A Feedback Nash Equilibrium for Affine-Quadratic Zero-Sum Stochastic Differential Games With Random Coefficients
- Title
- A Feedback Nash Equilibrium for Affine-Quadratic Zero-Sum Stochastic Differential Games With Random Coefficients
- Author
- 문준
- Keywords
- Stochastic systems; game theory; stochastic optimal control
- Issue Date
- 2020-10
- Publisher
- Institute of Electrical and Electronics Engineers Inc.
- Citation
- IEEE Control Systems Letters, v. 4, no. 4, page. 868-873
- Abstract
- We study the affine-quadratic zero-sum stochastic differential game with random coefficients, where the coefficients of the stochastic differential equation (SDE) are random processes and both additive and state multiplicative noise are included in the diffusion term of the corresponding SDE. By applying Itô-Kunita's formula to the quadratic random field, we develop a direct approach, also known as the completion of squares method, to characterize the explicit (feedback) Nash equilibrium and obtain the optimal game value. The characterized Nash equilibrium depends linearly on the state and the additional linear backward SDE. We also verify the optimality of the Nash equilibrium by characterizing the smooth solution of the stochastic Hamilton-Jacobi-Isaacs equation that is the second-order stochastic partial differential equation obtained from dynamic programming.
- URI
- https://ieeexplore.ieee.org/document/9094058https://repository.hanyang.ac.kr/handle/20.500.11754/172089
- ISSN
- 2475-1456
- DOI
- 10.1109/LCSYS.2020.2994642
- Appears in Collections:
- COLLEGE OF ENGINEERING[S](공과대학) > ELECTRICAL AND BIOMEDICAL ENGINEERING(전기·생체공학부) > Articles
- Files in This Item:
There are no files associated with this item.
- Export
- RIS (EndNote)
- XLS (Excel)
- XML