International Journal of Game Theory

, Volume 16, Issue 3, pp 161–186 | Cite as

Equal or proportional division of a surplus, and other methods

  • H. Moulin


A cooperative venture yields a nonnegative surplus. Agents are differentiated by their opportunity costs only. Two surplus sharing methods (equal sharing, proportional sharing) are characterized with the help of four axioms. Separability and No Advantageous Reallocation deal with coalitional changes in the opportunity costs. Additivity and Path Independence take into account variations in the surplus level.Any triple of these axioms characterizes equalor proportional sharing. Any pair of axioms characterize a distinct, infinite family of methods, compromising between equal and proportional sharing.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aczel J (1966) Functional equations and their applications. Academic Press, New YorkGoogle Scholar
  2. 2.
    Aumann RJ, Maschler M (1985) Game theoretic analysis of a bankruptcy from the talmud. J Econ Theory 36:195–213Google Scholar
  3. 3.
    Banker R (1981) Equity considerations in traditional full-cost allocation practices: an axiomatic perspective. In: Moriarty S (ed) Joint Cost Allocations. University of Oklahoma, NormanGoogle Scholar
  4. 4.
    Chun Y (1985) The Proportional solution for rights problems. Forthcoming in Math Soc SciencesGoogle Scholar
  5. 5.
    Kolm S (1976) Unequal inequalities. Journal of Economic Theory 12:416–442Google Scholar
  6. 6.
    Mirman L, Taumann Y (1982) Demand compatible equitable cost sharing prices. Maths of Operations Research 7(1):40–56Google Scholar
  7. 7.
    Moulin H (1985) Egalitarianism and utilitarianism in quasi-linear bargaining. Econometrica 53(1):49–68Google Scholar
  8. 8.
    Moulin H (1985) The separability axiom and equal-sharing methods. J Econ Theory 36/1: 120–148Google Scholar
  9. 9.
    Moulin H (1985) Binary choices with compensations. Mimeo, University of California, San DiegoGoogle Scholar
  10. 10.
    O'Neill B (1982) A problem of right arbitration in the talmud. Math Soc Sciences 2:345–371Google Scholar
  11. 11.
    Owen G (1982) Game theory, 2nd ed. Academic Press, New YorkGoogle Scholar
  12. 12.
    Peleg B (1986) On the reduced game property and its converse. Int J of Game Theory 15/3: 187–200Google Scholar
  13. 13.
    Peleg S (1985) An axiomatization of the core of cooperative games without side-payments. Mimeo, the Hebrew University of JerusalemGoogle Scholar
  14. 14.
    Sobolev AI (1975) The characterization of the nucleolus by functional equations. In: Vorobiev NN (ed) Matematicheskie metodyv socialnix naukax. Vipusk 6:94–151Google Scholar
  15. 15.
    Young HP (1984) Consistency and optimality in taxation. Mimeo, University of MarylandGoogle Scholar
  16. 16.
    Young HP (1984) Taxation and bankruptcy. Mimeo, University of MarylandGoogle Scholar

Copyright information

© Physica-Verlag 1987

Authors and Affiliations

  • H. Moulin
    • 1
  1. 1.Department of EconomicsVirginia Polytechnic Institute and State UniversityBlacksburg

Personalised recommendations