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Values of non-transferable utility games

In: Handbook of Game Theory with Economic Applications

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  • McLean, Richard P.

Abstract

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.

Suggested Citation

  • McLean, Richard P., 2002. "Values of non-transferable utility games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 55, pages 2077-2120, Elsevier.
    • Handle: RePEc:eee:gamchp:3-55
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    Cited by:

    1. Gustavo Bergantiños & Juan Vidal-Puga, 2005. "The Consistent Coalitional Value," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 832-851, November.
    2. de Clippel, Geoffroy & Pérez-Castrillo, David & Wettstein, David, 2012. "Egalitarian equivalence under asymmetric information," Games and Economic Behavior, Elsevier, vol. 75(1), pages 413-423.
    3. Laruelle, Annick & Valenciano, Federico, 2007. "Bargaining in committees as an extension of Nash's bargaining theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 291-305, January.
    4. Gao, Wayne Yuan & Li, Ming & Xu, Sheng, 2023. "Logical differencing in dyadic network formation models with nontransferable utilities," Journal of Econometrics, Elsevier, vol. 235(1), pages 302-324.
    5. Barry O'Neill, 2014. "Networks of Rights in Conflict: A Talmudic Example," Discussion Paper Series dp677, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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    JEL classification:

    • C - Mathematical and Quantitative Methods

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