Norm Establishment with Punishment Qualification Constraint for the Metanorm Game Model

In an autonomous system, rational agents aim to maximize their benefits. Whereas selfish agents gradually give up cooperation with others and only request services, which leads to the phenomenon of Free-riding. This phenomenon generally exists in the real society and application system. Therefore, how to reduce the behavior which is similar to free-riding has become an important research topic. Social norms provide an effective way to promote cooperation for autonomous systems. Axelrod's metanorm game model achieves the emergence of social norms by conducting punishment to connivance based of punishing defection. However, from a practical point of view, not everyone is qualified to punish pampers. Therefore, this paper develops an Qualification of Law Enforcement (QOLE) model to solve the limitation the metanorm model. The norm emergence of the QOLE model is examined on the Boldness and Vengefulness Learning (BVL) algorithm with the Monte Carlo simulation procedure, and it is found that the norm of Qualification of Law Enforcement model cannot be established in the lattice, small-world network and scale-free network. Therefore, we propose an improved learning algorithm based on the historical knowledge of the punishment omission score of agents and solve the limitation of BVL algorithm. Moreover, it overcomes the limitation of the original metanorm model cannot be established on the scale-free network.