An anticipative feedback solution for the infinite-horizon, linear-quadratic, dynamic, Stackelberg game.
This paper derives and illustrates a new suboptimal-consistent feedback solution for an infinite-horizon, linear-quadratic, dynamic, Stackelberg game. This solution lies in the same solution space as the infinite-horizon, dynamic-programming, feedback solution but puts the leader in a preferred equilibrium position. The idea comes from \textit{F. Kydland} [J. Econ. Theory 15, 307--324 (1977; Zbl 0375.90089)] who suggested deriving a consistent feedback solution for an infinite-horizon, linear-quadratic, dynamic, Stackelberg game by varying the coefficients in the player's linear constant-coefficient decision rules. Here feedback is understood in the sense of setting a current control vector as a function of a predetermined state vector. The proposed solution is derived for discrete- and continuous-time games and is called the anticipative feedback solution. The solution is illustrated with a numerical example of a duopoly model.
scientific article; zbMATH DE number 1768095
scientific article