AI 中文总结
研究黑手党游戏中累积怀疑与吸收动力学，引入基于代理公式，玩家依角色改怀疑分数，幸存玩家按累积怀疑概率被淘汰，经模拟研究人口规模等影响，还探讨侦探作用，模型建立微观与宏观联系。
AI 中文摘要
黑手党游戏（又称狼人游戏）描述了一个身份被隐藏的少数协调群体与一个主要由不知情平民组成的较大善良阵营之间的竞争，平民试图识别并消灭前者。我们引入了一种基于代理的公式，其中白天的决策不是通过统一随机投票来表示。相反，随机配对的代理根据他们的角色修改特定玩家的公共怀疑分数，随后一名幸存玩家以与其累积怀疑成正比的概率被淘汰。这些分数在整个游戏中持续存在，产生了一个依赖历史的随机过程，有两个相互竞争的吸收结果：黑手党被消灭或黑手党与善良阵营之间的数量平衡。我们通过广泛的蒙特卡罗模拟研究了人口规模、初始黑手党规模和完全知情侦探的存在的影响。在没有侦探的情况下，随机执行近似预测，在黑手党稀释和早期阶段，黑手党灭绝的累积概率表现为$F(\tau)\sim (\tau/N)^{N_m}$，与模拟结果一致，随着$N_m/N$的减小。获胜概率曲线还表现出以人口规模$N_c$为特征的经验有限大小交叉。通过$N_c$重新缩放人口大致使不同初始黑手党人口获得的曲线坍缩。完全知情的侦探大大缩短了黑手党生存时间，并引入了对人口组成的额外依赖，对于这种依赖，相同的单参数重新缩放是不够的。该模型提供了微观指控历史与隐藏角色游戏宏观吸收统计之间的最小联系。
英文摘要
The Mafia game, also known as Werewolf, describes a competition between a coordinated minority whose identities are concealed and a larger good faction composed primarily of uninformed civilians attempting to identify and eliminate them. We introduce an agent-based formulation in which the daytime decision is not represented by uniform random voting. Instead, randomly paired agents modify player-specific public suspicion scores according to their roles, and one surviving player is subsequently eliminated with probability proportional to their accumulated suspicion. These scores persist throughout the game, producing a history-dependent stochastic process with two competing absorbing outcomes: elimination of the mafia or numerical parity between the mafia and the good faction. We investigate the effects of population size, initial mafia size, and the presence of perfectly informed detectives through extensive Monte Carlo simulations. In the absence of detectives, a random-execution approximation predicts that, in the dilute-mafia and early-time regime, the cumulative probability of mafia extinction behaves as $F(τ)\sim (τ/N)^{N_m}$, in agreement with simulations as $N_m/N$ decreases. The winning-probability curves also exhibit an empirical finite-size crossover characterized by a population scale $N_c$. Rescaling the population by $N_c$ approximately collapses the curves obtained for different initial mafia populations. Perfectly informed detectives substantially shorten mafia-survival times and introduce an additional dependence on population composition for which the same one-parameter rescaling is insufficient. The model provides a minimal connection between microscopic histories of accusation and the macroscopic absorption statistics of hidden-role games.
Comments9 pages, 4 figures
