It is well known since Owen (Management Science, 1968) that the weights in the weighted Shapley value cannot be interpreted as a measure of power (i.e. of the ability to bargain) of the players. This paper proposes a new weight scheme for the Shapley value. Weights in this framework have to be...

We propose a variation of the Hart and Mas-Colell non-cooperative bargaining model for n-person games in coalitional form. This strategic game implements, in the limit, a new NTU-value for the class of monotonic games. This value coincides with the Maschler and Owen value for hyperplane games,...

Using techniques from the non-standard analysis, a non-standard analogue of the Aumann-Shapley random order value of non-atomic games is provided. The paper introduces the notion of effectively ergodic family of automorphism groups. It is shown that for a wide class of games, the non-standard...

This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's marginal contribution during the bargaining process. The...

A formal scheme is described for coalition formation in a game of interconnected participants with monotonic utility functions. Special coalitions are studied which have an advantage over the rest in the sense of higher utility for each of the participants taken separately.

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a...

An expanded model of value in cooperative games is presented in which value has either a linear or a proportional mode, and NTU value has either an input or an output basis. In TU games, the modes correspond to the Shapley (1953) and proportional (Feldman (1999) and Ortmann (2000)) values. In...