 The agents are at Aumann correlated equilibrium if at each possible world \(\omega \in \Omega\), no agent will want to deviate from his recommended strategy, given that the others follow their recommended strategies. Hence, Aumann correlated equilibrium uniquely specifies the strategy of each agent, by explicitly introducing a space of possible worlds to which agents can correlate their acts. The deviations \(g_i\) are required to be functions of \(f_i\), that is, compositions of some other function with \(f_i\), because \(i\) is informed of \(f_i (\omega)\) only, and so can only distinguish between the possible worlds of \(\Omega\) that are distinguished by \(f_i\). As noted already, the primary difference between Aumann’s notion of correlated equilibrium and the endogenous correlated equilibrium is that in Aumann’s correlated equilibrium, the agents correlate their strategies to some event \(\omega \in \Omega\) that is external to the game. One way to view this difference is that agents who correlate their strategies exogenously can calculate their expected utilities conditional on their own strategies.