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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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    References listed on IDEAS

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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 & 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.
    3. Pierpaolo Battigalli & Martin Dufwenberg, 2020. "Belief-Dependent Motivations and Psychological Game Theory," CESifo Working Paper Series 8285, CESifo.
    4. Pierpaolo Battigalli & Nicodemo De Vito, 2018. "Beliefs, Plans, and Perceived Intentions in Dynamic Games," Working Papers 629, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    5. Pierpaolo Battigalli & Martin Dufwenberg, 2019. "Psychological Game Theory," Working Papers 646, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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    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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