A noncooperative equilibrium of \(n\)-person game with fractional loss function (Q2753292)

This paper deals with the properties and existence of an equilibrium point for a noncooperative \(n\)-person game with fractional loss function (\(n\)-person fractional game). In many cases it is difficult to search directly for an equilibrium point of the \(n\) person fractional game. So the authors consider an \(n\)-person game with a loss function including the parameter function and study the properties and existence of an equilibrium point for the parametric \(n\)-person game. They show that under various conditions, an equilibrium point of the \(n\)-person parametric game with a special parameter function is an equilibrium point of the \(n\)-person fractional game. Finally it is shown that an equilibrium point of the game with a special parameter with respect to \(\varepsilon>0\) is an \(\varepsilon\)-equilibrium point of the fractional game.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].