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An epistemic analysis of the Harsanyi transformation

Author

Listed:
  • Harborne W. Stuart Jr.

    (Columbia Business School, Uris Hall 420, 3022 Broadway, New York, NY 10027)

  • Hong Hu

    (46 Qin Lao Hu Tong, Beijing, China 100009)

Abstract

Harsanyi (1967-68) proposed a method for transforming uncertainty over the strategy sets of players into uncertainty over their payoffs. The transformation appears to rely on an assumption that the players are rational, or, indeed, that they are rational and that there is common belief of rationality. Such an assumption would be awkward from the perspective of the epistemic program, which is often interested in the implications of irrationality or a lack of common belief of rationality. This paper shows that without common belief of rationality, such implications are not necessarily maintained under a Harsanyi transformation. The paper then shows how, with the belief-system model of Aumann and Brandenburger (1995), such implications can be maintained in the absence of common belief of rationality.

Suggested Citation

  • Harborne W. Stuart Jr. & Hong Hu, 2002. "An epistemic analysis of the Harsanyi transformation," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 517-525.
    • Handle: RePEc:spr:jogath:v:30:y:2002:i:4:p:517-525
    Note: Received: December 2000/Revised: February 2002
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    Cited by:

    1. Yasuo Sasaki, 2016. "An Equivalence Result on the Reduction of Games with Unawareness," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-27, September.
    2. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    3. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    4. Bahel, Eric & Haller, Hans, 2013. "Cycles with undistinguished actions and extended Rock–Paper–Scissors games," Economics Letters, Elsevier, vol. 120(3), pages 588-591.
    5. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 465-492, April.
    6. Wen Tian & Qin Fang & Xuefang Zhou & Fan Yang, 2022. "The Method of Trajectory Selection Based on Bayesian Game Model," Sustainability, MDPI, vol. 14(18), pages 1-17, September.
    7. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    8. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.

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