@article{Zhou2022, 
author = {Qinglong Zhou and Gaofeng Zong},
title = {A stochastic linear-quadratic differential game with time-inconsistency},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {7},
pages = {2550-2567},
keywords = {time-inconsistency, stochastic linear-quadratic differential game, equilibrium strategy, BSDE, forward-backward stochastic differential equation},
url = {https://www.sciopen.com/article/10.3934/era.2022131},
doi = {10.3934/era.2022131},
abstract = {We consider a general stochastic linear-quadratic differential game with time-inconsistency. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and derive a sufficient condition for equilibrium strategies via a system of forward-backward stochastic differential equation. When the state is one-dimensional and the coefficients are all deterministic, we find an explicit equilibrium strategy. The uniqueness of such equilibrium strategy is also given.}
}