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Kuhn’s theorem for games of the extensive form with unawareness

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  • Foo, Ki Vin
  • Schipper, Burkhard C.

Abstract

We extend Kuhn’s Theorem to games of the extensive form with unawareness. We prove that if a game of the extensive form with unawareness has perfect recall, then for each mixed strategy there is an equivalent behavior strategy. We show that the converse does not hold under unawareness without restricting the evolution of the player’s awareness to constant awareness along paths of play. Both directions of Kuhn’s Theorem for games of the extensive form with unawareness require a condition complementary to perfect recall that rules out falsely believing in some events when the player is unaware of the actual past events.

Suggested Citation

  • Foo, Ki Vin & Schipper, Burkhard C., 2026. "Kuhn’s theorem for games of the extensive form with unawareness," Games and Economic Behavior, Elsevier, vol. 159(C), pages 564-583.
    • Handle: RePEc:eee:gamebe:v:159:y:2026:i:c:p:564-583
    DOI: 10.1016/j.geb.2026.07.007
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    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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