In the mutual fund investment, two critical decisions to be made are the quantity of shares purchased by investors and the portfolio choice rule by mutual fund manager. By recognizing the fact that the payoffs of the two agents are closely related to their jointly dynamic fund flows, which are considerably affected by the flows of investors' uninsurable labor income, we show that, the two agents' decisions will appear to be strategically interdependent and it can be analyzed in a manner of stochastic differential game. In this paper, we also show that whether one agent's decision will take into account another agent's risk attitude depends on their cooperative relationship. We conclude that, instead of the absolute value of risk aversion level commonly supported by single agent model, the investment decision in a simultaneous two-agent game model is related to the relative level of their risk aversion degree.