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Discovery and Equilibrium in Games with Unawareness

Author

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  • Burkhard C. Schipper

    (Department of Economics, University of California Davis)

Abstract
Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are ``self-destroying'' as a player's representation of the game may change after playing it once. We define discovery processes where at each state there is an extensive-form game with unawareness that together with the players' play determines the transition to possibly another extensive-form game with unawareness in which players are now aware of actions that they have discovered. A discovery process is rationalizable if players play extensive-form rationalizable strategies in each game with unawareness. We show that for any game with unawareness there is a rationalizable discovery process that leads to a self-confirming game that possesses a self-confirming equilibrium in extensive-form rationalizable strategies. This notion of equilibrium can be interpreted as steady-state of both a discovery and learning process.

Suggested Citation

  • Burkhard C. Schipper, 2021. "Discovery and Equilibrium in Games with Unawareness," Working Papers 340, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:340
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    Citations

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    Cited by:

    1. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    2. 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.
    3. Gaia Belardinelli & Burkhard C. Schipper, 2023. "Implicit Knowledge in Unawareness Structures," Working Papers 360, University of California, Davis, Department of Economics.
    4. Heifetz Aviad & Meier Martin & Schipper Burkhard C., 2021. "Prudent Rationalizability in Generalized Extensive-form Games with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 525-556, June.
    5. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    6. Martin Meier & Burkhard C. Schipper, 2022. "Conditional dominance in games with unawareness," Working Papers 351, University of California, Davis, Department of Economics.
    7. Perea, Andrés, 2022. "Common belief in rationality in games with unawareness," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 11-30.

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    More about this item

    Keywords

    Self-confirming equilibrium; conjectural equilibrium; extensive-form rationalizability; unawareness; extensive-form games; equilibrium; learning; discovery;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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