International Journal of Game Theory

, Volume 39, Issue 1–2, pp 71–88 | Cite as

Bargaining among groups: an axiomatic viewpoint

Original Paper


We introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant α ≥ 0 such that the “bargaining power” of a group is proportional to cα, where c is the cardinality of the group.


Bargaining solution Group bargaining Joint bargaining paradox 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aumann M, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36: 195–213CrossRefGoogle Scholar
  2. Chae S, Heidhues P (2004) A group bargaining solution. Math Soc Sci 48: 37–52CrossRefGoogle Scholar
  3. Chambers C, Thomson W (2002) Group order preservation and the proportional rule for the adjudication of conflicting claims. Math Soc sci 44: 235–252CrossRefGoogle Scholar
  4. Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Res Logist Q 12: 223–259CrossRefGoogle Scholar
  5. Harsanyi J (1959) A bargaining model of the cooperative n-person game. In: Tucker A, Luce RD (eds) Contributions to the theory of games IV. Annals of Mathematical Studies 40, Princeton University Press, PrincetonGoogle Scholar
  6. Harsanyi JC (1977) Rational behavior and bargaining equilibrium in games and social situations. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  7. Horn H, Wolinsky A (1988) Worker substitutability and patterns of unionisation. Econ J 98: 484–497CrossRefGoogle Scholar
  8. Jun BH (1989) Non-cooperative bargaining and union formation. Rev Econ Stud 56: 59–76CrossRefGoogle Scholar
  9. Kalai E (1977a) Nonsymmetric Nash solutions and replications of 2-person bargaining. Int J Game Theory 6: 129–133CrossRefGoogle Scholar
  10. Kalai E (1977b) Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45: 1623–1630CrossRefGoogle Scholar
  11. Lensberg T (1988) Stability and the Nash solution. J Econ Theory 45: 330–341CrossRefGoogle Scholar
  12. Moulin H (1987) Equal or proportional division of a surplus, and other methods. Int J Game Theory 16: 161–186CrossRefGoogle Scholar
  13. Peters H (1992) Axiomatic bargaining theory. Kluwer, DordrechtGoogle Scholar
  14. Sobolev AI (1975) The characterization of optimality principles in cooperative games by functional equations. In: Vorobjev NN (ed) Mathematical methods in the social sciences, Issue 6. Institute of Physics and Mathematics, Academy of Science of the Lithuanian SSR, Vilnius, pp 94–151 (in Russian, English summary)Google Scholar
  15. Thomson W (1990) The consistency principle. In: IchiIshi T, Neyman A, Tauman Y (eds) Game theory and applications. Academic Press, New YorkGoogle Scholar
  16. Thomson W, Lensberg T (1989) Axiomatic theory of bargaining with a variable number of agents. Cambridge University Press, CambridgeGoogle Scholar
  17. Thomson W, Myerson RB (1980) Monotonicity and independence axioms. Int J Game Theory 9: 37–49CrossRefGoogle Scholar
  18. Young HP (1987) On dividing an amount according to individual claims or liabilities. Math Oper Res 12: 398–414CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsSeoul National UniversitySeoulKorea
  2. 2.Department of EconomicsRice UniversityHoustonUSA

Personalised recommendations