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Convexity versus average convexity: potential, pmas, the shapley value and simple games

Author

Listed:
  • Jesus Marin Solano
  • Carlos Rafels Pallarola

    (Universitat de Barcelona)

Abstract

Different propietats of convex and average convex games are developed in terms of unanimity coordinates. A set of necessary and sufficient conditions for the core of balanced games containing the Shapley value are given. Connections between convexity and average convexity, the Shapley value, the potential and population monotonic allocation schemes (PMAS) are shown. Average convex simple games are described. Finally, some differences between convexity and average convexity in relation with other well-known solution concepts of cooperative games are studied.

Suggested Citation

  • Jesus Marin Solano & Carlos Rafels Pallarola, 1996. "Convexity versus average convexity: potential, pmas, the shapley value and simple games," Working Papers in Economics 3, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:19963
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    Citations

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    Cited by:

    1. Slikker, M., 1998. "Average Convexity in Communication Situations," Other publications TiSEM 612b0000-a66a-435a-a707-2, Tilburg University, School of Economics and Management.
    2. Marco Slikker, 2005. "Link Monotonic Allocation Schemes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 473-489.
    3. Slikker, M., 1999. "Link Monotonic Allocation Schemes," Other publications TiSEM 42bfa59c-dba6-427e-ac48-9, Tilburg University, School of Economics and Management.
    4. Slikker, M., 1998. "Average Convexity in Communication Situations," Discussion Paper 1998-12, Tilburg University, Center for Economic Research.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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