The Kernel and Bargaining Set for Convex Games
Abstract
Convex games were introduced in a previous paper where it was shown that these are precisely the games for which the core has a certain regular structure. It was also shown that convex games have a unique von-Neumann- Morgenstern solution which coincides with the core, and that their Shapley value is essentially the center of gravity of the extreme points of the core. One purpose of the paper is to prove that the kernel (for the grand coalition) of convex games consists of a unique point. As such, it coincides with the nucleolus of the game and therefore occupies a central position in the core (which is different, in general, from that of the Shapley value). The authors also prove that the bargaining set M(sub 1)(Sup i) (for the grand coalition) coincides with the core. Thus, it appears that for convex games, many solution concepts either coincide with the core or occupy a central position within the core. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1971
- Accession Number
- AD0732666
Entities
People
- B. Peleg
- Lloyd Shapley
- M. Maschler
Organizations
- RAND Corporation