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 provide a new characterization of the Shapley value neither using the e¢ciency axiom nor the additivity axiom. In this characterization, e¢ciency is replaced by the gain-loss axiom (Einy and Haimanko, 2011, Game Econ Behav 73: 615–621), i.e., whenever the total worth generated does not change, a player can only gain at the expense of another one. Additivity and the equal treatment axiom are ...

A game on a convex geometry is a real-valued function de0ned on the family L of the closed sets of a closure operator which satis0es the 0nite Minkowski–Krein–Milman property. If L is the boolean algebra 2 then we obtain an n-person cooperative game. Faigle and Kern investigated games where L is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axiom...

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...

The Shapley value solution occupies a central place in fair division literature, specially in settings where a set of positions in a queue need to be shared between a set of agents using payments. But computing the Shapley value of an agent requires solving exponential number of optimization problems (marginal value problem). Moreover, it requires exact knowledge of valuation functions of agent...

We characterize the Extended, Generalized Shapley Value of McQuillin [6] using an ‘efficiency’ condition and two ‘balance’ conditions. One feature of this charaterization is that the conditions only have to apply for a single game.

Within the current Internet, autonomous ISPs implement bilateral agreements, with each ISP establishing agreements that suit its own local objective to maximize its profit. Peering agreements based on local views and bilateral settlements, while expedient, encourage selfish routing strategies and discriminatory interconnections. From a more global perspective, such settlements reduce aggregate ...

We design a simple non-cooperative mechanism in the classs of NTUgames. We study it in the context of a particular class of pure exchange economies. When the corresponding NTU game (N, V ) satisfies that V (N) is flat, the only payoff which arises in equilibrium is the Shapley NTU value.

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 ...

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...