Coevolution of consensus and cooperation in evolutionary Hegselmann–Krause dilemma with the cooperation cost. (March 2023) - Huang, Changwei; Hou, Yongzhao; Han, Wenchen
Abstract: In this work, we focus on the opinion consensus involved with evolutionary games based on Hegselmann–Krause model. Agents can choose to be defective, unwilling to change their opinions, or cooperative, willing to change opinions following the ordinary Hegselmann–Krause rule. The payoff of an agent is assumed as the local benefit, depicting the local consensus around this agent, paying the opinion variation cost, the effort to change the agent's opinion. Increasing the cost hinders the preference of cooperation and suppresses forging consensus. On the contrary, increasing the bounded confidence, as well as the average degree, helps agents gain a higher benefit and reach consensus. The consensus is the tradeoff between supportive factors, a high confidence bound or a large average degree, and the drawback, a high variation cost. When these two competitive factors share a same strength, it costs the longest time for the population reaching consensus. It is verified by numerical simulations on not only scale-free networks but also Erdös-Rényi random networks. Highlights: The coevolution of consensus and cooperation with costly interactions in complex networks is studied. Increasing the cost hinders the preference of cooperation and suppresses forging consensus. Increasing the bounded confidence, as well as the average degree, helps agents gain a higher benefit and reach consensus.