 Probabilistic methods are widely employed to represent beliefs of agents within and outside of games, witness  Bayesian epistemology.  Typically, a probabilistic belief model consists of two components: a space of possible states that the agent’s beliefs range over, plus a quantitative probability function denoting how probable the agent judges different propositions or states to be. In qualitative logical models, on the other hand, agentive belief is represented in varying degree of detail. The coarsest approach only distinguishes states the agent considers possible from those she rules out. This is the perspective of standard epistemic-doxastic logics, such as multi-agent S5 and KD45 discussed in  Section 3.6.  More fine-grained perspectives are employed in the plausibility models of Boutilier (1994) and Baltag and Smets (2008), where the range of epistemic options is structured further by plausibility orderings encoding which options agents take to be less or more likely. See also Sections  3.6.4  and  4.2.