The above models use a “crisp” notion of uncertainty, i.e., for each agent and state \(w\), any other state \(v\in W\) either is or is not possible at/more plausible than \(w\). However, there is an extensive body of literature focused on graded, or quantitative, models of uncertainty (Huber 2009; Halpern 2003). For instance, in the Game Theory literature it is standard to represent the players’ beliefs by probabilities (Aumann 1999b; Harsanyi 1967–68). The idea is simple: replace the plausibility orderings with probability distributions: