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Kuhn's Theorem for Games of the Extensive Form with Unawareness

Author

Listed:
  • Ki Vin Foo
  • Burkhard C. Schipper

    (Department of Economics, University of California Davis)

Abstract

We extend Kuhn's Theorem to games of the extensive form with unawareness. This extension is not obvious: First, games of the extensive form with non-trivial unawareness involve a forest of partially ordered game trees rather than just one game tree. An information set at a node in one tree may consist of nodes in a less expressive tree. Consequently, perfect recall takes a more complicated form as players may also become aware of new actions during the play. Second, strategies can only be partially an object of ex ante choice in games with unawareness. Finally, nodes that a player may expect to reach with a strategy profile may not be the nodes that actually occur with this strategy profile, requiring us to define appropriate notions of equivalence of strategies. We show if a game of the extensive form with unawareness has perfect recall, then for each mixed strategy there is an equivalent behavior strategy but the converse does not hold under unawareness.

Suggested Citation

  • 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.
  • Handle: RePEc:cda:wpaper:369
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    File URL: https://repec.dss.ucdavis.edu/files/e9htj0b0w86b327cj08hvsqdcu81/unawkuhn9.pdf
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    References listed on IDEAS

    as
    1. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, Decembrie.
    2. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    3. Dubey, Pradeep & Kaneko, Mamoru, 1985. "Information patterns and Nash equilibria in extensive games -- II," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 247-262, December.
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    13. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    14. 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.
    15. Schipper, Burkhard C. & Woo, Hee Yeul, 2019. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Quarterly Journal of Political Science, now publishers, vol. 14(1), pages 41-88, January.
    16. Leandro Rêgo & Joseph Halpern, 2012. "Generalized solution concepts in games with possibly unaware players," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 131-155, February.
    17. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 145, University of California, Davis, Department of Economics.
    18. Wichardt, Philipp C., 2008. "Existence of Nash equilibria in finite extensive form games with imperfect recall: A counterexample," Games and Economic Behavior, Elsevier, vol. 63(1), pages 366-369, May.
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    More about this item

    Keywords

    Perfect recall; mixed strategy; behavior strategy; unawareness;
    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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