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Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games

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  • Zambrano Eduardo

    (University of Notre Dame)

Abstract

When evaluating the rationality of a player in a game one has to examine counterfactuals such as "what would happen if the player were to do what he does not do?" In this paper I develop a model of a normal form game where counterfactuals of this sort are evaluated as in the philosophical literature (cf. Lewis, 1973; Stalnaker, 1968). According to this method one evaluates a statement like ``what would the player believe if he were to do what he does not do'' at the world that is closest to the actual world where the hypothetical deviation occurs. I show that in this model common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to follow from common knowledge of rationality. These assumptions suggest that rationalizability may not rely on weaker assumptions about belief consistency than Nash equilibrium.

Suggested Citation

  • Zambrano Eduardo, 2004. "Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-25, November.
    • Handle: RePEc:bpj:bejtec:v:topics.4:y:2004:i:1:n:8
    DOI: 10.2202/1534-598X.1020
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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. Oliver Board, 2006. "The Equivalence of Bayes and Causal Rationality in Games," Theory and Decision, Springer, vol. 61(1), pages 1-19, August.
    3. Kaushik Basu & Leonardo Becchetti & Luca Stanca, 2011. "Experiments with the Traveler’s Dilemma: welfare, strategic choice and implicit collusion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 575-595, October.
    4. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
    5. Kaushik Basu, 2016. "Beyond the Invisible Hand: Groundwork for a New Economics," Economics Books, Princeton University Press, edition 1, number 9299.
    6. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    7. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 6, University of California, Davis, Department of Economics.
    8. 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.

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