The existing literature on portfolio optimization generally assumes that investors are independent,and the returns of underlying assets are not correlated among different periods. In reality,however,investors often relate to each other,and the return series always have some dependencies among different time periods.Under the framework of the multi-period portfolio optimization and Nash equilibrium theories,using the relative performance of investors to describe their game behaviors,a multi-period portfolio game model is constructed which maximizes the expected utility of the relative terminal wealth of each investor. With the assumption of correlated return series,the analytical solutions of Nash equilibrium investment strategy and the corresponding value function are derived,and the relationship between the strategies derived from Nash equilibrium and the traditional ones is described. Finally,a simulation analysis of the two investment strategies,by using cumulative empirical distribution function and Sharpe index to compare the performance of the two strategies' is conducted,and how Nash equilibrium investment strategies change with the different coefficients of the investors' response sensitivity is analyzed. Results show that,when considering the relative performance of competitors,investors of Nash equilibrium,with respect to traditional investors,are more willing to tolerate higher risks to pursue higher profits,and the greater the response sensitivity coefficients,the higher risk they prefer.