IS BAYESIAN RATIONALITY COMPATIBLE WITH STRATEGIC RATIONALITY

In Bayesian game theory each player obeys the Savage axioms and there is common knowledge of this. We show that two of the less controversial axioms (ordering and dominance) are incompatible with some elementary game theoretic principles. We furthermore argue that our impossibility result is the consequence of a more fundamental conflict between the states of nature/acts framework of decision theory and the principles of strategic rationality.