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Adjustment Dynamics and Rational Play in Games

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  • J. Swinkels

Abstract

When a strategic situation arises repeatedly, the possibility arises that equilibrium predictions can be justified by a dynamic adjustment process. We examine myopic adjustment dynamics, a class that includes replicator dynamics from evolutionary game theory, simple models of imitation, models of experimentation and adjustment, and some simple learning dynamics. We present a series of theorems showing conditions under which behavior that is asymptotically stable under some such dynamic is strategically stable (Kohlberg and Mertens [1986]). This behavior is thus as if the agents in the economy satisfied the extremely stringent assumptions that game theory traditionally makes about rationality and beliefs.
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  • J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  • Handle: RePEc:cla:levarc:456
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    3. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    4. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
    5. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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