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Hypothetical knowledge and counterfactual reasoning

Author

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  • Joseph Y. Halpern

    (Dept. Computer Science, Cornell University, Ithaca, NY 14853, USA)

Abstract

Samet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information structures used to model it bear some resemblance to the way philosophers have used conditional logic to model counterfactuals, hypothetical knowledge cannot be reduced to conditional logic together with epistemic logic. Here it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator ">" and the knowledge operator "K", provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed.

Suggested Citation

  • Joseph Y. Halpern, 1999. "Hypothetical knowledge and counterfactual reasoning," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 315-330.
    • Handle: RePEc:spr:jogath:v:28:y:1999:i:3:p:315-330
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    Citations

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    Cited by:

    1. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    2. Jong Jae Lee, 2018. "Formalization of information: knowledge and belief," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 1007-1022, December.
    3. Graciela Kuechle, 2009. "What Happened To The Three‐Legged Centipede Game?," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 562-585, July.
    4. Thorsten Clausing, 2003. "Doxastic Conditions for Backward Induction," Theory and Decision, Springer, vol. 54(4), pages 315-336, June.
    5. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    6. Di Tillio, Alfredo & Halpern, Joseph Y. & Samet, Dov, 2014. "Conditional belief types," Games and Economic Behavior, Elsevier, vol. 87(C), pages 253-268.
    7. Joseph Y. Halpern & Rafael Pass, 2018. "Game theory with translucent players," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 949-976, September.
    8. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
    9. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    10. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    11. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.

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