A Two-person Zero-sum Game with Fractional Loss Function

In this paper, we investigate a two-person zero-sum game with fractional loss function, which we call the two-person zero-sum fractional game. We are interested in a game value and a saddle point of the two-person zero-sum game and observe that they exist under various conditions. But, in many cases, it seems to be difficult to search directly for a game value and a saddle point of the fractional game. Thus, we study the existence and the properties of a game value and a saddle point for the game with the loss function including a parameter, which we call the two-person zero-sum parametric game. We show that, under various conditions, a game value and a saddle point of the parametric game with a special parameter are those of the fractional game.