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Finding saddle points on polyhedra: Solving certain continuous minimax problems
Author(s) -
Monahan George E.
Publication year - 1996
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/(sici)1520-6750(199609)43:6<821::aid-nav3>3.0.co;2-6
Subject(s) - polyhedron , minimax , saddle point , computer science , stochastic game , mathematical optimization , mathematical economics , regular polygon , identification (biology) , saddle , nash equilibrium , mathematics , combinatorics , botany , geometry , biology
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. © 1996 John Wiley & Sons, Inc.