Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 47 | |
Number of page(s) | 41 | |
DOI | https://doi.org/10.1051/cocv/2024037 | |
Published online | 11 June 2024 |
Linear-quadratic two-person differential game: Nash game versus stackelberg game, local information versus global information
1
Zhongtai Securities Institute for Financial Studies, Shandong University,
Jinan,
Shandong
250100,
PR China
2
Univ Rennes, CNRS,
IRMAR-UMR 6625,
F-35000
Rennes,
France
3
Department of Applied Mathematics, The Hong Kong Polytechnic University,
Hong Kong
* Corresponding author: xwfeng@sdu.edu.cn
Received:
1
May
2023
Accepted:
15
April
2024
In this paper, we present a unified framework to study a variety of two-person dynamic decision problems, including stochastic (zero-sum, non-zero-sum) Nash game, Stackelberg game with global information. For these games, the solvability of these problems is discussed via progressive formulations respectively: the abstract quadratic functional, Hamiltonian system for open-loop, and Riccati equation for closed-loop (feedback) representation. Based on the unified framework, time consistency/inconsistency property of related equilibrium is studied. Then we introduce a new type of game, Stackelberg game with local information. For this, the classical best-response machinery adopted 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 also identified.
Mathematics Subject Classification: 93E20 / 49N10
Key words: Nash game / Stackelberg game / global information / local information / repeated game / time-consistency/inconsistency / backward—forward procedure
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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