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Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models by Moon, Jun; Kim, Wonhee is a Mathematics article available to read on EtoBox.
What is Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models about?
We consider the indefinite, linear-quadratic, mean-field-type stochastic zero-sum differential game for jump-diffusion models (I-LQ-MF-SZSDG-JD). Specifically, there are two players in the I-LQ-MF-SZSDG-JD, where Player 1 minimizes the objective functional, while Player 2 maximizes the same objective functional. In the I-LQ-MF-SZSDG-JD, the jump-diffusion-type state dynamics controlled by the two players and the objective functional include the mean-field variables, i.e., the expected values of state and control variables, and the parameters of the objective functional do not need to be (positive) definite matrices. These general settings of the I-LQ-MF-SZSDG-JD make the problem challenging, compared with the existing literature. By considering the interaction between two players and using the completion of the squares approach, we obtain the explicit feedback Nash equilibrium, which is linear in state and its expected value, and expressed as the coupled integro-Riccati differential equations (CIRDEs). Note that the interaction between the players is analyzed via a class of nonanticipative strategies and the “ordered interchangeability” property of multiple Nash equilibria in zero-
Who reads Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Moon, Jun; Kim, Wonhee
- Publisher
- MDPI AG; Basel: MDPI AG, 2013- (ISSN 2227-7390)
- Published
- 2020
- Language
- EN
- Field
- Mathematics (Physical Sciences)