 Now let us formally introduce a system of the agents’ beliefs into this framework. \(\Delta_k (S_{-k})\) denotes the set of probability distributions over the measurable space \((S_{-k}, \mathfrak{F}_k)\), where \(\mathfrak{F}_k\) denotes the Boolean algebra generated by the strategy combinations \(S_{-k}\). Each agent \(k\) has a probability distribution \(\mu_k \in \Delta_k(S_{-k})\), and this distribution determines the (Savage) expected utilities for each of \(k\)’s possible acts: