The present study is presented in order to determine the optimal investment portfolios between a bank and its customers, in the form of a two-level game by Stackelberg (leader-follower). The game is based on the Markowitz mean-variance model. Leader player portfolios (Bank 3) have included deposit portfolios in rival banks (Banks 1 and 2), investment in the real estate market, investment in the stock market and investment in the foreign exchange market. Also follower player portfolios (Bank 3 customers), including deposits in rival Banks(1,2), investment in the coin and gold market, investment in the foreign exchange market, investment in the housing and real estate market, investment in the car market, investment in the stock market. The data related to the mentioned assets covered 2009-2017, where the optimal investment portfolios of the players was first determined using GAMS software. Next, the problem was solved again using the meta-heuristic algorithm of Firefly in Matlab Software. Eventually, the optimal technique was chosen. Finally, the results of the study showed that the optimal investment portfolios for the leader player include investing in the real estate market and investing in the stock market, respectively. Also, the optimal investment portfolios of the following player include depositing in Bank 2, investing in the coin and gold market, investing in the stock market and investing in the real estate market, respectively. Manuscript profile