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Belief change, Rationality, and Strategic Reasoning in Sequential Games

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  • Pierpaolo Battigalli
  • Emiliano Catonini
  • Julien Manili

Abstract

A central aspect of strategic reasoning in sequential games consists in anticipating how co-players would react to information about past play, which in turn depends on how co-players update and revise their beliefs. Several notions of belief system have been used to model how players’ beliefs change as they obtain new information, some imposing considerably more discipline than others on how beliefs at different information sets are related. We highlight the differences between these notions of belief system in terms of introspection about one’s own conditional beliefs, but we also show that such differences do not affect the essential aspects of rational planning and the behavioral implications of strategic reasoning, as captured by rationalizability.

Suggested Citation

  • Pierpaolo Battigalli & Emiliano Catonini & Julien Manili, 2021. "Belief change, Rationality, and Strategic Reasoning in Sequential Games," Working Papers 679, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:679
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    Citations

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    Cited by:

    1. Emiliano Catonini, 2022. "A Dutch book argument for belief consistency," Papers 2202.10121, arXiv.org.
    2. Shuige Liu, 2024. "Level-$k$ Reasoning, Cognitive Hierarchy, and Rationalizability," Papers 2404.19623, arXiv.org, revised May 2024.
    3. Pierpaolo Battigalli & Emiliano Catonini, 2022. "The Epistemic Spirit of Divinity," Working Papers 681, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Catonini, Emiliano & Penta, Antonio, 2022. "Backward Induction Reasoning beyond Backward Induction," TSE Working Papers 22-1298, Toulouse School of Economics (TSE).
    5. Emiliano Catonini & Antonio Penta, 2022. "Backward Induction Reasoning beyond Backward Induction," Working Papers 1315, Barcelona School of Economics.
    6. Battigalli, P. & Catonini, E. & Manili, J., 2023. "Belief change, rationality, and strategic reasoning in sequential games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 527-551.
    7. Emiliano Cantonini & Antonio Penta, 2022. "Backward induction reasoning beyond backward induction," Economics Working Papers 1815, Department of Economics and Business, Universitat Pompeu Fabra.

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    More about this item

    Keywords

    Sequential games; chain rule; partial introspection; rational planning; rationalizability. JEL Codes: C72; C73; D83.;
    All these keywords.

    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
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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