Constrained nonzero-sum games with partially controllable strategies

The present paper deals with a class of nonzero-sum, two-person games with finite strategies when there are constraints on the strategies selected by the players. The constraints arise due to the subjective difficulty that each player often has in assigning to the states probabilities with which he is completely satisfied, and the model specifies how much each player must perturb his initial probability estimate in order to change his maximum utility alternative from the alternative originally best under the initial estimate. It is shown that the Nash-equilibrium solution of this class of nonzero-sum games can be characterized by an equivalent nonlinear program which leads in some cases to a pair of complementary eigenvalue problems. Applications to normal or approximate solutions of linear programming problems are also indicated.