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Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics

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  • Oyama, Daisuke
  • Takahashi, Satoru
  • Hofbauer, Josef

Abstract

This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are given by a normal form supermodular game. The stationary states of the dynamics correspond to the Nash equilibria of the stage game. It is shown that if the stage game has a monotone potential maximizer, then the corresponding stationary state is uniquely linearly absorbing and globally accessible for any small degree of friction. Among binary supermodular games, a simple example of a unanimity game with three players is provided where there are multiple globally accessible states for a small friction.

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File URL: http://mpra.ub.uni-muenchen.de/6721/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6721.

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Date of creation: 02 May 2003
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Handle: RePEc:pra:mprapa:6721

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Keywords: equilibrium selection; perfect foresight dynamics; supermodular game; strategic complementarity; stochastic dominance; potential; monotone potential;

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References

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  1. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  2. Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers 9802, University of Vienna, Department of Economics.
  3. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
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  7. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  8. 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.
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  10. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Selten,Reinhard, . "An axiomatic theory of a risk dominance measure for bipolar games with linear incentives," Discussion Paper Serie B 252, University of Bonn, Germany.
  12. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  13. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
  14. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
  15. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  16. 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.
  17. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  18. Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
  19. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  20. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  21. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
  22. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
  23. 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.
  24. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
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Citations

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Cited by:
  1. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
  2. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
  3. Okada, Daijiro & Tercieux, Olivier, 2012. "Log-linear dynamics and local potential," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1140-1164.
  4. Fujishima, Shota, 2013. "Evolutionary implementation of optimal city size distributions," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 404-410.
  5. 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.
  6. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  7. 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.
  8. 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.
  9. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
  10. Oyama, Daisuke, 2006. "History versus Expectations in Economic Geography Reconsidered," MPRA Paper 9287, University Library of Munich, Germany.
  11. 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.
  12. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
  13. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
  14. 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.
  15. 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.

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