This work contributes to the field of human-system interaction modeling through an artificial intelligence approach. It focuses on the cooperative realization of a complex task. For this purpose, we propose a human-agent interaction model based on game theory to describe the decision making between the human operator and the assistant agent. The proposed model is based on searching Nash equilibria for a repeated two-player game in which each player has a choice between two actions. In particular, the assistant agent knows how to calculate the equilibrium that depends on information coming from the context (human operator and work environment). This approach allows us to consider a context aware human-machine system. Then, the assistant agent knows how to optimize its intervention with regard to the human operator assisted by this agent during a complex task. For the validation of our model, we highlight the efficiency of the assistant agent using this principle by considering a road traffic simulator using Netlogo. An analysis of the simulation results is provided to illustrate the effectiveness of our approach.