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Some Characterizations of Convex Games

In: Recent Advances in Optimization

Author

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  • Juan Enrique Martínez-Legaz

    (Universitat Autònoma de Barcelona)

Abstract

Summary Several characterizations of convexity for totally balanced games are presented. As a preliminary result, it is first shown that the core of any subgame of a nonnegative totally balanced game can be easily obtained from the maximum average value (MAV) function of the game. This result is then used to get a characterization of convex games in terms of MAV functions. It is also proved that a game is convex if and only if all of its marginal games are totally balanced.

Suggested Citation

  • Juan Enrique Martínez-Legaz, 2006. "Some Characterizations of Convex Games," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 293-303, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-28258-7_18
    DOI: 10.1007/3-540-28258-0_18
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    Citations

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    Cited by:

    1. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Convex Games Versus Clan Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 363-372.
    2. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2011. "Convex games, clan games, and their marginal games," Center for Mathematical Economics Working Papers 368, Center for Mathematical Economics, Bielefeld University.
    3. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
    4. Brânzei, R. & Tijs, S.H. & Zarzuelo, J., 2007. "Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes," Discussion Paper 2007-54, Tilburg University, Center for Economic Research.
    5. Brânzei, R. & Tijs, S.H. & Zarzuelo, J., 2007. "Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes," Other publications TiSEM 5549df35-acc3-4890-be43-4, Tilburg University, School of Economics and Management.
    6. Rodica Branzei & Stef Tijs & S. Zeynep Alparslan Gok, 2008. "Some Characterizations of Convex Interval Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 219-226, December.

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