Extensions of solution concepts by means of muliplicative \(\epsilon\)-tax games (Q1091286)

Multiplicative \(\epsilon\)-tax games are introduced that are obtained from a game by imposing a tax on any proper coalition. The imposed tax is proportional to the relative reward to the coalition for its formation from the individuals. Of particular interest is the balanced (quasi- balanced, respectively) \(\epsilon\)-tax game for which the imposed tax is minimal. This least balanced (quasi-balanced) \(\epsilon\)-tax game is used to extend the concept of the core (\(\tau\)-value). In a similar way the stable core of a game is introduced by considering the least convex \(\epsilon\)-tax game.