Games with saddle points

Abstract

The theorems in [7] dealing with classes 1A, 2A and 2B do not depend on the strategy sets being disjoint, and include all Silverman games where at least one player has an optimal pure strategy, except the symmetric 1 by 1 case: THEOREM 2.1. In the symmetric Silverman game (S,T,ν), suppose that there is an element c in S such that c < Tci for all ci in S, and that S n (c,Tc) = Φ. Then pure strategy c is optimal. PROOF. Let A(x,y) be the payoff function. By symmetry the game value is 0. Since A(c,y) = 1,0 or ν according as y < c, y = c or y ≥ Tc, we have A(c, y) ≥ 0 for every y in S.