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Interactive epistemology in simple dynamic games with a continuum of strategies

Author

Listed:
  • Pierpaolo Battigalli

    (Bocconi University)

  • Pietro Tebaldi

    (University of Chicago)

Abstract

We extend the epistemic analysis of dynamic games of Battigalli and Siniscalchi (J Econ Theory 88:188–230, 1999, J Econ Theory 106:356–391, 2002, Res Econ 61:165–184, 2007) from finite dynamic games to all simple games, that is, finite and infinite-horizon multistage games with finite action sets at nonterminal stages and compact action sets at terminal stages. We prove a generalization of Lubin’s (Proc Am Math Soc 43:118–122, 1974) extension result to deal with conditional probability systems and strong belief. With this, we can provide a short proof of the following result: in every simple dynamic game, strong rationalizability characterizes the behavioral implications of rationality and common strong belief in rationality.

Suggested Citation

  • Pierpaolo Battigalli & Pietro Tebaldi, 2019. "Interactive epistemology in simple dynamic games with a continuum of strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 737-763, October.
    • Handle: RePEc:spr:joecth:v:68:y:2019:i:3:d:10.1007_s00199-018-1142-8
    DOI: 10.1007/s00199-018-1142-8
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    Cited by:

    1. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    2. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    3. Battigalli, Pierpaolo & Corrao, Roberto & Sanna, Federico, 2020. "Epistemic game theory without types structures: An application to psychological games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 28-57.
    4. Pierpaolo Battigalli & Martin Dufwenberg, 2022. "Belief-Dependent Motivations and Psychological Game Theory," Journal of Economic Literature, American Economic Association, vol. 60(3), pages 833-882, September.
    5. Shi-Woei Lin & Januardi Januardi, 2023. "Two-period pricing and utilization decisions in a dual-channel service-only supply chain," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 605-635, June.
    6. Pierpaolo Battigalli & Martin Dufwenberg, 2019. "Psychological Game Theory," Working Papers 646, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Shi‐Woei Lin & Januardi, 2023. "Two‐stage pricing of perishable food supply chain with quality‐keeping and waste reduction efforts," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(3), pages 1749-1766, April.

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    More about this item

    Keywords

    Epistemic game theory; Simple infinite dynamic game; Strong belief; Strong rationalizability;
    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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