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Basic solutions of discrete games. (English) Zbl 0041.25403

Contrib. Theory of Games, Ann. Math. Stud. 24, 27-35 (1950).
The authors show that the basic solutions of a game can be found systematically by a finite, though prolonged and inconvenient process. It consists of considering all square \(r\times r\) submatrices of the pay-off matrix for \(r=1,2,\dots\), finding simple solutions for them (if they exist), and ascertaining whether these two vectors, with added zeros for the components which do not appear in the submatrix, are also a solution of the whole game. This process leads always to a solution at some value of \(r\). (If it does so for \(r=1\), then the matrix has a saddle point and the solution consists of two pure strategies). The authors give also an explicit formula for the value of the game and for the solution vectors, dependent on the elements on the adjoint matrix to the \(r\times r\) matrix, which produces them.
Reviewer: Stefan Vajda

MSC:

91A05 2-person games

Keywords:

discrete games

Citations:

Zbl 0041.25302