An anticipative feedback solution for the infinite-horizon, linear-quadratic, dynamic, Stackelberg game

Abstract 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 Kydland (J. Econ. Theory 15 (1977)) 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.

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