Morris, P. Introduction to Game Theory. The decision taker will have preferences between choices. Preferences can be revealed through hypothetical gambles. Consistent preferences give unique utilities. A principle of decision making is that it should be based only on maximising the expected utility.
Bayesian methods use subjective probabilities.
We can order our beliefs in the likelihood of outcomes, and use these, like preferences, to give utilities. We can then use Bayes' Theorem to see how the beliefs become updated in the light of experimental evidence. Decisions made after strong experimental evidence should be relatively insensitive to our initial beliefs. Statistical decision theory concerns decisions made under uncertainty against an irrational opponent. Data are often collected to tell us about the opponent's choice.