When realizing multiagent optimal consensus control, it may encounter the situation that malicious agents transmit false information. Besides, due to the unreliability of information interaction and the uncertainty of the system itself, the agent may not fully know its own cost function. In this article, an improved Bayesian graphical game method is proposed to solve the optimal consensus problem of linear dynamical networks in the presence of false information. The agent’s probabilistic estimate of the uncertainty is named belief, and the update of probability estimate is named belief update. An information tradeoff principle is designed to solve the belief update problem in the presence of malicious neighbors. The principle can not only reduce the loss caused by false information but also force malicious agents to switch from deception to cooperation. On this basis, a new belief update method with information tradeoff principle is established. It is proved that this new belief update method has a faster convergence rate than the Bayesian belief update method when malicious neighbors exist. As an illustrative example, the graphical game solution is applied to the formation tracking control problem of a quad-rotor unmanned aerial vehicle swarm. Theoretical proof and simulation comparisons can illustrate the proposed method’s advantages.