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On the Cores of cooperative games and the stability of the Weber set

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Abstract

In this paper conditions are given guaranteeing that the Core equals the D-core (the set of unDominated imputations). Under these conditions, we prove the non-emptiness of the intersection of the Weber set with the imputation set. This intersection has a special stability property: it is externally stable. As a consequence we can give a new characterization (th. 3.2) for the convexity of a cooperative game in terms of its stability (von Neumann-Morgenstern solutions) using the Weber set.

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Authors and Affiliations

  1. Department of Actuarial, Financial and Economic Mathematics, University of Barcelona, Avda. Diagonal 690, 08034, Barcelona, Spain

    Carles Rafels

  2. Department of Econometrics, Tilburg University, P.O. Box 90153, LE Tilburg, The Netherlands

    Stef Tijs

Authors
  1. Carles Rafels
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  2. Stef Tijs
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Additional information

The authors are grateful to Chih Chang who read the manuscript and an anonymous referee.

This work has been supported by a Spanish research grant DGICYT, project PB95-0679.

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Rafels, C., Tijs, S. On the Cores of cooperative games and the stability of the Weber set. Int J Game Theory 26, 491–499 (1997). https://doi.org/10.1007/BF01813887

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  • DOI: https://doi.org/10.1007/BF01813887

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