The equivalence of bayes and causal rationality in games

• Published in: Theory and decision 2006-08, Vol.61 (1), p.1-19
• Main Author: BOARD, Oliver
• Format: Article
• Language: English
• Subjects: Applied sciences; Bayesian analysis; Decision analysis; Decision theory; Decision theory. Utility theory; Equilibrium; Exact sciences and technology; Expected utility; Game theory; Games of strategy; Impeachment; Mathematical methods; Operational research and scientific management; Operational research. Management science; Probability; Probability distribution; Rationality; Scandals; Studies
• ISSN: 0040-5833; 1573-7187
• DOI: 10.1007/s11238-006-7868-y

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. [PUBLICATION ABSTRACT]