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Rationalizable Foresight Dynamics: Evolution and Rationalizability

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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File URL: http://homepage.univie.ac.at/Papers.Econ/RePEc/vie/viennp/vie0302.pdf
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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
Contact details of provider: Web page: http://www.univie.ac.at/vwl

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  1. 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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  12. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  13. Itzhak Gilboa & Akihiko Matsui, 1990. "A Model of Random Matching," Discussion Papers 887, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
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  16. Josef HOFBAUER & Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers vie9802, University of Vienna, Department of Economics.
  17. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-57, January.
  18. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  19. Alos-Ferrer, C., 1998. "Dynamic Systems with a Continuum of Randomly Matched Agents," Papers 9801, Washington St. Louis - School of Business and Political Economy.
  20. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  21. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  22. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  23. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
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