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Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics

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  • Josef Hofbauer
  • Daisuke Oyama
  • Satoru Takahashi

Abstract

The paper studies equilibrium selection in supermodular games based on a class of perfect foresight dynamics, introduced by Matsui and Matsuyama (JET 1995) and further developed by Hofbauer and Sorger (JET 1999, IGTR 2002) and Oyama (JET 2002). A normal form game is played repeatedly in a large society of rational agents. There are frictions: opportunities to revise actions follow independent Poisson processes. Each agent forms his belief about the future evolution of action distribution in the society to take an action that maximizes his expected discounted payoff. A perfect foresight path is defined to be a feasible path of action distribution to which every agent at revision opportunity takes a best response. A Nash equilibrium is said to be globally accessible if for each initial condition, there exists a perfect foresight path converging to this equilibrium; a Nash equilibrium is said to be absorbing if there exists no perfect foresight path escaping from a neighborhood of this equilibrium. By appealing to the monotonicity of the correspondence whose fixed points are perfect foresight paths, a unique Nash equilibrium that is absorbing and globally accessible for small frictions is identified for certain classes of supermodular games. Our equilibrium selection results are compared with those obtained via different approaches, such as the one that examines the robustness of equilibria to incomplete information (Kajii and Morris, Econometrica 1997)

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 339.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:339

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Keywords: equilibrium selection; perfect foresight dynamics; supermodular games; potential;

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References

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  1. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  2. Akihiko Matsui & Daisuke Oyama, 2002. "Rationalizable Foresight Dynamics: Evolution and Rationalizability," Vienna Economics Papers 0302, University of Vienna, Department of Economics.
  3. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers 11920, Iowa State University, Department of Economics.
  4. Matsuyama, Kiminori, 1992. "The market size, entrepreneurship, and the big push," Journal of the Japanese and International Economies, Elsevier, vol. 6(4), pages 347-364, December.
  5. Josef HOFBAUER & Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers vie9802, University of Vienna, Department of Economics.
  6. Akihiko Matsui & Kiminori Matsuyama, 1991. "An Approach to Equilibrium Selection," Discussion Papers 1065, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  19. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
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Citations

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Cited by:
  1. 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.
  2. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
  3. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
  4. Oyama, Daisuke, 2006. "Agglomeration under Forward-Looking Expectations: Potentials and Global Stability," MPRA Paper 15239, University Library of Munich, Germany.
  5. Calcagno, Riccardo & Sugaya, Takuo & Kamada, Yuichiro & Lovo, Stefano, 2014. "Asynchronicity and coordination in common and opposing interest games," Theoretical Economics, Econometric Society, vol. 9(2), May.
  6. Okada, Daijiro & Tercieux, Olivier, 2012. "Log-linear dynamics and local potential," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1140-1164.
  7. 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.
  8. Oyama, Daisuke, 2006. "History versus Expectations in Economic Geography Reconsidered," MPRA Paper 9287, University Library of Munich, Germany.
  9. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
  10. J. Durieu & P. Solal & O. Tercieux, 2011. "Adaptive learning and p-best response sets," International Journal of Game Theory, Springer, vol. 40(4), pages 735-747, November.
  11. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  12. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany.
  13. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
  14. Takahashi, Satoru, 2008. "The number of pure Nash equilibria in a random game with nondecreasing best responses," Games and Economic Behavior, Elsevier, vol. 63(1), pages 328-340, May.
  15. Fujishima, Shota, 2013. "Evolutionary implementation of optimal city size distributions," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 404-410.

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