The multi-agent collaborative pursuit problem is a typical problem in the multi-agent coordination and collaboration research. Aiming at the pursuit problem of single escaper with learning ability, a multi-agent collaborative pursuit algorithm based on game theory and Q-learning was proposed. Firstly, a cooperative pursuit team was established and a game model of cooperative pursuit was built. Secondly, through the learning of the escaper’s strategy choices, the trajectory of the escaper’s limited Step-T cumulative reward was established, and the trajectory was adjusted to the pursuer’s strategy set. Finally, the Nash equilibrium solution was obtained by solving the cooperative pursuit game, and the equilibrium strategy was executed by each agent to complete the pursuit task. At the same time, in order to solve the problem that there may be multiple equilibrium solutions, the virtual action behavior selection algorithm was added to select the optimal equilibrium strategy. C# simulation experiments show that, the proposed algorithm can effectively solve the pursuit problem of single escaper with learning ability in the obstacle environment, and the comparative analysis of experimental data shows that the pursuit efficiency of the algorithm under the same conditions is better than that of pure game or pure learning.

For the complex tasks with time constraints, which can dynamically be added to environment, a task allocation model based on game theory was established, and a task allocation method was proposed, which made Computer Generated Actor (CGA) be able to choose its actions according to the local information owned by itself, and ensured that CGA learned a strict pure strategy Nash equlilibrium quickly by using fictitious play method on behavior coordination. The simulation results show that this method is reasonable, and it can effectively solve the dynamic task allocation problem.