标题： 资产交换模型中的欺骗特征 显示英文标题

标题： Hallmarks of Deception in Asset-Exchange Models

摘要： 我们研究了在存在概率作弊者的情况下，Bennati-Dragulescu-Yakovenko金钱游戏的瞬态和稳态动力学，这些作弊者可以通过声称自己没有钱来隐瞒自己的财务状况。 我们分析地推导了每个玩家的稳态财富分布，并展示了如何从每个玩家的财富相对方差中推断出隐藏作弊者的存在。 在有限数量的作弊者与无限多诚实玩家共存的情景中，我们确定了一个临界作弊概率，在该概率下，作弊者拥有的总财富会发生二阶不连续变化。 在此点以下，失去金钱的转移概率大于获得金钱的概率；相反，在此点以上，方向则相反。 我们进一步确定了一个临界作弊概率，此时作弊者集体拥有游戏中一半的总财富。 最后，我们提供了作弊者和诚实玩家可以增减财富的速率的界限，有助于更深入地理解资产交换模型中的欺骗行为。 显示英文摘要

摘要： We investigate the transient and steady-state dynamics of the Bennati-Dragulescu-Yakovenko money game in the presence of probabilistic cheaters, who can misrepresent their financial status by claiming to have no money. We derive the steady-state wealth distribution per player analytically, and show how the presence of hidden cheaters can be inferred from the relative variance of wealth per player. In scenarios with a finite number of cheaters amidst an infinite pool of honest players, we identify a critical probability of cheating at which the total wealth owned by the cheaters experiences a second-order discontinuity. Below this point, the transition probability to lose money is larger than the probability to gain; conversely, above this point, the direction is reversed. We further establish a threshold cheating probability at which cheaters collectively possess half of the total wealth in the game. Lastly, we provide bounds on the rate at which both cheaters and honest players can gain or lose wealth, contributing to a deeper understanding of deception in asset exchange models.