发表机构
Indian Statistical Institute（印度统计研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过统计与博弈论框架分析三人拍卖桥牌，发现原始计分规则存在激励缺陷，提出叫牌依赖修正，并利用GS-CFR等方法证明修改方案显著改变收益分配与叫牌行为，凸显计分规则设计的重要性。
AI 中文摘要
三人拍卖桥牌是一种有限不完全信息博弈，其中动态伙伴关系在计分、战略激励和收益分配之间创造了独特的相互作用。本文开发了一个统一的统计与博弈论框架，用于评估传统计分规则与旨在改善战略激励的修改机制。我们首先识别了原始方案中的一个结构性缺陷：与叫牌无关的满贯奖金可能使较低合约严格比更高合约更具吸引力。一种与叫牌相关的修正消除了这种激励扭曲。然后，我们使用高阶矩分析、公平性度量、纳什均衡分析和一般和反事实遗憾最小化（GS-CFR）来比较这两种方案。结果显示收益分布形状存在显著差异，并揭示尽管两种方案在物理座位间保持高度平衡，修改方案在战略角色间显著增加了不平等性。该博弈被证明既非零和也非常和，这促使采用一般和而非极小极大分析。完整博弈的GS-CFR进一步表明，在修改方案下，叫牌方的收益大幅增加，同时防守方收益减少，并且叫牌行为从分离型转向部分混同型。这些发现表明，计分规则设计可以从根本上重塑不完全信息博弈中的激励、收益分配和信息传递。所提出的框架提供了一种系统的方法，从统计和战略两个角度评估此类机制。
英文摘要
Three-player Auction Bridge is a finite imperfect-information game in which dynamic partnerships create a distinctive interaction between scoring, strategic incentives, and payoff distribution. This paper develops a unified statistical and game-theoretic framework to evaluate a traditional scoring rule against a modified mechanism designed to improve strategic incentives. We first identify a structural defect in the original scheme: a bid-invariant slam bonus can make lower contracts strictly more attractive than higher ones. A bid-dependent correction removes this incentive distortion. We then compare the two schemes using higher-moment analysis, fairness measures, Nash equilibrium analysis, and General-Sum Counterfactual Regret Minimization (GS-CFR). The results show significant differences in the shape of the payoff distributions and reveal that, although both schemes remain highly balanced across physical seats, the modified scheme substantially increases inequality across strategic roles. The game is shown to be neither zero-sum nor constant-sum, motivating a general-sum rather than minimax analysis. Full-game GS-CFR further indicates a substantial increase in the bidder's payoff under the modified scheme, accompanied by a reduction in defender payoff and a shift from separating to partially pooling bidding behavior. These findings demonstrate that scoring-rule design can fundamentally reshape incentives, payoff distribution, and information transmission in imperfect-information games. The proposed framework provides a systematic approach to evaluating such mechanisms from both statistical and strategic perspectives.
Comments26 pages, 2 figures
