The equitable division of a joint cost (or a jointly produced output) among agents with different shares or types of output (or input) commodities, is a central theme of the theory of cooperative games with transferable utility. Ever since Shapley's seminal contribution in 1953, this question...

This chapter surveys a class of solution concepts for n -person games without transferable utility — NTU games for short — that are based on varying notions of “fair division”. An NTU game is a specification of payoffs attainable by members of each coalition through some joint course of...

This survey captures the main contributions in the area described by the title that were published up to 1997. (Unfortunately, it does not capture all of them.) The variations that are the subject of this chapter are those axiomatically characterized solutions which are obtained by varying...

This chapter surveys some of the literature in game theory that has emerged from Shapley's seminal paper on the Value. The survey includes both contributions which offer different interpretations of the Shapley value as well as several different ways to characterize the value axiomatically. The...

An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for...

On several classes of n-person NTU games that have at least one Shapley NTU value, Aumann characterized this solution by six axioms: Non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives (IIA). Each of the first five axioms is...

n agents located along a river generate residues that then require cleaning to return the river to its natural state, which entails some cost. We propose several rules to distribute the total pollutant-cleaning cost among all the agents. We provide axiomatic characterizations using properties...

Selected applications of the NTU Shapley value to settings other than that of general equilibrium in perfect competition. Three models are considered: Taxation and Redistribution, Public Goods, and Fixed Prices. In each case, the value leads to significant conceptual insights which, while...

In an economic or social situation where agents have to group in order to achieve common goals, how can we calculate the coalitional rents of the agents arising from the coalition formation? Once we have formalized the situation via a TU-game and a network describing the economic structure, we...