Recently, reputation-based indirect reciprocity has been widely applied to the study on fairness behavior. Previous works mainly investigate indirect reciprocity by considering compulsory participation. While in reality, individuals may choose voluntary participation according to the opponent's reputation. It is still unclear how such reputation-based voluntary participation influences the evolution of fairness. To address this question, we introduce indirect reciprocity with voluntary participation into the dictator game (DG). We respectively consider good dictators or recipients can voluntarily participate in games when the opponents are assessed as bad. We theoretically calculate the fairness level under all social norms of third-order information. Our findings reveal that several social norms induce the high fairness level in both scenarios. However, more social norms lead to a high fairness level for voluntary participation of recipients, compared with the one of good dictators. The results also hold when the probability of voluntary participation is not low. Our results demonstrate that recipients' voluntary participation is more effective in promoting the emergence of fairness behavior.

翻译：近期，基于声誉的间接互惠被广泛用于研究公平行为。以往的研究主要考虑强制参与下的间接互惠，而在现实中，个体可能根据对手的声誉选择自愿参与。这种基于声誉的自愿参与如何影响公平行为的演化尚不明确。为解决这一问题，我们将包含自愿参与机制的间接互惠引入独裁者博弈（DG）。我们分别考虑在对手被判定为不良时，良好的独裁者或接受者可以自愿参与博弈。通过理论计算，我们获得了所有三阶信息社会规范下的公平水平。研究结果表明，在两种情境下均有若干社会规范可诱导高公平水平。但与良好独裁者自愿参与相比，接受者自愿参与情境下能实现高公平水平的社会规范更多。当自愿参与概率不低于某一阈值时，该结论依然成立。我们的结果证明，接受者的自愿参与能更有效地促进公平行为的涌现。