FINDING SADDLE-POINTS ON POLYHEDRA - SOLVING CERTAIN CONTINUOUS MINIMAX PROBLEMS

This article reviews procedures for computing saddle points of certain continuous concave-convex functions defined on polyhedra and investig ates how certain parameters and payoff functions influence equilibrium solutions. The discussion centers on two widely studied applications: missile defense and market-share attraction games. In both settings, each player allocates a limited resource, called effort, among a finit e number of alternatives. Equilibrium solutions to these two-person ga mes are particularly easy to compute under a proportional effectivenes s hypothesis, either in closed form or in a finite number of steps. On e of the more interesting qualitative properties we establish is the i dentification of conditions under which the maximizing player can igno re the values of the alternatives in determining allocation decisions. (C) 1996 John Wiley & Sons, Inc.