Based on the background of the banking industry in China, this paper establishes Cournot, Bertrand and Stackelberg mixed oligopoly competition models with deposit and interest rates as strategic variables between a representative state-owned bank and a representative foreign bank. We discuss and compare the equilibrium deposits, interest rates and profits in different market structures. More importantly, considering the endogenous timing setup and taking the extended game with observable delay as the basic model, we analyze the competition results of the mixed duopoly at different market structures and make numerical simulations in order to get the outcomes of the extended game. It is found that, in the deposit competition with endogenous timing, if two banks have the same deposit return rate, the simultaneous move could become the final result; If the deposit return of the foreign bank is more than twice that of the state-owned bank, all SPNEs of the extended game are sequential, i.e one bank will lead, the other will follow. If the state-owned bank’s profit in Cournot is larger than that of the state-owned bank as the Stackelberg follower, the only SPNE will be (E, L), i.e. the state-owned bank will lead and the foreign bank will follow. Additionally, in the interest rate competition with endogenous timing, if the degree of nationalization is no larger than 75% as well as two banks have the same deposit return rate, the final SPNEs of the extended game are sequential and the simultaneous move can not become the SPNE.