A two-person zero-sum game with fractional loss function

A two-person zero-sum game with fractional loss function

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Article ID: iaor2001940
Country: Japan
Volume: 43
Issue: 1
Start Page Number: 209
End Page Number: 218
Publication Date: Mar 2000
Journal: Journal of the Operations Research Society of Japan
Authors: , ,
Keywords: programming: fractional
Abstract:

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.

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