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On Concavification and Convex Games

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Author Info

  • Yaron Azrieli

    (Tel Aviv University)

  • Ehud Lehrer

    (Tel Aviv University)

Abstract

We propose a new geometric approach for the analysis of cooperative games. A cooperative game is viewed as a real valued function $u$ defined on a finite set of points in the unit simplex. We define the \emph{concavification} of $u$ on the simplex as the minimal concave function on the simplex which is greater than or equal to $u$. The concavification of $u$ induces a game which is the \emph{totally balanced cover} of the game. The concavification of $u$ is used to characterize well-known classes of games, such as balanced, totally balanced, exact and convex games. As a consequence of the analysis it turns out that a game is convex if and only if each one of its sub-games is exact.

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File URL: http://128.118.178.162/eps/game/papers/0408/0408002.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0408002.

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Length: 13 pages
Date of creation: 16 Aug 2004
Date of revision:
Handle: RePEc:wpa:wuwpga:0408002

Note: Type of Document - pdf; pages: 13
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Web page: http://128.118.178.162

Related research

Keywords: concavification; convex games; core; totally balanced; exact games;

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Cited by:
  1. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2006. "Convex games versus clan games," Working Papers 381, Bielefeld University, Center for Mathematical Economics.
  2. Péter Csóka & P. Herings & László Kóczy, 2011. "Balancedness conditions for exact games," Computational Statistics, Springer, vol. 74(1), pages 41-52, August.
  3. Ehud Lehrer, 2009. "A new integral for capacities," Economic Theory, Springer, vol. 39(1), pages 157-176, April.
  4. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2005. "Convex games, clan games, and their marginal games," Working Papers 368, Bielefeld University, Center for Mathematical Economics.
  5. Yaron Azrieli & Ehud Lehrer, 2005. "Cooperative investment games or population games," Game Theory and Information 0503007, EconWPA.

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