In decision theory, the decision-making units are individuals with preferences over the possible consequences of their actions. Since the consequence of a given action depend on the state of the environment, the decision-maker’s beliefs about the state of the environment are crucial to assess the rationality of a particular decision. So, the formal description of a decision problem includes the possible outcomes and states of the environment, the decision maker’s preferences over these outcome, and a description of the decision maker’s beliefs about the state of nature (i.e., the decision maker’s doxastic state). A decision-theoretic choice rule can be used to make recommendations to the decision maker about what she should choose (or to predict what the decision-maker will choose). A standard example of a choice rule is maximization of (subjective) expected utility, underlying the Bayesian view of rationality. It presupposes that the decision maker’s preferences and beliefs can be represented by numerical utilities and probabilities,  respectively.[2]  (We postpone the formal representation of this, and the other choice rules such as weak and strict dominance, until we have presented the formal models of beliefs in games in Section 2.)