Games with Unique Solutions Which Are Nonconvex

by W. F. Lucas

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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.

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