Skip to main content

Advertisement

Log in

Bargaining sets and the core in partitioning games

  • Original Paper
  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

Partitioning games are useful on two counts: first, in modeling situations with restricted cooperative possibilities between the agents; second, as a general framework for many unrestricted cooperative games generated by combinatorial optimization problems.We show that the family of partitioning games defined on a fixed basic collection is closed under the strategic equivalence of games, and also for taking the monotonic cover of games. Based on these properties we establish the coincidence of the Mas-Colell, the classical, the semireactive, and the reactive bargaining setswith the core for interesting balanced subclasses of partitioning games, including assignment games, tree-restricted superadditive games, and simple network games.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

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

  • Aumann RJ, Maschler M (1964) The bargaining set for cooperative games. In: Dresher M, Shapley LS, Tucker AW(eds) Advances in game theory. Princeton University Press, Princeton, pp 443–476

    Google Scholar 

  • Davis M, Maschler M (1967) Existence of stable payoff configurations for cooperative games. In: Shubik M(eds) Essays in mathematical economics in honour of Oskar Morgenstern. Princeton University Press, Princeton, pp 39–52

    Google Scholar 

  • Granot D (1994) On a new bargaining set for cooperative games. Working paper, Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, Canada

  • Granot D, Granot F (1992) On some network flow games. Math Oper Res 17: 792–841

    Article  Google Scholar 

  • Granot D, Granot F, Zhu WR (1997) The reactive bargaining set of some flow games and of superadditive simple games. Int J Game Theory 26: 207–214

    Google Scholar 

  • Holzman R (2000) The comparability of the classical and the Mas-Colell bargaining sets. Int J Game Theory 29: 543–553

    Article  Google Scholar 

  • Kalai E, Zemel E (1982) Generalized network problems yielding totally balanced games. Oper Res 30: 998–1008

    Article  Google Scholar 

  • Kaneko M, Wooders MH (1982) Cores of partitioning games. Math Soc Sci 3: 313–327

    Article  Google Scholar 

  • Kuipers J (1994) Combinatorial methods in cooperative game theory. Ph.D. Thesis, University of Limburg, Maastricht, The Netherlands

  • Le Breton M, Owen G, Weber S (1992) Strongly balanced cooperative games. Int J Game Theory 20: 419–427

    Article  Google Scholar 

  • Mas-Colell A (1989) An equivalence theorem for a bargaining set. J Math Econ 18: 129–139

    Article  Google Scholar 

  • Myerson R (1977) Graphs and cooperation in games. Math Oper Res 2: 225–229

    Article  Google Scholar 

  • Owen G (1992) The assignment game: the reduced game. Annales D’Economie et de Statistique 25(26): 71–79

    Google Scholar 

  • Owen G (1986) Values of graph-restricted games. SIAM J Algebr Discrete Methods 7: 210–220

    Article  Google Scholar 

  • Peleg B, Sudhölter P (2003) Introduction to the theory of cooperative games. Kluwer, Boston

    Google Scholar 

  • Potters JAM, Reijnierse J (1995) Γ-component additive games. Int J Game Theory 24: 49–56

    Article  Google Scholar 

  • Quint T (1991) Necessary and sufficient conditions for balancedness in partitioning games. Math Soc Sci 22: 87–91

    Article  Google Scholar 

  • Shapley LS, Shubik M (1972) The assignment game I: the core. Int J Game Theory 1: 111–130

    Article  Google Scholar 

  • Solymosi T (1999) On the bargaining set, kernel and core of superadditive games. Int J Game Theory 28: 229–240

    Article  Google Scholar 

  • Solymosi T, Raghavan TES, Tijs S (2003) Bargaining sets and the core in permutation games. Cent Eur J Oper Res 11: 93–101

    Google Scholar 

  • Sudhölter P, Potters JAM (2001) The semireactive bargaining set of a cooperative game. Int J Game Theory 30: 117–139

    Article  Google Scholar 

  • Vasin AA, Gurvich VA (1977) Reconcilable sets of coalitions. (in Russian) In: Questions in applied mathematics, Sibirsk. Energet. Inst., Akad. Nauk SSSR Sibirsk. Otdel., Irkutsk, pp 20–30

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tamás Solymosi.

Additional information

Prepared during the author’s Bolyai János Research Fellowship. Also supported by OTKA grant T46194.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solymosi, T. Bargaining sets and the core in partitioning games. Cent Eur J Oper Res 16, 425–440 (2008). https://doi.org/10.1007/s10100-008-0070-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-008-0070-2

Keywords

Navigation