A Perturbation on Two-Person Zero-Sum Games
Yutaka Kimura, Yoichi Sawasaki, Kensuke Tanaka · Birkhäuser Boston eBooks · 2000
In this paper, we investigate a two-person zero-sum game perturbed by constrained functions. We need, under the various conditions, to show that there exists a saddle point for the game. But, in many cases, it seems to be difficult to search directly for a saddle point. If there exists a max-inf (or mini-sup ) of the perturbed game, the game has a saddle value and then, under some conditions, Player I (or Player II) has a weak optimal solution for the modified perturbed game with conjugate loss functions transformed by the upper envelope of the continuous affine functions from below. Moreover, if loss functions of the original game are convex and lower semicontinuous, using its biconjugete loss functions, we show that the original perturbed game has a saddle point.