Accession Number:

AD0652649

Title:

GAMES WITH UNIQUE SOLUTIONS WHICH ARE NONCONVEX,

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CALIF

Personal Author(s):

• Lucas,W. F.

Report Date:

1967-05-01

Pagination or Media Count:

10.0

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