Chapter 55 Values of non-transferable utility games

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 action. The players confront the problem of choosing a payoff or solution that is feasible for the group as a whole. This is a bargaining problem and its solution may be reasonably required to satisfy various criteria, and different sets of rules or axioms will characterize different solutions or classes of solutions. For transferable utility games, the main axiomatic solution is the Shapley Value and this chapter deals with values of NTU games , i.e., solutions for NTU games that coincide with the Shapley value in the transferable utility case. We survey axiomatic characterizations of the Shapley NTU value, the Harsanyi solution, the Egalitarian solution and the non-symmetric generalizations of each. In addition, we discuss approaches to some of these solutions using the notions of potential and consistency for NTU games with finitely many as well as infinitely many players.