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Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics

  • Daisuke Oyama
  • Satoru Takahashi
  • Josef Hofbauer

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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  1. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 617-50, May.
  2. 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.
  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.
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  5. Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers 9802, University of Vienna, Department of Economics.
  6. Akihiko Matsui & Daisuke Oyama, 2002. "Rationalizable Foresight Dynamics: Evolution and Rationalizability," Vienna Economics Papers 0302, University of Vienna, Department of Economics.
  7. 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.
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  18. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  19. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  20. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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  26. 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, June.
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