On Concavification and Convex Games

Yaron Azrieli and Ehud Lehrer ()

Game Theory and Information from University Library of Munich, Germany

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.

Keywords: concavification; convex games; core; totally balanced; exact games (search for similar items in EconPapers)
JEL-codes: C7 D8 (search for similar items in EconPapers)
Pages: 13 pages
Date: 2004-08-16
New Economics Papers: this item is included in nep-mic
Note: Type of Document - pdf; pages: 13
References: Add references at CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0408/0408002.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpga:0408002

Access Statistics for this paper

More papers in Game Theory and Information from University Library of Munich, Germany
Bibliographic data for series maintained by EconWPA ( this e-mail address is bad, please contact ).