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Rationalizable Foresight Dynamics: Evolution and Rationalizability

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Author Info
Akihiko Matsui ()
Daisuke Oyama ()

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Abstract

This paper considers a adjustment process in a society with a continuum of agents. Each agent takes an action upon entry and commits to it until he is replaced by his successor at a stochastic point in time. In this society, rationality is common Knowledge, but beliefs may not be coordinated with each other. A rationalizable foresight path is a feasible path of action distribution along which every agent takes an action that maximizes his expected discounted payoff against another path which is in turn a rationalizable foresight path. An action distribution is accessible from another distribution under rationalizable foresight if there exists a rationalizable foresight path from the latter to the former. An action distribution is said to be a stable state under rationalizable foresight if no rationalizable foresight path departs from the distribution. A set of action distributions is said to be a stable set under rationalizable if it is closed under accessibility and any two elements of the set are mutually accessible. Stable sets under rationalizable foresight always exist. These concepts are compared with the corresponding concepts under perfect foresight. Every stabel state under rationalizable foresight is shown to be stabel under perfect foresight. But the converse is not true. An example is provided to illustrate that the stability under rationalizable foresight gives a sharper prediction than under perfect foresight.

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Paper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 0302.

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Date of creation: Sep 2002
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Handle: RePEc:vie:viennp:0302

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Find related papers by 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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
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  2. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  3. Burdzy, Krzysztof & Frankel, David M & Pauzner, Ady, 2001. "Fast Equilibrium Selection by Rational Players Living in a Changing World," Econometrica, Econometric Society, vol. 69(1), pages 163-89, January.
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  4. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
  5. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  6. Krugman, Paul, 1991. "History versus Expectations," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 651-67, May. [Downloadable!] (restricted)
  7. 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. [Downloadable!]
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  8. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-57, January. [Downloadable!] (restricted)
  9. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
  10. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December. [Downloadable!] (restricted)
  11. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May. [Downloadable!] (restricted)
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  1. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Levine's Bibliography 666156000000000420, UCLA Department of Economics. [Downloadable!]
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