In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming duality and the finite intersection property of compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum game theory. In the last section we apply these results to derive necessary and sufficient conditions for strong Lagrangean duality for a large class of optimization problems.

Lagrangian and linear programming duality, finite dimensional separation, game theory, minimax theory
hdl.handle.net/1765/1219
Econometric Institute Research Papers
Erasmus School of Economics

Frenk, J.B.G, Kas, P, & Kassay, G. (2004). On linear programming duality and necessary and sufficient conditions in minimax theory (No. EI 2004-14). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/1219