The Shapley Value for Directed Graph Games

The Shapley value for directed graph games

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 not violate the subordination of players. We assume that in order to cooperate players may join only ...

Shapley value for assignment games ∗

We consider the problem of the axiomatization of the Shapley value on the class of assignment games. We show that Shapley’s original [21], Young’s [24], Chun’s [7], van den Brink’s [2], (5-6) Hart and Mas-Colell’s [12] potential function and consistency approaches and Roth’s [19] characterization do not work on the class of assignment games. We also consider Myerson’s [15] axiomatization of the...

The Shapley value for bicooperative games

The aim of the present paper is to study a one-point solution concept for bicooperative games. For these games introduced by Bilbao (Cooperative Games on Combinatorial Structures, 2000), we define a one-point solution called the Shapley value, since this value can be interpreted in a similar way to the classical Shapley value for cooperative games. The main result of the paper is an axiomatic c...

The average covering tree value for directed graph games

We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on th...

Shapley value for constant-sum games