Accession Number:

AD0647250

Title:

THE KERNEL AND BARGAINING SET FOR CONVEX GAMES

Descriptive Note:

Research memo.

Corporate Author:

HEBREW UNIV JERUSALEM (ISRAEL) DEPT OF MATHEMATICS

Personal Author(s):

• Maschler, M.
• Peleg, B.
• Shapley, L. S.

Report Date:

1967-02-01

Pagination or Media Count:

16.0

Abstract:

Many solution concepts for cooperative games agree or partially agree if the game happens to be convex. For example, convex games have a unique von- Neumann Morgenstern solution which coincides with the core. Also, the Shapley value is a center of gravity of the extreme points of the core of a convex game namely, the center of gravity when the extreme points are assigned appropriate multiplicities. It is proved in this paper that the kernel for the grand coalition of a convex game lies in the relative interior of its core and that the bargaining set for the grand coalition coincides with the core.

Descriptors:

• *CONVEX SETS
• *GAME THEORY
• BARGAINING
• COMBINATORIAL ANALYSIS
• ECONOMICS
• ISRAEL
• SET THEORY

Subject Categories:

• Economics and Cost Analysis
• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE