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access icon free Linear-quadratic mean-field game for stochastic large-population systems with jump diffusion

  • Author(s): Min Li 1 ; Na Li 2 ; Zhen Wu 1
    • View affiliations
  • Source: Volume 14, Issue 3, 12 February 2020, p. 481 – 489
    DOI:  10.1049/iet-cta.2019.0270 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 11/03/2019, Accepted 04/11/2019, Revised 29/09/2019, Published 06/11/2019

This study is concerned with linear-quadratic mean-field game problem for a class of stochastic large-population systems with Poisson processes. The control is allowed to enter the jump diffusion terms of the individuals' state equation. By virtue of the stochastic Hamiltonian system and Riccati equation for limiting control problem, the decentralised optimal strategies are represented in the open-loop and closed-loop forms, respectively. Different from the existing results, the limit representation of average term is proposed in closed-loop form via the separation technique. Meanwhile, the decentralised optimal strategies are verified to be the -Nash equilibrium of the original problem. Finally, two practical control problems in engineering and economics areas are presented to demonstrate the good performance of theoretical results.

Inspec keywords: stochastic systems; Riccati equations; stochastic processes; closed loop systems; linear quadratic control; stochastic games; game theory

Other keywords: decentralised optimal strategies; linear-quadratic mean-field game; mean-field game problem; average term; practical control problems; Poisson processes; stochastic large-population systems; limit representation; closed-loop form; jump diffusion; Riccati equation; control problem; open-loop; individuals; stochastic Hamiltonian system

Subjects: Optimal control; Game theory; Probability theory, stochastic processes, and statistics

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