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

✍ Scribed by Baoline Chen; Peter A. Zadrozny

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 191 KB
• Volume: 26
• Category: Article
• ISSN: 0165-1889
• DOI: 10.1016/s0165-1889(01)00077-x

✦ Synopsis

This paper derives and illustrates a new suboptimal-consistent feedback solution for an inÿnitehorizon, linear-quadratic, dynamic, Stackelberg game. This solution lies in the same solution space as the inÿnite-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 inÿnite-horizon, linear-quadratic, dynamic, Stackelberg game by varying the coe cients in the player's linear constant-coe cient 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.