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

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Game Theory
  • Interdisciplinary Science
  • Mathematics

Readers

  • Game Theory.
  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.