Trust plays an important role in human society. However, how does trust evolve is a huge challenge. The trust game is a well-known paradigm to measure the evolution of trust in a population. Reward and punishment as the common types of incentives can be used to improve the trustworthiness. However, it remains unclear how reward and punishment actually influence the evolutionary dynamics of trust. Here, we introduce individual reward and punishment into the N-player trust game model in an infinite well-mixed population, where investors use a part of the returned fund to reward trustworthy trustees and meanwhile punish untrustworthy trustees. We then investigate the evolutionary dynamics of trust by means of replicator equations. We show that the introduction of reward and punishment can lead to the stable coexistence state of investors and trustworthy trustees, which indicates that the evolution of trust can be greatly promoted. We reveal that the attraction domain of the coexistence state becomes larger as investors increase the incentive strength from the returned fund for reward and punishment. In addition, we find that the increase of the reward coefficient can enlarge the attraction domain of the coexistence state, which implies that reward can better promote the evolution of trust than punishment.

信任在人类社会中扮演着重要的角色。然而，信任如何演变是一个巨大的挑战。信任博弈是一种众所周知的范式，用于衡量群体中信任的演变。奖励和惩罚作为常见的激励类型可以用来提高可信度。然而，目前尚不清楚奖励和惩罚实际上如何影响信任的进化动态。在这里，我们将个体奖励和惩罚引入到N- 无限混合群体中的玩家信任博弈模型，投资者用一部分返还的资金奖励可信赖的受托人，同时惩罚不值得信赖的受托人。然后，我们通过复制器方程研究信任的进化动力学。我们表明，奖励和惩罚的引入可以导致投资者和可信赖受托人的稳定共存状态，这表明可以极大地促进信任的演变。我们发现，随着投资者增加回报基金的奖励和惩罚的激励强度，共存状态的吸引域变得更大。此外，我们发现奖励系数的增加可以扩大共存状态的吸引力域，