Balancedness Conditions for Exact Games

13 Pages Posted: 2 Sep 2008

See all articles by Péter Csóka

Péter Csóka

Corvinus University of Budapest; Hungarian Academy of Sciences (HAS) - Research Centre for Economic and Regional Studies (HAS)

P. Jean-Jacques Herings

Maastricht University

Laszlo A. Koczy

Hungarian Academy of Sciences (HAS) - Research Centre for Economic and Regional Studies (HAS); Quantitative Social and Management Sciences Research Group, Budapest University of Technology and Economics

Date Written: August, 28 2008

Abstract

We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced.

The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition, but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another.

Keywords: Totally Balanced Games, Exact Games, Convex Games

JEL Classification: C71, C61

Suggested Citation

Csóka, Péter and Herings, P. Jean-Jacques and Koczy, Laszlo A., Balancedness Conditions for Exact Games (August, 28 2008). Available at SSRN: https://ssrn.com/abstract=1260184 or http://dx.doi.org/10.2139/ssrn.1260184

Péter Csóka

Corvinus University of Budapest ( email )

Fővám tér 8.
Budapest, 1093
Hungary

Hungarian Academy of Sciences (HAS) - Research Centre for Economic and Regional Studies (HAS) ( email )

Tóth Kálmán utca 4.
Budapest, 1097
Hungary

P. Jean-Jacques Herings (Contact Author)

Maastricht University ( email )

Department of Economics
P.O. Box 616
6200 MD Maastricht
Netherlands
+31 43 3883636 (Phone)
+31 43 3884878 (Fax)

HOME PAGE: http://www.personeel.unimaas.nl/p.herings/herings.htm

Laszlo A. Koczy

Hungarian Academy of Sciences (HAS) - Research Centre for Economic and Regional Studies (HAS) ( email )

Budaörsi 45
Budapest, H-1112
Hungary

HOME PAGE: http://www.mtakti.hu/en/kutatok/laszlo-a-koczy/276/

Quantitative Social and Management Sciences Research Group, Budapest University of Technology and Economics ( email )

Magyar Tudósok krt. 2.
Budapest, 1117
Hungary

HOME PAGE: http://qsms.mokk.bme.hu/index.php/koczy/

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