Iteration Schemes for Solving Rectangular Games

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Iteration Schemes for Solving Rectangular Games
Harold N Shapiro
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Thus we see that the j-th compo- nent never occurs as a maximum in the T steps preceding the n-th step. Let A^'^'^ be the matrix obtained from A by deleting the j-th row, and let U "^'(m) be the vector obtained from U(m) by deleting the j-th component. If we then apply the iteration scheme to A^'^', taking as initial vectors U "^ (n-T) and V(n-T), 8 we clearly have that the first T+1 vectors of the respective U -^ ' arid V series are U^ J^n-w), w = T, T-1, ... , 0 ; V(n-w), w = T, T-1, . . . , ...0 . Setting ''•(j)(n-w) = U^J^n-w) - [max U^ J^n-T)]l^_-L, (3. 6) V(n-w) = V(n-x, j) - [min V(n-T)]lg, we may apply the inductive hypothesis to obtain 1- 1 (3. 7) raaxU^-'^n) - min V(n)

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