On n-person game solutions and convex programs with essentially unconstrained duals 1

A special class of the Charnes-Kortanek “convex nucleus” solutions Is studied in which the minimized functional is separable (monotropic). This class includes Euclidean distance, Hellinger measure, Bose-Einstein entropic measure and the Charnes-Cooper relative entropic solutions. It is shown that the dual convex programs are “essentially” unconstrained and that a simple explicit inversion formula connects optimal primal and dual solutions.