We provide a new characterization of the weighted Banzhaf value derived from some postulates in a recent paper by Radzik, Nowak and Driessen [7]. Our approach owes much to the work by Lehrer [4] on the classical Banzhaf value based on the idea of amalgamation of pairs of players and an induction...

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values....

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values....

The family of weighted Shapley values for cooperative n-person transferable utility games is studied. We assume first that the weights of the players are given exogenously and provide two axiomatic characterizations of the corresponding weighted Shapley value. Our first characterization is based...

The paper provides two characterizations of probabilistic values satisfying three classical axioms (linearity, dummy player and any of three "symmetry" axioms) together with a new probabilistic-efficiency axiom. This new axiom requires that players of a game allocate the total amount of their...

This paper gives a full characterization of matrices with rows and columns having properties closely related to the (quasi-) convexity-concavity of functions. The matrix games described by such payoff matrices well approximate continuous games on the unit square with payoff functions F (x, y)...

In this paper we study a family of efficient, symmetric and linear values for TU-games, described by some formula generalizing the Shapley value. These values appear to have surprising properties described in terms of the axioms: Fair treatment, monotonicity and two types of acceptability. The...

This paper gives wide characterization of n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity properties. The characterization is done in terms of the existence of two-point-strategy Nash equilibria, that is equilibria...

This paper considers two-person non-zero-sum games on the unit square with payoff functions having a new property called poor convexity. This property describes “something between” the classical convexity and quasi-convexity. It is proved that various types of such games have Nash equilibria...