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Epistemic Game Theory without Types Structures: An Application to Psychological Games

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  • Pierpaolo Battigalli
  • Roberto Corrao
  • Federico Sanna

Abstract

We consider multi-stage games with incomplete information and observable actions, and we analyze strategic reasoning by means of epistemic events within a "total" state space made of all the profiles of behaviors (paths of play) and possibly incoherent infinite hierarchies of conditional beliefs. Thus, we do not rely on types structures, or similar epistemic models. Subjective rationality is defined by the conjunction of coherence of belief hierarchies, rational planning, and consistency between plan and on-path behavior. Since consistent hierarchies uniquely induce beliefs about behavior and belief hierarchies of others, we can define rationality and common strong belief in rationality, and analyze their behavioral and low-order beliefs implications, which are characterized by strong rationalizability. Our approach allows to extend known techniques to the epistemic analysis of psychological games where the utilities of outcomes depend on beliefs of order k or lower. This covers almost all applications of psychological game theory. JEL Classification Numbers: C72, C73, D82. Keywords: Epistemic game theory, hierarchies of beliefs, consistency, subjective rationality, strong rationalizability, psychological games.

Suggested Citation

  • 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.
    • Handle: RePEc:igi:igierp:641
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    Cited by:

    1. Attanasi, Giuseppe & Rimbaud, Claire & Villeval, Marie Claire, 2019. "Embezzlement and guilt aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 409-429.
    2. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    3. Pierpaolo Battigalli & Nicolò Generoso, 2021. "Information Flows and Memory in Games," Working Papers 678, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Pierpaolo Battigalli & Martin Dufwenberg, 2019. "Psychological Game Theory," Working Papers 646, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    5. Jagau, Stephan & Perea, Andrés, 2022. "Common belief in rationality in psychological games," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    6. 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.
    7. Pierpaolo Battigalli & Roberto Corrao & Martin Dufwenberg, 2019. "Incorporating Belief-Dependent Motivation in Games Abstract:Psychological game theory (PGT), introduced by Geanakoplos, Pearce & Stacchetti (1989) and significantly generalized by Battigalli & Dufwenb," Working Papers 642, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. Battigalli, Pierpaolo & Corrao, Roberto & Dufwenberg, Martin, 2019. "Incorporating belief-dependent motivation in games," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 185-218.

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    More about this item

    Keywords

    epistemic game theory; hierarchies of beliefs; consistency; subjective rationality; strong rationalizability; psychological games.;
    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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