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Expected payoffs: example Player 2 C(1/3) R(2/3) T(3/4) 2 3 1 1 Player 1 M(O 4 0 4 2 3 B(1/4) 4 5 1 0 7 Mixed strategies:p1=(3/4,0,%);p2=(0,1/3,2/3) Player 1 >EU1(T,p2)=3×(1/3)+1×(2/3)=5/3,EU1(M,p2)=0×(1/3)+2×(23)=4/3 EU1(B,p2)=5×(1/3)+0×(2/3)=5/3.v/(D1,P2)=5/3 Player 2: EU2(L,p1)=2×(3/4)+4×(14)=5/2,EU2(C,p)=3×(3/4)+3×(4)=5/2, EU2(R,p1)=1×(3/4)+7×(1/4)=5/2.v(1,P2)=5/2Expected payoffs: example Player 2 L (0) C (1/3) R (2/3) Player 1 T (3/4) 0 , 2 3 , 3 1 , 1 M (0) 4 , 0 0 , 4 2 , 3 B (1/4) 3 , 4 5 , 1 0 , 7 15 ◼ Mixed strategies: p1=( 3/4, 0, ¼ ); p2=( 0, 1/3, 2/3 ). ◼ Player 1: ➢ EU1 (T, p2 )=3(1/3)+1(2/3)=5/3, EU1 (M, p2 )=0(1/3)+2(2/3)=4/3 EU1 (B, p2 )=5(1/3)+0(2/3)=5/3. v1 (p1 , p2 ) = 5/3 ◼ Player 2: ➢ EU2 (L, p1 )=2(3/4)+4(1/4)=5/2, EU2 (C, p1 )=3(3/4)+3(1/4)=5/2, EU2 (R, p1 )=1(3/4)+7(1/4)=5/2. v1 (p1 , p2 ) = 5/2
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