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The sigma-core of a cooperative game

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Abstract

This paper is concerned with the existence of (σ-additive) measures in the core of a cooperative game. The main theorem shows, for a capacityu on the Borel sets of a metric space, that to each additive set function, majorized byu and agreeing withu on a system of closed sets, there exists a measure having these same properties. This theorem is applied, in combination with known core theorems, to the case of a cooperative game defined on the Borel sets of a metric space and whose conjugate is a capacity.

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Authors and Affiliations

  1. Department of Statistics School of Mathematics, University of Hull, HU6 7RX, HULL, England

    June M. Parker

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  1. June M. Parker
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Parker, J.M. The sigma-core of a cooperative game. Manuscripta Math 70, 247–253 (1991). https://doi.org/10.1007/BF02568374

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  • DOI: https://doi.org/10.1007/BF02568374

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