This paper uses a distributed approach fault tolerant control to solve the Nash equilibrium (NE) search problem for integral multi-agent systems (MAS) subject to undesirable sensor faults. In partial information games, information exchange between agents plays an essential role in ensuring the successful completion of the NE search. A flexible observer-based control algorithm has been proposed to compensate for the adverse effects of sensor faults. It reduces the influence of sensor faults on group decisions-making and realizing the optimization of group strategy. The distributed design can guarantee that the MAS can gradually approach the NE regardless of sensor faults. Finally, the effectiveness of the technology is illustrated through a simulation example.