 To preserve the symmetry between the players that characterizes the ordinary PD, we may wish to modify the asynchronous game. Let us take extended PD to be played in stages. First each player chooses a first move \((\bC \text{ or } \bD)\) and a second move \((\bCu, \bDu, \bI, \text{ or } \bO)\). Next a referee determines who moves first, giving each player an equal chance. Finally the outcome is computed in the appropriate way. For example, suppose Row plays \((\bD, \bO)\) (meaning that he will defect if he moves first and do the opposite of his opponent if he moves second) and Column plays \((\bC, \bDu)\). Then Row will get \(P\) if he goes first and \(T\) if he goes second, which implies that his expected payoff is \(\tfrac{1}{2}(P+T)\). Column will get \(S\) if she goes first and \(P\) if she goes second, giving her an expected payoff of \(\tfrac{1}{2}(P+S)\). It is straightforward, but tedious, to calculate the entire eight by eight payoff matrix. After doing so, the reader may observe that, like the farmer's dilemma, the symmetric form of the extended PD is an equilibrium PD, but not a dominance PD. The sole nash equilibrium occurs when both players adopt the strategy \((\bD, \bDu)\), thereby achieving the inferior payoffs of \((P,P)\).