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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, fi nite and infi nite-horizon games with finite action sets at non-terminal stages and compact action sets at terminal stages. We prove a generalization of Lubins (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 in finite 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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    1. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    4. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
    5. Giuseppe Attanasi & Pierpaolo Battigalli & Rosemarie Nagel, 2013. "Disclosure of Belief-Dependent Preferences in a Trust Game," Working Papers 506, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Battigalli, Pierpaolo & Charness, Gary & Dufwenberg, Martin, 2013. "Deception: The role of guilt," Journal of Economic Behavior & Organization, Elsevier, vol. 93(C), pages 227-232.
    7. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    8. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    9. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
    10. Battigalli Pierpaolo & Prestipino Andrea, 2013. "Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 1-53, May.
    11. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    12. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
    13. Pierpaolo Battigalli, 2006. "Rationalization In Signaling Games: Theory And Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 67-93.
    14. Harrington, Joseph E., 2017. "A theory of collusion with partial mutual understanding," Research in Economics, Elsevier, vol. 71(1), pages 140-158.
    15. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    16. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
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    Cited by:

    1. 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.
    2. Pierpaolo Battigalli & Martin Dufwenberg, 2019. "Psychological Game Theory," Working Papers 646, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Pierpaolo Battigalli & Roberto Corrao & Federico Sanna, 2019. "Epistemic Game Theory without Types Structures: An Application to Psychological Games," Working Papers 641, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

    More about this item

    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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