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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. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  2. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Departmental Working Papers, Rutgers University, Department of Economics 200807, Rutgers University, Department of Economics.
  3. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, Econometric Society, vol. 69(5), pages 1373-80, September.
  4. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany.
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  7. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
  8. 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, vol. 7(3), pages 251-267, 09.
  9. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
  10. David M. Frankel & Stephen Morris & Ady Pauzner, 2000. "Equilibrium Selection in Global Games with Strategic Complementarities," Econometric Society World Congress 2000 Contributed Papers 1490, Econometric Society.
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  12. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1283-1310, November.
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