Decisions in games: why there should be a special exemption from Bayesian rationality

I examine the Bayesian foundations of game theory and advance three main theses: (i) that if Bayesianism is to be used in game theory, then simpler versions of it are methodologically preferable to the more sophisticated ones; (ii) that it is dubious whether the Savage (or Anscombe and Aumann) axiom system can yield an axiomatic justification for Bayesianism in game theory; and (iii) that there exist other foundational frameworks for games which are at least as convincing as the Bayesian one.