A new coalitional value is proposed under the hypothesis of isolated unions. The main difference between this value and the Aumann–Drèze value is that the allocations within each union are not given by the Shapley value of the restricted game but proportionally to the Shapley value of the original game. Axiomatic characterizations of the new value, examples illustrating its application and a co...

This paper is a revised version of TI-discussion paper 8-95-249, \ An axiomatization of the Shapley value using component eeciency and fairness". I would like to thank Gerard van der Laan and Eric van Damme for useful remarks on a previous draft of this paper. Financial support from the Netherlands organization for scientiic research (NWO) ESR-grant 510-01-0504 is gratefully acknowledged. Abstr...

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it an O...

The Shapley value and Banzhaf index are two well known indices for measuring the power a player has in a voting game. However, the problem of computing these indices is computationally hard. To overcome this problem, we analyze approximation methods for computing these indices. Although these methods have polynomial time complexity, finding an approximate Shapley value using them is easier than...

In this paper, a general expression of the Shapley value for fuzzy games on vague sets is proposed, where the player participation levels are vague sets. The existence and uniqueness of the given Shapley value are showed by establishing axiomatic system. When the fuzzy games on vague sets are convex, the given Shapley value is a vague population monotonic allocation function (VPMAF) and an elem...

The Shapley value, one of the most widespread concepts in Operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. Recently much research work has been done in order to extend OR models and methods, in particular cooperative game theory, for situations with interval data. This paper focuses on the Shapley value ...

We consider the travelling salesperson game (TSG) in which agents correspond to a set of locations, and the cost of each subset of locations is the length of the optimal tour for that subset. The Shapley value, one of the most important normative division schemes in cooperative games, is a principled way of dividing transport costs among such locations. We prove that approximating the Shapley v...

In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation between two adjacent players is established by a directed line segment. Directed path, connecting the initial player with the terminal player, form the coalition ...

objective: to classify different types of acute leukemia based on cooperative game theory and shapley value. materials and methods: in this study, patients data were collected from flow cytometry tests of the iran blood transfusion organization (ibto) have been used. 304 different diagnosed samples in 8 classes of acute leukemia were investigated. samples were initially in numerical format. i...

We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these games, the “value” of a set S of agents is determined only by a critical subset T ⊆ S of the agents and not the entirety of S due to a budget constraint that l...