Accession Number : AD0732689

Title :   Cores of Convex Games,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Shapley,Lloyd S.

Report Date : APR 1971

Pagination or Media Count : 38

Abstract : The core of an n-person game is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is one that is based on a convex set function (see below); intuitively this means that the incentives for joining a coalition increase as the coalition grows, so that one would expect a 'snowballing' or 'bandwagon' effect when the game is played cooperatively. In the paper the author shows that the core of a convex game is not empty--in fact, it is quite large--and that it has an especially regular structure. The author further shows that certain other cooperative solution concepts are related in a simple way to the core. Specifically the value of a convex game is the center of gravity of the extreme points of the core, and the von Neumann-Morgenstern stable set solution of a convex game is unique and coincides with the core. (Author)

Descriptors :   (*GAME THEORY, CONVEX SETS), MATHEMATICAL PROGRAMMING, INEQUALITIES, MEASURE THEORY, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE