Perpetrators leverage the untraceable feature to conduct illegal behaviors leading security issues with respect to mixing coins. Generally, bad coins are blocked based on a common blacklist. However, the blacklist may not be updated in time, which results in that bad coins escape the blocking. Consequently, perpetrators can still conduct illicit behaviors such as money laundering. In this paper, we apply game theory under imperfect information to study how coins' quality restrain these illicit behaviors under the incomplete scenario. More specifically, we propose a strategy for participants to submit deposits if they hope to mix coins with others even if they are not in blacklist at this time. The deposits will not be refunded when participants are included in the blacklist after mixing. Therefore, no participants have incentives to mix with bad coins. At the last part of this paper, we also simulate the incomes for participants, which indicates that deposits strategy is effective to prevent illicit behaviors.

中文翻译：

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混合不同质量硬币的博弈论方法

犯罪者利用无法追踪的特征进行非法行为，导致与混合硬币有关的安全问题。一般来说，坏币是根据一个普通的黑名单来阻止的。但是，黑名单可能没有及时更新，导致坏币逃逸。因此，犯罪者仍然可以进行洗钱等非法行为。在本文中，我们应用不完全信息下的博弈论来研究不完全情况下硬币的质量如何抑制这些非法行为。更具体地说，我们提出了一种策略，如果参与者希望将硬币与其他人混合，即使他们此时不在黑名单中，也可以提交存款。参赛者混入黑名单后，押金不予退还。所以，没有参与者有动机与坏币混合。在本文的最后一部分，我们还模拟了参与者的收入，这表明存款策略可以有效地防止非法行为。