On the Extreme Points of the Core of Neighbour Games and Assignment Games

Tilburg University, CentER Working Paper No. 1999-43

Posted: 24 Mar 2000

See all articles by Herbert Hamers

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Flip Klijn

Autonomous University of Barcelona - Department of Economics and Economic History

Tamas Solymosi

Corvinus University of Budapest

Date Written: 1999

Abstract

Neighbour games arise from certain matching or sequencing situations in which only some specific pairs of players can obtain a positive gain. As a consequence, neighbour games are as well assignment games as line graph restricted games. We will show that the intersection of the class of assignment games and the class of line graph restricted games yields the class of neighbour games. Further, we give a necessary and sufficient condition for the convexity of neighbour games. In spite of the possible non-convexity of neighbour games, it turns out that for any neighbour game the extreme points of the core are marginal vectors. Moreover, we prove this for assignment games in general. Hence, for any assignment game the core is the convex hull of some marginal vectors.

Keyword: game theory

JEL Classification: C71, C78

Suggested Citation

Hamers, Herbert and Klijn, Flip and Solymosi, Tamas, On the Extreme Points of the Core of Neighbour Games and Assignment Games (1999). Tilburg University, CentER Working Paper No. 1999-43, Available at SSRN: https://ssrn.com/abstract=199901

Herbert Hamers (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Flip Klijn

Autonomous University of Barcelona - Department of Economics and Economic History ( email )

Edifici B - Campus Bellaterra
Barcelona, 08193
Spain

Tamas Solymosi

Corvinus University of Budapest ( email )

1828 Budapest
Pf. 489
Hungary
36-1-217 4505 (Phone)

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