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Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics

  • Daisuke Oyama
  • Satoru Takahashi
  • Josef Hofbauer

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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File URL: http://www.e.u-tokyo.ac.jp/~oyama/papers/pfd_supmod.031126.pdf
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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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  1. Kiminori Matsuyama, 1990. "Increasing Returns, Industrialization and Indeterminacy of Equilibrium," Discussion Papers 878, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
  3. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 1-23, March.
  4. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
  5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  6. J. Hofbauer, 1999. "The spatially dominant equilibrium of a game," Annals of Operations Research, Springer, vol. 89(0), pages 233-251, January.
  7. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  8. 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.
  9. Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Discussion Paper 1990-52, Tilburg University, Center for Economic Research.
  10. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  11. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  12. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  13. Selten, Reinhard, 1995. "An axiomatic theory of a risk dominance measure for bipolar games with linear incentives," Games and Economic Behavior, Elsevier, vol. 8(1), pages 213-263.
  14. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  15. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation for Research in Economics, Yale University.
  16. 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.
  17. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521578967, June.
  18. M. Kandori & R. Rob, 2010. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Levine's Working Paper Archive 502, David K. Levine.
  19. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  20. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  22. David M. Frankel & Stephen Morris & Ady Pauzner, 2001. "Equilibrium Selection in Global Games with Strategic Complementarities," Cowles Foundation Discussion Papers 1336, Cowles Foundation for Research in Economics, Yale University.
  23. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  24. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
  25. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521570176, June.
  26. 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.
  27. 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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