ϵ-Nash equilibrium of anticipative large-population LQ game with partial observations

In this paper, we study a class of large-population linear-quadratic game problem that is driven by an anticipative signal-observation system with a correlation between the initial value of the signal and the observation noise. Firstly, we utilize a method of enlargement of filtration to transform the anticipative signal-observation system into a higher-dimensional non-anticipative one, and construct an extended equivalent large-population adapted game problem. Secondly, for each individual, by separation principle, filtering theory, and squared compensatory technology, we derive a closed-form decentralized equilibrium strategy for a limiting adapted version with a freezing term instead of average state, and obtain a consistency condition consisting of a forward-backward stochastic differential system with the coefficients affected by the correlation function. Finally, we prove for the extended equivalent large-population adapted game, the & varepsilon;-Nash equilibrium properties of the decentralized strategy designed by means of locally observed information.