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, under the scenario of endogenous timing, and 1) the assumption that the foreign bank’s deposit return rate is more than twice that of the state-owned bank and 2) the degree of nationalization of state-owned bank is no less that 1/4, the SPNE of deposit extended game is (L, L), i.e. both banks will choose to move later, neither player has so called “first mover advantage” which leads to the Cournot outcome and payoffs. When the degree of privatization is more than 3/4 and both banks have the same deposit return rate, the SPNE of interest rate extended game is (E, L), i.e. the state-owned bank will lead and the foreign bank will follow.