Definition C.1 A pair of mixed strategies (X* Sn, Y* Sm) is a Nash equilibrium if EI(X, Y*) ≤ EI(X*, Y*) for every mixed X Sn and EII(X*, Y) ≤ EII(X*, Y*) for every mixed Y Sm. If (X*, Y*) is a Nash equilibrium we denote by vA = EI(X*, Y*) and vB = EII(X*, Y*) as the optimal payoff to each player. Written out with the matrices, (X*, Y*) is a Nash equilibrium if
, for every X Sn,
, for every Y Sm.
Definition C.2 A strategy X0 Sn is a best response strategy to a given strategy Y0 Sm for player II, if
Similarly, a strategy Y0 Sm is a