Constrained games as complementary eigenvalue problems

A class of two-person nonzero sum games where the strategy choices are constrained in some form for each player is analyzed here to show the equivalent nonlinear programs which must be solved for the Cournot-Nash equilibrium. This equilibrium solution is shown in appropriate cases to lead to complementary eigenvalue problems, which have applications in normal solutions of stochastic LP models and optimal design problems in linear regression theory.