Second of all, when there are more than two players, the above results only hold if players can believe that the choices of their opponents are correlated (Bradenburger &amp; Dekel 1987; Brandenburger &amp; Friedenberg 2008). The following example from Brandenburger &amp; Friedenberg (2008) illustrates this point. Consider the following three person game where Ann’s strategies are \(S_A=\{u,d\}\), Bob’s strategies are \(S_B=\{l,r\}\) and Charles’ strategies are \(S_C=\{x,y,z\}\) and their respective  preferences for each outcome are given in the corresponding cell: