GAMES WITH UNIQUE SOLUTIONS WHICH ARE NONCONVEX,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1967
- Accession Number
- AD0652649
Entities
People
- W. F. Lucas
Organizations
- RAND Corporation