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Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games

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  • Rafels, Carles
  • Ybern, Neus

Abstract

In this paper we characterize convex games by means of Owen's multilinear extension and the marginal worth vectors associated with even or odd permutations. Therefore we have obtained a refinement of the classic theorem; Shapley (1971), Ichiishi (1981) in order to characterize the convexity of a game by its marginal worth vectors. We also give new expressions for the marginal worth vectors in relation to unanimity coordinates and the first partial derivatives of Owen's multilinear extension. A sufficient condition for the convexity is given and also one application to the integer part of a convex game.

Suggested Citation

  • Rafels, Carles & Ybern, Neus, 1995. "Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 113-126.
    • Handle: RePEc:spr:jogath:v:24:y:1995:i:2:p:113-26
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    Cited by:

    1. Trine Platz & Herbert Hamers & Marieke Quant, 2014. "C-complete sets for compromise stable games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 213-223, October.
    2. Platz, T.T. & Hamers, H.J.M. & Quant, M., 2011. "Characterizing Compromise Stability of Games Using Larginal Vectors," Discussion Paper 2011-058, Tilburg University, Center for Economic Research.
    3. van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2002. "Convexity and Marginal Vectors," Other publications TiSEM 1cdf99c9-0e92-4aae-9a92-3, Tilburg University, School of Economics and Management.
    4. Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.
    5. Fco. Javier Martinez de Albeniz Salas & Carlos Rafels Pallarola, 2002. "A Note on Shapleys Convex Measure Games," Working Papers in Economics 91, Universitat de Barcelona. Espai de Recerca en Economia.
    6. van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2002. "Convexity and Marginal Vectors," Discussion Paper 2002-53, Tilburg University, Center for Economic Research.

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