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A note on external angles of the core of convex TU games, marginal worth vectors and the Weber set

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  • Sergei Pechersky

Abstract

The paper studies the structure of external angles of the core of convex TU games. It is shown that the external angle at a vertex of the core is proportional to the number of marginal worth vectors defining the vertex. A notion of difference of two convex compact sets is used to define the Weber set of a TU game and to give another proof of the Weber theorem. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Sergei Pechersky, 2015. "A note on external angles of the core of convex TU games, marginal worth vectors and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 487-498, May.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:487-498
    DOI: 10.1007/s00182-014-0441-y
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    1. Dragan, I. & Potters, J.A.M. & Tijs, S.H., 1989. "Superadditivity for solutions of coalitional games," Other publications TiSEM 283e2594-e3a0-418d-ae5e-2, Tilburg University, School of Economics and Management.
    2. Gonzalez-Diaz, Julio & Sanchez-Rodriguez, Estela, 2008. "Cores of convex and strictly convex games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 100-105, January.
    3. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    4. Ichiishi,Tatsuro, 1993. "The Cooperative Nature of the Firm," Cambridge Books, Cambridge University Press, number 9780521414449, November.
    5. Jeroen Kuipers & Dries Vermeulen & Mark Voorneveld, 2010. "A generalization of the Shapley–Ichiishi result," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 585-602, October.
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    Cited by:

    1. Marcello Basili, 2018. "Aggregation of experts’ opinions and conditional consensus opinion," Department of Economics University of Siena 780, Department of Economics, University of Siena.
    2. Marcello Basili & Federico Crudu, 2021. "Aggregation of Experts Opinions and the Assessment of Tipping Points. Catastrophic Forecasts for Higher Temperature Changes," Department of Economics University of Siena 868, Department of Economics, University of Siena.
    3. Estela Sánchez-Rodríguez & Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Iago Núñez Lugilde, 2024. "Coalition-weighted Shapley values," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 547-577, June.
    4. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2022. "The average-of-awards rule for claims problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 863-888, November.

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