We relate some minimax functions of matrices to some spectral functions of matrices. If A is a nonnegative n X n matrix, v(A) is the gametheoretic value of A, and p(A) is the spectral radius of A, then v(A) < p(A). Necessary and sufficient conditions for v(A) = p(A) are given. It follows that if A is nonnegative and irreducible and n > 1, then v(A) < p(A… (More)