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From Common Knowledge of Rationality to Backward Induction

Author

Listed:
  • Antonio Quesada

    (Departamento de Fundamentos del Análisis Económico, Universidad de Murcia, 30100 Espinardo (Murcia), Spain)

Abstract

With the only assumption that a player knows the strategy he chooses, it is proved in a generalized version of Aumann's (1995) epistemic model that, in a generic game with perfect information, common knowledge of rationality is equivalent to common knowledge of the fact that the backward induction strategy profile is chosen. This result shows that Aumann's backward induction theorem holds without stipulating partition knowledge structures nor presuming that the epistemic operator defines knowledge in the strict sense.

Suggested Citation

  • Antonio Quesada, 2003. "From Common Knowledge of Rationality to Backward Induction," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 127-137.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:02:n:s0219198903000933
    DOI: 10.1142/S0219198903000933
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    Citations

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    Cited by:

    1. Perea ý Monsuwé, A., 2006. "Epistemic foundations for backward induction: an overview," Research Memorandum 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
    3. Graciela Kuechle, 2009. "What Happened To The Three‐Legged Centipede Game?," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 562-585, July.
    4. Giacomo Bonanno, 2018. "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 1001-1032, September.
    5. Perea, Andrés, 2008. "Minimal belief revision leads to backward induction," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 1-26, July.

    More about this item

    Keywords

    Aumann's knowledge system; backward induction; common knowledge of rationality; forward knowledge of rationality; generic perfect information game;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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