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Prudent Rationalizability in Generalized Extensive-form Games with Unawareness

Author

Listed:
  • Heifetz Aviad

    (The Economics and Management Department, The Open University of Israel, Ra'anana, Israel)

  • Meier Martin

    (Department of Economics, University of Bath, Bath, UK)

  • Schipper Burkhard C.

    (Department of Economics, University of California, Davis, USA)

Abstract

We define a cautious version of extensive-form rationalizability for generalized extensive-form games with unawareness that we call prudent rationalizability. It is an extensive-form analog of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:bejtec:v:21:y:2021:i:2:p:525-556:n:9
    DOI: 10.1515/bejte-2020-2013
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    Citations

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    Cited by:

    1. Martin Meier & Burkhard C. Schipper, 2022. "Conditional dominance in games with unawareness," Working Papers 351, University of California, Davis, Department of Economics.
    2. Alejandro Francetich & Burkhard Schipper, 2025. "Rationalizable Screening and Disclosure under Unawareness," Working Papers 374, University of California, Davis, Department of Economics.
    3. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    4. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    5. Ying Xue Li & Burkhard Schipper, 2025. "Disclosure under Unawareness: An Experiment," Working Papers 370, University of California, Davis, Department of Economics.
    6. Ki Vin Foo & Burkhard C. Schipper, 2025. "Kuhn's Theorem for Games of the Extensive Form with Unawareness," Working Papers 369, University of California, Davis, Department of Economics.
    7. Norimasa Kobayashi & Yasuo Sasaki, 2024. "Rationalizable self-confirming equilibrium in static games with unawareness," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 765-790, September.
    8. Auster, Sarah & Pavoni, Nicola, 2024. "Optimal delegation and information transmission under limited awareness," Theoretical Economics, Econometric Society, vol. 19(1), January.
    9. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.
    10. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    11. Alejandro Francetich & Burkhard C. Schipper, 2025. "Discrete Screening," Papers 2510.20921, arXiv.org.
    12. Gaia Belardinelli & Burkhard C. Schipper, 2023. "Implicit Knowledge in Unawareness Structures," Working Papers 360, University of California, Davis, Department of Economics.

    More about this item

    Keywords

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    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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