稳定分配，不稳定支付路径：Shapley值与自愿联盟形成
Stable Allocations, Unstable Payment Paths: The Shapley Value and Voluntary Coalition Formation
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中文总结 AI 辅助
本文研究Shapley值支付路径下玩家自愿进入的可行性，提出支付流方法实现自愿且预算平衡的分配，并揭示自愿进入与联盟稳定性间的潜在冲突。
中文摘要 AI 辅助
Shapley值的随机顺序解释同时指定了一个最终分配和一条支付路径：当一位玩家进入时，她在该时刻获得其边际贡献。我们询问玩家是否会自愿遵循这条路径。如果玩家的边际贡献预期会随着联盟的增长而上升，她可能更愿意等待。这在凸博弈中造成了紧张关系。Shapley分配属于核，但除可加博弈外，相关的边际贡献支付路径并不支持自愿进入。我们通过引入支付流来分离这两个对象，该支付流分配每次联盟转变时产生的剩余。当允许带符号支付时，每个有效分配都可以通过一个局部的、预算平衡的自愿流来实现。我们通过最小化与Shapley流的距离来选择一种规范实现，并表明该问题在对称基数博弈中会大幅简化。然后我们考虑等额剩余分享，即未支付给进入者的任何转变剩余在现有成员之间平均分配。此类中最接近的自愿流内生地选择一个分配。在两种玩家类型的情况下，所选分配是Shapley分配与平均分配之间的一个依赖博弈的仿射组合。例子既展示了支付限制的作用，也展示了自愿进入与联盟稳定性之间可能存在的冲突。
英文摘要
The random-order interpretation of the Shapley value specifies both a terminal allocation and a payment path: each entrant is paid her marginal contribution at the time of entry. We embed this path in a finite dynamic entry problem in which a selected player may accept immediately or defer and allow another outsider to enter first. A flow is fully voluntary when immediate acceptance is optimal at every decision state. Although this criterion is defined through optimal continuation values, backward induction yields an equivalent system of linear inequalities in full-consent continuation values. The distinction between allocation and path is sharp in convex games: the Shapley allocation lies in the core, but the Shapley flow is fully voluntary only in additive games. Nevertheless, every efficient allocation admits a budget-balanced fully voluntary implementation when signed payments are available. We select a canonical implementation by minimizing distance from the Shapley flow, derive a reduced quadratic program for symmetric cardinality games, and study equal residual sharing, which selects the terminal allocation endogenously. With two player types, the selected allocation is an affine combination of the Shapley and equal-division allocations. Examples illustrate the effects of payment restrictions and a possible conflict between full voluntariness and coalitional stability.
发表机构
- Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。
