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