Optimally Combined Incentive for Cooperation Among Interacting Agents in Population Games

• 成果类型: Article
• 署名作者: Wang, Shengxian; Cao, Ming; Chen, Xiaojie
• 署名单位: Anhui Normal University; University of Electronic Science & Technology of China; University of Groningen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3529852
• 发表日期: 2025
• 页码: 4562-4577
• 关键词: costs; games; Protocols; stem; mathematical models; incentive schemes; indexes; computer simulation; TOPOLOGY; Stability criteria; Cooperative behavior; evolutionary game theory; Hamilton-Jacobi-Bellman equation; optimal control theory; optimally combined incentive protocol

摘要

Combined prosocial incentives, integrating reward for cooperators and punishment for defectors, are effective tools to promote cooperation among competing agents in population games. Existing research concentrated on how to adjust reward or punishment, as two mutually exclusive tools, during the evolutionary process to achieve the desired proportion of cooperators in the population, and less attention has been given to exploring a combined incentive-based control policy that can steer the system to the full cooperation state at the lowest cost. In this work, we propose a combined incentive scheme in a population of agents whose conflicting interactions are described by the prisoner's dilemma game on complete graphs and regular networks, respectively. By devising an index function for quantifying the implementation costs of the combined incentives, we analytically construct the optimally combined incentive protocol by using optimal control theory. By means of theoretical analysis, we identify the mathematical conditions, under which the optimally combined incentive scheme requires the minimal amount of cost. In addition to numerical calculations, we further perform computer simulations to verify our theoretical results and explore their robustness on different types of network structures.