Journal of Applied Mathematics and Decision Sciences
Volume 2009 (2009), Article ID 342089, 14 pages
Research Article

Convex Interval Games

1Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey
2Department of Mathematics, Faculty of Arts and Sciences, Süleyman Demirel University, 32260 Isparta, Turkey
3Faculty of Computer Science, Alexandru Ioan Cuza University, 700483 Iaşi, Romania
4CentER and Department of Econometrics and OR, Tilburg University, P.O. Box 90153, 5000LE Tilburg, The Netherlands
5Department of Mathematics, University of Genoa, 16126 Genoa, Italy

Received 23 October 2008; Accepted 24 March 2009

Academic Editor: Graham Wood

Copyright © 2009 S. Z. Alparslan Gök et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Convex interval games are introduced and characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. The notion of population monotonic interval allocation scheme (pmias) in the interval setting is introduced and it is proved that each element of the Weber set of a convex interval game is extendable to such a pmias. A square operator is introduced which allows us to obtain interval solutions starting from the corresponding classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.