The modified nucleolus: Properties and axiomatizations (original) (raw)
Abstract
A new solution concept for cooperative transferable utility games is introduced, which is strongly related to the nucleolus and therefore called modified nucleolus. It takes into account both the “power”, i.e. the worth, and the “blocking power” of a coalition, i.e. the amount which the coalition cannot be prevented from by the complement coalition. It can be shown that the modified nucleolus is reasonable, individually rational for weakly superadditive games, coincides with the prenucleolus for constant-sum games, and is contained in the core for convex games. Finally this paper proposes two axiomatizations of this solution concept on the set of games on an infinite universe of players which are similar to Sobolev's characterization of the prenucleolus.
Access this article
Subscribe and save
- Starting from 10 chapters or articles per month
- Access and download chapters and articles from more than 300k books and 2,500 journals
- Cancel anytime View plans
Buy Now
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
- Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Research Logist. Quarterly 12: 223–259
Google Scholar - Einy E (1985) The desirability relation of simple games. Math Social Sc 10: 155–168
Google Scholar - Kohlberg E (1971) On the nucleolus of a characteristic function game. SIAM Journal Appl Math 20: 62–66
Google Scholar - Kopelowitz A (1967) Computation of the kernel of simple games and the nucleolus of_n_-person games. Research Program in Game Th and Math Economics, Dept of Math, The Hebrew University of Jerusalem RM 31
- Maschler M (1992) The bargaining set, kernel, and nucleolus: a survey. In: Aumann RJ, Hart S (eds) Handbook of Game Theory 1, Elsevier Science Publishers BV, 591–665
- Maschler M, Peleg B (1966) A characterization, existence proof and dimension bounds for the kernel of a game. Pacific J Math 18: 289–328
Google Scholar - Maschler M, Peleg B, Shapley LS (1972) The kernel and bargaining set for convex games. Int Journal of Game Theory 1: 73–93
Google Scholar - Maschler M, Peleg B, Shapley LS (1979) Geometric properties of the kernel, nucleolus, and related solution concepts. Math of Operations Res 4: 303–338
Google Scholar - Milnor JW (1952) Reasonable outcomes for n-person games. The Rand Corporation 916
- Ostmann A (1987) On the minimal representation of homogeneous games. Int Journal of Game Theory 16: 69–81
Google Scholar - Peleg B (1968) On weights of constant-sum majority games. SIAM Journal Appl Math 16: 527–532
Google Scholar - Peleg B (1988/89) Introduction to the theory of cooperative games. Research Memoranda No 81–88, Center for Research in Math Economics and Game Theory, The Hebrew University, Jerusalem Israel
Google Scholar - Rosenmüller J (1987) Homogeneous games: recursive structure and computation. Math of Operations Research 12: 309–330
Google Scholar - Sankaran JK (1992) On finding the nucleolus of an_n_-person cooperative game. Int Journal of Game Theory 21
- Schmeidler D (1966) The nucleolus of a characteristic function game. Research Program in Game Th and Math Econ, The Hebrew University of Jerusalem RM 23
- Shapley LS (1953) A value for_n-person games. In: Kuhn H, Tucker AW (eds) Contributions to the Theorie of Games II, Princeton University Press_ 307–317
- Shapley LS (1971) Cores of convex games. Int Journal of Game Theory 1: 11–26
Google Scholar - Sobolev AI (1975) The characterization of optimality principles in cooperative games by functional equations. In: Vorobiev NN (ed) Math Methods Social Sci 6, Academy of Sciences of the Lithunian SSR, Vilnius 95–151 (in Russian)
- Sudhölter P (1993a) Independence for characterizing axioms of the pre-nucleolus. Working Paper 220, Institute of Mathematical Economics, University of Bielefeld
- Sudhölter P (1993b) The modified nucleolus of a cooperative game. Habilitation Thesis, University of Bielefeld
Author information
Authors and Affiliations
- Institute of Mathematical Economics-JMW-University of Bielefeld, Postfach 100131, 33501, Bielefeld, Germany
Peter Sudhölter
Additional information
This work is partly based on Sections 1, 2, 3, 5 of a habilitation thesis (Sudhölter (1993b)) submitted to the Department of Economics, University of Bielefeld, Germany. Helpful discussions with M. Maschler and J. Rosenmüller are gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Sudhölter, P. The modified nucleolus: Properties and axiomatizations.Int J Game Theory 26, 147–182 (1997). https://doi.org/10.1007/BF01295846
- Received: 15 November 1994
- Revised: 15 August 1995
- Issue date: June 1997
- DOI: https://doi.org/10.1007/BF01295846