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On Concavification and Convex Games

  • Yaron Azrieli

    (Tel Aviv University)

  • Ehud Lehrer

    (Tel Aviv University)

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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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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