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On the Value of Some Infinite Matrix Games

Departamento de Métodos Cuantitativos para a Economía, Facultade de Ciencias Económicas e Empresariais, Avda. Xóan XXIII, s/n, 15704-Santiago de Compostela, Spain
eclmn1{at}usc.es

It is shown that a zero-sum two-person noncooperative game A defined by a bounded infinite matrix in which each row converges to the same real number ß and each column to the same real number has a value V(A) if and only if ß, in which case V(A) ß. For any game defined by a bounded infinite matrix A ; (a_ij), a necessary condition for V(A) to exist is that inf_j lim inf_ia_ij sup_i lim sup_ja_ij.

Key Words: Two-person games; infinite matrix games; value of a game
History: Received: December 17, 1999; revision received: July 10, 2000;