Linear-quadratic Stackelberg differential game: local information versus global information
Résumé
We first present a unified framework to fit a variety of two-person differential decision problems, including especially stochastic (zero-sum, non zero-sum) Nash game, Stackelberg game with global information. Next, solvability of these problems are also discussed via three forms respectively: an abstract quadratic functional representation, Hamiltonian system for open-loop, and Riccati equation for closed-loop (feedback). Then, we introduce a new type Stackelberg game with local information for which the classical best-response machinery used for global information is no longer workable. As resolution, a repeated game approach is employed to construct the equilibrium strategies via a backward-and forward-procedure. Moreover, connection of local information pattern to time-inconsistency is also revealed. Finally, relations among zero-sum Nash game, zero-sum Stackelberg game with global information and local information are identified.
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