This paper deals with non-zero sum differential game with a focus on the pursuit-evasion problem. The ideas of differential game theory and cooperative control are integrated to cope with practical situations in which the information sharing is distributed and may change in time. First, if the game is under global information, linear feedback Nash strategies for single-pursuer single-evader and multiple-pursuer single-evader are derived sequentially. Then, if the game is under distributed information, i.e., players have limited information of others, the distributed Nash strategies are designed since the classical approach is not capable to handle the lack of information. Finally, simulation results are presented for those cases.