The Shapley value (Shapley (1953)) is one of the most prominent one-point solution concepts in cooperative game theory that divides revenues (or cost, power) that can be obtained by cooperation of players in the game. The Shapley value is mathematically characterized by properties that have...

We consider the problem of computing the influence of a neuronal structure in a brain network. Abraham, Kotter, Krumnack, and Wanke (2006) computed this influence by using the Shapley value of a coalitional game corresponding to a directed network as a rating. Kotter, Reid, Krumnack, Wanke, and...

In this paper we consider spanning tree problems, where n players want to be connected to a source as cheap as possible. We introduce and analyze (n!) vertex oriented construct and charge procedures for such spanning tree situations leading in n steps to a minimum cost spanning tree and a cost...

In this paper we introduce two values for cooperative games with communication graph structure. For cooperative games the shapley value distributes the worth of the grand coalition amongst the players by taking into account the worths that can be obtained by any coalition of players, but does...

In this paper we introduce the concept of quasi-building set that may underlie the coalitional structure of a cooperative game with restricted communication between the players. Each feasible coalition, including the set of all players, contains a nonempty subset called the choice set of the...

The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is defined as the average of marginal contribution vectors corresponding to all permutations that do...

This paper introduces a new class of interactive cooperative purchasing situations and provides an explicit alternative characterization of the nucleolus of cooperative games, which offers an alternative to Kohlberg (1971). In our cooperative purchasing situation, the unit price of a commodity...

Some new axiomatic characterizations and recursive formulas of the Shapley value are presented. In the results, dual games and the self-duality of the value implicitly play an important role. A set of non-cooperative games which implement the Shapley value on the class of all games is given