Emergence of Social Norms in Metanorms Game With High-Order Interaction Topology

Abstract

In an autonomous system, rational agents aim to maximize their benefits. Rational 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. In addition, the traditional pairwise interaction network cannot truly reflect the interaction properties of cooperative events. 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 on punishing defection. However, links in networks only allow for pairwise interactions. Therefore, we introduce hypergraphs, which are more suitable to reflect group interaction to model metanorm games. The establishment efforts of norms are examined on hypergraphs (uniform random hypergraph (URH), hyperdegree-heterogeneous random hypergraphs, and real-world hypergraphs). We show that the difference in group sizes affects norms emergence of agents and realize the establishment of social norms on URH. To a certain extent, the probability of being seen is positively correlated with agents' vengefulness and learning time and negatively correlated with boldness. However, the usage of the boldness and vengefulness learning (BV-learning) algorithm on HRHs cannot make norms emergence because leavers cannot participate in learning and the fixed learning step. Therefore, we propose the dynamic relevance BV-learning algorithm to overcome the aforementioned problems, so hub agents and leavers can jointly establish better social norms. We also verify the evolution process of agents' cooperation rate by BV-learning and the dynamic relevance BV-learning, respectively, which demonstrate that the establishment of social norms can indeed promote agents' cooperation. Finally, in order to illustrate the universality of the dynamic relevance BV-learning clearly, we study norms establishment on real-world hypergraphs by and compare it with BV-learning. It can be found that the dynamic relevance BV-learning can effectively establish social norms on real-world hypergraphs.