# On Concavification and Convex Games

## Author Info

• Yaron Azrieli

(Tel Aviv University)

• Ehud Lehrer

(Tel Aviv University)

Registered author(s):

## 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://econwpa.repec.org/eps/game/papers/0408/0408002.pdf

## 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 Contact details of provider: Web page: http://econwpa.repec.org

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