<p>In this paper, we consider a market consisted of the government and a large number of homogeneous banks with system risk. While the banks are subdivided into a set of distinct states according to the bank safety index, which includes healthy(H), sub-healthy(S), and on the verge of bankruptcy(B). This model is inspired by the SIR model of epidemics. And the transition probability between states is characterized by three market factors, which are self-operation, inter-bank and governments bailouts. From the perspective of macro and micro economy, we set up the linear quadratic games of the government and the individual banks, and solve the optimal controls by the Pontryagin maximum principle and Hamilton-Jacobi-Bellman method, respectively. As a result, we obtain the optimal government bailouts, corrected by the individual bank strategy in some specific cases. Furthermore, we give the economic explanations for the results.</p>