 In Aumann’s model, a description of each possible world \(\omega\) includes descriptions of the following: the game \(\Gamma\), the agent’s private information partitions, and the actions chosen by each agent at \(\omega\), and each agent’s prior probability distribution \(\mu_k(\cdot)\) over \(\Omega\). The basic idea is that conditional on \(\omega\), everyone knows everything that can be the object of uncertainty on the part of any agent, but in general, no agent necessarily knows which world \(\omega\) is the actual world. The agents can use their priors to calculate the probabilities that the various act combinations \(\boldsymbol{s} \in S\) are played. If the agents’ priors are such that for all \(i, j \in N,\) \(\mu_i(\omega) = 0\) iff \(\mu_j (\omega) = 0,\) then the agents’ priors are mutually absolutely continuous. If the agents’ priors all agree, that is, \(\mu_1 (\omega) = \ldots = \mu_n (\omega) = \mu(\omega)\) for each \(\omega \in \Omega\), then it is said that the common prior assumption, or CPA, is satisfied. If agents are following an Aumann correlated equilibrium \(f\) and the CPA is satisfied, then \(f\) is an objective Aumann correlated equilibrium. An Aumann correlated equilibrium is a Nash equilibrium if the CPA is satisfied and the agents’ distributions satisfy probabilistic  independence.[28]