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Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition by E. N. Barron

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Appendix C: Two-Person Nonzero Sum Games

Definition C.1    A pair of mixed strategies (X* images Sn, Y* images Sm) is a Nash equilibrium if EI(X, Y*) ≤ EI(X*, Y*) for every mixed X images Sn and EII(X*, Y) ≤ EII(X*, Y*) for every mixed Y images 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

images,    for every X images Sn,

images,    for every Y images Sm.

Definition C.2    A strategy X0 images Sn is a best response strategy to a given strategy Y0 Sm for player II, if

Similarly, a strategy Y0 Sm is a

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