从位置偏好恢复加权Shapley值

中文摘要 AI 辅助

加权Shapley值通过正权重和有序优先级类别表示不对称性。我们在Roth的转移效用博弈中位置彩票框架下，赋予这些参数以偏好解释。在共同校准、零性、普通风险中性、一致效率性和一致正性条件下，一致博弈中的位置值是概率等价物。这些概率的Luce条件化刻画了Kalai-Samet族，并等价于伙伴一致性。我们将条件化区分为显示优先级的传递性、支持的成对确定性和正赔率的不变性。两人观测允许加权Shapley扩展，当且仅当显示优先级是传递的且类内赔率满足乘积规则。该扩展是唯一的：成对比较识别优先级类别和每类内的权重比率。更大的一致博弈对支持和份额提供额外限制。我们给出构造性证明，确立五个公理的独立性，并解释启发式解释的范围和局限。

英文摘要

Weighted Shapley values represent asymmetry through positive weights and ordered priority classes. We give these parameters a preference interpretation in Roth's framework of lotteries over positions in transferable-utility games. Under common calibration, nullity, ordinary risk neutrality, unanimity efficiency, and unanimity positivity, position values in unanimity games are probability equivalents. Luce conditioning of these probabilities characterizes the Kalai-Samet family and is equivalent to partnership consistency. We separate conditioning into transitivity of revealed priority, pairwise determination of support, and invariance of positive odds. Two-player observations admit a weighted Shapley extension exactly when revealed priority is transitive and within-class odds satisfy a product rule. The extension is unique: pairwise comparisons identify the priority classes and weight ratios within each class. Larger unanimity games provide additional restrictions on supports and shares. We give constructive proofs, establish independence of the five axioms, and explain the scope and limits of the elicitation interpretation.

发表机构

• Istanbul Technical University（伊斯坦布尔技术大学）

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