International Journal of Game Theory

, Volume 19, Issue 2, pp 219–232 | Cite as

Cores and large cores when population varies

  • H. Moulin
Article

Abstract

In a TU cooperative game with populationN, a monotonic core allocation allocates each surplusv (S) among the agents of coalitionS in such a way that agenti's share never decreases when the coalition to which he belongs expands.

We investigate the property of largeness (Sharkey [1982]) for monotonic cores. We show the following result. Given a convex TU game and an upper bound on each agent' share in each coalition containing him, if the upper bound depends only upon the size of the coalition and varies monotonically as the size increases, then there exists a monotonic core allocation meeting this system of upper bounds. We apply this result to the provision of a public good problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bennett E (1983) The aspiration approach to predicting coalition formation and pay-off distribution in sidepayment games, International Journal of Game Theory, 12, 1–28Google Scholar
  2. Champsaur P (1975) How to share the cost of a public good? International Journal of Game Theory, 4, 113–129Google Scholar
  3. Dutta B, Ray D (1989) A concept of egalitarianism under participation constraints, Econometrica, 57, 3, 615–636Google Scholar
  4. Foley D (1967) Resource allocation and the public sector, Yale Economic Essays, 7, 1, 45–98Google Scholar
  5. Hart S (1985) An axiomatization of Harsanyi's nontransferable utility solution, Econometrica, 53, 6, 1295–1314Google Scholar
  6. Ichiishi T (1981) Super-modularity: applications to convex games and to the greedy algorithm for LP, Journal of Economic Theory, 25, 283–286Google Scholar
  7. Ichiishi T (1987) Private communicationGoogle Scholar
  8. Ichiishi T (1988) Comparative cooperative game theory, Mimeo, Ohio State UniversityGoogle Scholar
  9. Moulin H (1987) Egalitarian equivalent cost sharing of a public good, Econometrica, 55, 4, 963–977Google Scholar
  10. Moulin H (1989) All Sorry to Disagree: a general principle for the provision of non-rival goods, Mimeo, Duke UniversityGoogle Scholar
  11. Moulin H (1990) Fair division under joint ownership: recent results and open problems, Social Choice and Welfare, 7, 2, 149–170Google Scholar
  12. Peleg B (1986) A proof that the core of an ordinal convex game is a Von Neuman Morgenstern solution, Mathematical Social Sciences, 11, 83–87Google Scholar
  13. Sharkey W (1982) Cooperative games with large cores, International Journal of Game Theory, 11: 175–182Google Scholar
  14. Sprumont Y (1989) Population monotonic allocation schemes for cooperative games with transferable utility, forthcoming, Games and Economic BehaviorGoogle Scholar
  15. Thomson W (1983) The fair division of a fixed supply among a growing population, Mathematics of Operations Research, 8, 319–326Google Scholar

Copyright information

© Physica-Verlag 1990

Authors and Affiliations

  • H. Moulin
    • 1
  1. 1.Department of EconomicsDuke UniversityDurhamUSA

Personalised recommendations