An Anticipative Feedback Solution for Infinite-Horizon Linear-Quadratic Dynamic Stackelberg Games

The purpose of the paper is to derive and illustrate a new suboptimal-consistent feedback solution for infinite-horizon linear-quadratic dynamic Stackelberg games which is in the same solution space as the infinite-horizon dynamic programming feedback solution, but which puts the leader in a preferred equilibrium position. The idea for the solution comes from Kydland's (1977) suggestion to derive a consistent feedback solution (where "feedback" is understood in the general sense of setting a current control vector as a function of a predetermined state vector) for an infinite-horizon linear-quadratic dynamic Stackelberg game by varying coefficients in players' linear constant-coefficient decision rules. The proposed solution is derived for discrete- and continuous-time versions of the game and is called the anticipative feedback (AF) solution. The AF solution is illustrated with a numerical example of a duopoly model.