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The Equivalence of Bayes and Causal Rationality in Games

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  • Oliver Board

Abstract

In a seminal paper, Aumann (1987, Econometrica 55, 1–18) showed how the choices of rational players could be analyzed in a unified state space framework. His innovation was to include the choices of the players in the description of the states, thus abolishing Savage’s (1954, The Foundations of Statistics. Wiley, New York) distinction between acts and consequences. But this simplification comes at a price: Aumann’s notion of Bayes rationality does not allow players to evaluate what would happen were they to deviate from their actual choices. We show how the addition of a causal structure to the framework enables us to analyze such counterfactual statements, and use it to introduce a notion of causal rationality. Under a plausible causal independence condition, the two notions are shown to be equivalent. If we are prepared to accept this condition we can dispense with the causal apparatus and retain Aumann’s original framework. Copyright Springer 2006

Suggested Citation

  • Oliver Board, 2006. "The Equivalence of Bayes and Causal Rationality in Games," Theory and Decision, Springer, vol. 61(1), pages 1-19, August.
    • Handle: RePEc:kap:theord:v:61:y:2006:i:1:p:1-19
    DOI: 10.1007/s11238-006-7868-y
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    References listed on IDEAS

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    Cited by:

    1. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 6, University of California, Davis, Department of Economics.
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    3. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    4. Cyril Hédoin, 2016. "Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals," Games, MDPI, vol. 7(4), pages 1-17, November.
    5. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.

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