Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2024

Linear-quadratic Stackelberg differential game: local information versus global information

Xinwei Feng
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Ying Hu
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  • IdHAL : ying-hu

Abstract

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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hal-03812039 , version 1 (12-10-2022)

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Xinwei Feng, Ying Hu, Jianhui Huang. Linear-quadratic Stackelberg differential game: local information versus global information. ESAIM: Control, Optimisation and Calculus of Variations, 2024, 30 (Paper No. 47), 41 pp. ⟨10.1051/cocv/2024037⟩. ⟨hal-03812039⟩
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