A leader-based cooperation-prompt protocol for the prisoner's dilemma game in multi-agent systems

In this paper, we propose a new protocol that prompts the cooperation rate of a multi-agent system, the members of which compete based on the prisoner's dilemma game. The main idea of this algorithm is to introduce a smart leader to the system, which can be viewed as a third player in the original bilateral game. The leader is motivated by its own benefit, but as a result of its attempt to maximum the expectational personal benefit, the system's cooperation rate is actually improved. This phenomenon is common in reality in some complicated situations. We studied the condition in which the leader maximums its expectational payoff, and proved the optimal condition's existence and uniqueness. Furthermore, we adopted a feed-back control method to ensure that the system globally converges to and remains stable in the optimal point. The simulation results illustrate the practicability and efficiency of our algorithm in reality system.