Incomplete Information Mean-Field Games and Related Riccati Equations

Min Li (), Tianyang Nie (), Shujun Wang () and Ke Yan ()
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Min Li: Shandong University
Tianyang Nie: Shandong University
Shujun Wang: Shandong University
Ke Yan: Shandong University

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 3, No 15, 2487-2508

Abstract: Abstract We study a class of mean-field games with incomplete information in this paper. For each agent, the state is given by a linear forward stochastic differential equation with common noise. Moreover, both the state and control variables can enter the diffusion coefficients of the state equation. We deduce the open-loop adapted decentralized strategies and feedback decentralized strategies by a mean-field forward–backward stochastic differential equation and Riccati equations, respectively. The well-posedness of the corresponding consistency condition system is obtained and the limiting state-average turns out to be the solution of a mean-field stochastic differential equation driven by common noise. We also verify the $$\varepsilon $$ ε -Nash equilibrium property of the decentralized strategies. Finally, a network security problem is studied to illustrate our results as an application.

Keywords: Common noise; Forward–backward stochastic differential equation; Mean-field game; Incomplete information; Riccati equation; $$\varepsilon $$ ε -Nash equilibrium (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02508-0

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