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Rationalizable Foresight Dynamics: Evolution and Rationalizability

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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.

Suggested Citation

  • Akihiko Matsui & Daisuke Oyama, 2002. "Rationalizable Foresight Dynamics: Evolution and Rationalizability," Vienna Economics Papers 0302, University of Vienna, Department of Economics.
  • Handle: RePEc:vie:viennp:0302
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    Cited by:

    1. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    2. Antoci, Angelo & Gay, Antonio & Landi, Massimiliano & Sacco, Pier Luigi, 2008. "Global analysis of an expectations augmented evolutionary dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3877-3894, December.
    3. George W. Evans & Roger Guesnerie & Bruce Mcgough, 2010. "Eductive stability in real business cycle models," PSE Working Papers halshs-00565011, HAL.
    4. Angelo Antoci & Massimiliano Landi, 2006. "Expectations, Animal Spirits, and Evolutionary Dynamics," Macroeconomics Working Papers 22057, East Asian Bureau of Economic Research.
    5. Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
    6. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2011. "Perfect foresight dynamics in binary supermodular games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(3), pages 251-267, September.
    7. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.

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    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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