankel & Stephen Morris & Ady Pauzner, 2001. "Equilibrium Selection in Global Games with Strategic Complementarities," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1336, Cowles Foundation for Research in Economics, Yale University.
  5. Josef HOFBAUER & Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers, University of Vienna, Department of Economics vie9802, University of Vienna, Department of Economics.
  6. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2011. "Perfect foresight dynamics in binary supermodular games," International Journal of Economic Theory, The International Society for Economic Theory, The International Society for Economic Theory, vol. 7(3), pages 251-267, 09.
  7. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Economics Working Papers, Institute for Advanced Study, School of Social Science 0085, Institute for Advanced Study, School of Social Science.
  8. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany.
  9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 124-143, May.
  10. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, Elsevier, vol. 65(2), pages 415-434, April.
  11. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, Econometric Society, vol. 69(5), pages 1373-80, September.
  12. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, Elsevier, vol. 5(3), pages 387-424, July.
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