Linear-Quadratic Two-Person Differential Game: Nash Game Versus Stackelberg Game, Local Information Versus Global Information

Xinwei Feng, Ying Hu, Jianhui Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)1-41
Number of pages41
JournalESAIM - Control, Optimisation and Calculus of Variations
DOIs
Publication statusPublished - Jun 2024

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