Skip to main content
Log in

An axiomatization of the weighted NTU value

  • Papers
  • Published:
International Journal of Game Theory Aims and scope Submit manuscript

Abstract

Non-symmetric generalizations of the non-transferable utility (NTU) are defined and characterized axiomatically. The first of these is a weighted NTU value that is identical to the (symmetric) NTU value when players have the same weights. On the class of transferable utility games, this weighted NTU value coincides with the weighted Shapley value and on the pure bargaining games it coincides with the non-symmetric Nash bargaining solution. A further extension, the random order NTU value, is also defined and axiomatized and its relationship to the core is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aumann RJ (1985) An Axiomatization of the Non-Transferable Utility Value, Econometrica, 53, 599–612

    Google Scholar 

  • Harsanyi JC (1963) A Simplified Bargaining Model for the n-Person Cooperative Game, International Economic Review, 4, 194–220

    Google Scholar 

  • Harsanyi JC, Selten R (1972) A Generalized Nash Solution for Two Person Bargaining Games with Incomplete Information, Management Science, 18, 80–106

    Google Scholar 

  • Hart S (1985) An Axiomatization of Harsanyi's Non-Transferable Utility Solution, Econometrica, 53, 1295–1313

    Google Scholar 

  • Ichiishi T (1981) Supermodularity: Applications to Convex Games and the Greedy Algorithm for LP, Journal of Economic Theory, 25, 283–286

    Google Scholar 

  • Imai H (1983) On Harsanyi's Solution, International Journal of Game Theory, 12, 161–179

    Google Scholar 

  • Kalai E (1977a) Nonsymmetric Nash Solutions and Replications of Two Person Bargaining, International Journal of Game Theory, 6, 129–133

    Google Scholar 

  • Kalai E (1977b) Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons, Econometrica, 45, 1623–1630

    Google Scholar 

  • Kalai E, Samet D (1985) Monotonic Solutions to General Cooperative Games, Econometrica, 53, 307–327

    Google Scholar 

  • Kalai E, Samet D (1987) On Weighted Shapley Values, International Journal of Game Theory, 16, 205–222

    Google Scholar 

  • Kern R (1985) The Shapley Transfer Value Without Zero Weights, International Journal of Game Theory, 14, 73–92

    Google Scholar 

  • McLean RP (1988) Non-Symmetric Generalizations of the NTU Value and Harsanyi Solution, mimeo, Department of Economics, Rutgers University

  • Nash J (1950) The Bargaining Problem, Econometrica, 28, 155–162

    Google Scholar 

  • Peleg B (1986) A Proof that the Core of an Ordinal Convex Game is a Von Neumann-Morgenstern Solution, Mathematical Social Sciences, 11, 83–87

    Google Scholar 

  • Peters H (1986) Simultaneity of Issues and Additivity in Bargaining, Econometrica, 54, 155–169

    Google Scholar 

  • Roth A (1979) Axiomatic Models of Bargaining. Lecture Notes in Economics and Mathematical Systems No. 170, Springer Verlag: New York, Heidelberg, Berlin

    Google Scholar 

  • Shapley L (1953a) Additive and Non-Additive Set Functions, Ph. D. Thesis, Department of Mathematics, Princeton University

  • Shapley L (1953b) A Value for n-Person Games, in Contributions to the Theory of Games, vol. II. Princeton University Press: Princeton, 307–317

    Google Scholar 

  • Shapley L (1969) Utility Comparison and the Theory of Games, in La Decision. Paris: Editions du Centres National de la Recherche Scientifique

    Google Scholar 

  • Shapley L (1971) Cores of Convex Games, International Journal of Game Theory, 1, 11–26

    Google Scholar 

  • Sharkey W (1981) Convex Games Without Side Payments, International Journal of Game Theory, 11, 101–106

    Google Scholar 

  • Svejnar J (1986) Bargaining Power, Fear of Disagreement and Wage Settlement: Theory and Evidence From U. S. Industry, Econometrica, 54, 1055–1078

    Google Scholar 

  • Weber R (1988) Probabilistic Values for Games, in The Shapley Value: Essays in Honor of Lloyd Shapley, Cambridge University Press: Cambridge

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Levy, A., McLean, R.P. An axiomatization of the weighted NTU value. Int J Game Theory 19, 339–351 (1991). https://doi.org/10.1007/BF01766425

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01766425

Key Words

Navigation