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# Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics

## Author

Listed:
• 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)

## Suggested Citation

• Josef Hofbauer & Daisuke Oyama & Satoru Takahashi, 2004. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Econometric Society 2004 North American Winter Meetings 339, Econometric Society.
• Handle: RePEc:ecm:nawm04:339
as

File URL: http://www.e.u-tokyo.ac.jp/~oyama/papers/supmod.html
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## References listed on IDEAS

as
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### Keywords

equilibrium selection; perfect foresight dynamics; supermodular games; potential;
All these keywords.

### JEL classification:

• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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