Research on reputation-based indirect reciprocity has found profound achievements, elucidating its role in promoting cooperation over selfish actions. However, some evaluation methodologies have limitations, such as the image scoring model, a classic first-order paradigm. Several studies have suggested that higher-order rules with more individual information can enhance the stability of cooperation. In this study, we introduce a reputation incentive mechanism to explore the cooperative differences among various evaluation rules. Specifically, players evaluate their opponents' actions following first-order and second-order evaluation rules, respectively. Given that players possess varying degrees of social influence, the evaluative intensity is influenced by the neighbor environment and updated in each round. This resultant fluctuations in reputation exhibit heterogeneity and dynamism. Numerical simulations based on the spatial prisoner's dilemma game demonstrate that under stringent conditions, the first-order rule can sustain cooperation, while the second-order rule may fail, leading to complete group defection. Under more relaxed conditions, the second-order rule proves more effective in promoting full cooperation than the first-order rule. Our research contributes to understanding the guidance and influence of reputation on collective behavior.

中文翻译：

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空间囚徒困境博弈中声誉评价规则的合作稳定性分析


基于声誉的间接互惠研究取得了深远的成果，阐明了其在促进合作而非自私行为方面的作用。然而，一些评估方法存在局限性，例如图像评分模型，这是一种经典的一阶范式。多项研究表明，具有更多个体信息的高阶规则可以增强合作的稳定性。在本研究中，我们引入了声誉激励机制来探索各种评估规则之间的合作差异。具体来说，玩家分别按照一阶和二阶评估规则评估对手的行为。由于玩家具有不同程度的社会影响力，因此评价强度会受到周围环境的影响并在每轮中更新。由此产生的声誉波动表现出异质性和动态性。基于空间囚徒困境博弈的数值模拟表明，在严格条件下，一阶规则可以维持合作，而二阶规则可能会失败，导致群体完全背叛。在更宽松的条件下，二阶规则比一阶规则更能有效促进充分合作。我们的研究有助于理解声誉对集体行为的指导和影响。