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...

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...

It is now almost a common truth that society needs to avoid environment contamination or damage become significant for nature protection programs of the government and wild life preservation efforts. A possible outcome of such efforts might occasionally be a voluntary solution, which results...

In this paper the random order approach to values of non-atomic games is reformulated by generating random orders from a fixed subgroup of automorphisms, $\Theta$ that admits an invariant probability measurable group structure. The resulting $\Theta$-symmetric random order value operator is...

Gul (Econometrica, 1989) introduces a non-cooperative bargaining procedure and claims that the payoffs of the resulting efficient stationary subgame perfect equilibria are close to the Shapley value of the underlying transferable utility game (when the discount factor is close to 1). We exhibit...

For each outcome (i.e.~a payoff vector augmented with a coalition structure) of a TU-game with a non-empty coalition structure core there exists a finite sequence of successively dominating outcomes that terminates in the coalition structure core. In order to obtain this result a restrictive...

Cooperative and noncooperative games have no representation of players's basis utilities. Basis utility is the natural reference point on a player's utility scale that enables the determination the marginal utility of any payoff or allocation. A player's basis utility can be determined by an...

This paper strengthens the result of Sengupta and Sengupta (1996). We show that for the class of games with nonempty cores the core can be reached in a bounded number of proposals and counterproposals. Our result is more general than this: the boundedness holds for any two imputations with an...