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Cores and large cores when population varies

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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.

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Authors and Affiliations

  1. Department of Economics, Duke University, 27706, Durham, NC, USA

    H. Moulin

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  1. H. Moulin
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Additional information

Stimulating conversations with Tatsuro Ichiishi and Yves Sprumont are gratefully acknowledged. Special thanks are due to William Thomson for useful comments.

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Moulin, H. Cores and large cores when population varies. Int J Game Theory 19, 219–232 (1990). https://doi.org/10.1007/BF01761077

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  • DOI: https://doi.org/10.1007/BF01761077

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