Accession Number : AD0652649
Title : GAMES WITH UNIQUE SOLUTIONS WHICH ARE NONCONVEX,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Lucas,W. F.
Report Date : MAY 1967
Pagination or Media Count : 10
Abstract : Describes an eight-person Von Neumann-Morgenstern game with a solution of a type not previously reported: a polyhedron within four dimensions, unique and nonconvex. Previously known unique solutions have always been convex polyhedrons. The essential idea is the existence of a line L with a large Dom L. This property can be generalized in many dimensions in such a way as to describe many other games that maintain the corresponding L as a subset of the core. Large classes of interesting solutions will be obtained, many of them unique and nonconvex. These results suggest the possibility that not all n-person games have solutions, probably the most important unresolved issue in game theory.
Descriptors : (*GAME THEORY, *PROBLEM SOLVING), REAL NUMBERS, VECTOR ANALYSIS, MATHEMATICS
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE