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Common belief of rationality in games of perfect information

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  • Samet, Dov

Abstract

Aumann (1995) showed that for games with perfect information common knowledge of substantive rationality implies backward induction. Substantive rationality is defined in epistemic terms, that is, in terms of knowledge. We show that when substantive rationality is defined in doxastic terms, that is, in terms of belief, then common belief of substantive rationality implies backward induction. Aumann (1998) showed that material rationality implies backward induction in the centipede game. This result does not hold when rationality is defined doxastically. However, if beliefs are interpersonally consistent then common belief of material rationality in the centipede game implies common belief of backward induction.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 79 (2013)
Issue (Month): C ()
Pages: 192-200

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Handle: RePEc:eee:gamebe:v:79:y:2013:i:c:p:192-200

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Perfect information; Common belief; Rationality; Backward induction; Centipede game;

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  1. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  2. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  3. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
  4. Pierpaolo Battigali & Giacomo Bonanno, . "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Department of Economics 98-14, California Davis - Department of Economics.
  5. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
  6. Klaus Nehring & Giacomo Bonanno, 2003. "Assessing The Truth Axiom Under Incomplete Information," Working Papers 973, University of California, Davis, Department of Economics.
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Cited by:
  1. Zuazo Gain, Peio, 2014. "Uncertain Information Structures and Backward Induction," IKERLANAK Ikerlanak;2014-79, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

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