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Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics

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  • Daisuke Oyama
  • Satoru Takahashi
  • Josef Hofbauer

Abstract

This paper studies equilibrium selection in supermodular games based on perfect foresight dynamics. A normal form game is played repeatedly in a large society of rational agents. There are frictions: opportunities to revise actions follow independent Poison processes. Each agent forms his belief about the future evolution of the action distribution in the society, and takes an action that maximizes his expected discounted payoff. A perfect foresight path is defined to be a feasible path of the action distribution along which every agent with a revision opportunity takes a best response to this path itself. A Nash equilibrium is said to be absorbing if any perfect foresight path converges to this equilibrium whenever the initial distribution is suffciently close to the equilibrium; a Nash equilibrium is said to be globally accessible if for each initial distribution, there exists a perfect foresight path converging to this equilibrium. By exploiting the monotone structure of the dynamics, the unique Nash equilibrium that is absorbing and globally accessible for any small degree of friction is identified for certain classes of supermodular games. For games with monotone potentials, the selection of the monotone potential maximizer is obtained. Complete characterizations for absorption and global accessibiltiy are given for binary supermodular games. An example demonstrates that unanimity games may have multiple globally accessible equilibria for a small friction.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 666156000000000420.

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Date of creation: 11 Dec 2003
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Handle: RePEc:cla:levrem:666156000000000420

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References

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  1. Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers 9802, University of Vienna, Department of Economics.
  2. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
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  20. Kaneda Mitsuhiro, 1995. "Industrialization under Perfect Foresight: A World Economy with a Continuum of Countries," Journal of Economic Theory, Elsevier, vol. 66(2), pages 437-462, August.
  21. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
  22. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  23. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
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Citations

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Cited by:
  1. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Departmental Working Papers 200807, Rutgers University, Department of Economics.
  2. 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.
  3. 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.
  4. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
  5. Fujishima, Shota, 2013. "Evolutionary implementation of optimal city size distributions," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 404-410.
  6. Oyama, Daisuke, 2006. "History versus Expectations in Economic Geography Reconsidered," MPRA Paper 9287, University Library of Munich, Germany.
  7. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
  8. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
  9. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
  10. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  11. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
  12. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
  13. 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.
  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. 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.

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