Symmetric dual nonlinear programming and matrix game equivalence ✩

We present some equivalences between some symmetric dualities in nonlinear programming and some matrix games. We study three pairs of dual problems: Wolfe, Mond–Weir and fractional types. For each pair, the paper presents two different zero-sum games whose Nash equilibria correspond to the solutions of the pair of nonlinear symmetric dual problems. And certain conclusions about symmetric dual fractional programming and its special cases are also treated.  2004 Elsevier Inc. All rights reserved.