Adaptive Incentive Controls for Stackelberg Games with Unknown Cost Functionals

摘要

This thesis used the certainity equivalence approach and the theory of self-tuning regulators to derive an iterative method which generates an optimal incentive control for the leader in a static, two-player Stackelberg game with unknown cost functionals. The method uses all available degrees of freedom to restrict the incentive matrix to a diagonal structure. This restriction assures the leader of a unique optimal incentive control. Convergence to the optimal incentive control has been proven for the scalar problem and simulation studies have shown good convergence results for the second order problem. It is expected that this method is extendable in its present form to a general n-th order problem. The iterative method is applied to a scalar economic example involving government regulation of a monopoly. A simulation study of the problem revealed that the desired regulation was indeed achieved. The effectiveness of the method is demonstrated on a general second order numerical problem. Future research regarding application of optimal incentive controls to Stackelberg games with unknown cost functionals may now focus on two general areas. Starting with the iterative method detailed in this thesis, one may abandon the diagonal incentive matrix structure and attempt to use the resulting degrees of freedom to satisfy other useful criteria. An example of this is given by the minimum sensitivity design approach mentioned earlier. It is desirable to extend the existing methods to dynamical systems and to problems involving more than two players.