Finding saddle points on polyhedra: Solving certain continuous minimax problems

Finding saddle points on polyhedra: Solving certain continuous minimax problems

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Article ID: iaor1997656
Country: United States
Volume: 43
Issue: 6
Start Page Number: 821
End Page Number: 838
Publication Date: Sep 1996
Journal: Naval Research Logistics
Authors:
Abstract:

This article reviews procedures for computing saddle points of certain continuous concave-convex functions defined on polyhedra and investigates 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 finite number of alternatives. Equilibrium solutions to these two-person games are particularly easy to compute under a proportional effectiveness hypothesis, either in closed form or in a finite number of steps. One of the more interesting qualitative properties we establish is the identification of conditions under which the maximizing player can ignore the values of the alternatives in determining allocation decisions.

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