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Interactive Epistemology in Simple Dynamic Games with a Continuum of Strategies

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  • Pierpaolo Battigalli
  • Gabriele Beneduci
  • Pietro Tebaldi

Abstract

We extend the epistemic analysis of dynamic games of Battigalli and Siniscalchi (1999, 2002, 2007) from finite dynamic games to all simple games, that is, finite and infinite-horizon games with finite action sets at non-terminal stages and compact action sets at terminal stages. We prove a generalization of Lubin's (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. Keywords: Epistemic game theory, simple infinite dynamic game, strong belief, strong rationalizability.

Suggested Citation

  • Pierpaolo Battigalli & Gabriele Beneduci & Pietro Tebaldi, 2017. "Interactive Epistemology in Simple Dynamic Games with a Continuum of Strategies," Working Papers 602, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:602
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    Cited by:

    1. Pierfrancesco Guarino, 2025. "Topology-free type structures with conditioning events," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(4), pages 1107-1166, June.
    2. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    3. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    4. De Vito, Nicodemo, 2024. "Complete conditional type structures," Games and Economic Behavior, Elsevier, vol. 148(C), pages 427-448.
    5. 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.
    6. Pierpaolo Battigalli & Martin Dufwenberg, 2019. "Psychological Game Theory," Working Papers 646, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Pierpaolo Battigalli & Davide Bordoli, 2023. "Sophisticated Reasoning, Learning, and Equilibrium in Repeated Games with Imperfect Feedback," Working Papers 702, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. 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.
    9. 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.
    10. 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.

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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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