Econ Papers Daily / 期刊论文
大老板博弈中的沙普利值与弱参与者力量
The Shapley value and the strength of weak players in big boss games
摘要
Big Boss Games represent a specific class of cooperative games where a single veto player, known as the Big Boss, plays a central role in determining resource allocation and maintaining coalition stability. In this paper, we introduce a novel allocation scheme for Big Boss games, based on two classical solution concepts: the Shapley value and the \(\tau \)-value. This scheme generates a coalitionally stable allocation that effectively accounts for the contributions of weaker players. Specifically, we consider a diagonal of the core that includes the Big Boss’s maximum aspirations, the \(\tau \)-value, and those of the weaker players. From these allocations, we select the one that is closest to the Shapley value, referred to as the Projected Shapley Value allocation (PSV allocation). Through our analysis, we identify a new property of Big Boss games, particularly the relationship between the allocation discrepancies assigned by the \(\tau \)-value and the Shapley value, with a particular focus on the Big Boss and the other players. Additionally, we provide a new characterization of convexity within this context. Finally, we conduct a statistical analysis to assess the position of the PSV allocation within the core, especially in cases where computing the Shapley value is computationally challenging. Similar content being viewed by others
中文摘要
大老板博弈是一类特殊的合作博弈，其中被称为"大老板"的单一否决权玩家在决定资源分配和维护联盟稳定性方面发挥着核心作用。本文基于两个经典解概念——沙普利值和τ值——为大老板博弈提出了一种新的分配方案。该方案能够产生联盟稳定的分配结果，有效体现弱势玩家的贡献。具体而言，我们考虑核心的对角线，该对角线包含大老板的最大期望值、τ值以及弱势玩家的期望值。从这些分配方案中，我们选取最接近沙普利值的分配方案，称为投影沙普利值分配（PSV分配）。通过分析，我们发现了大老板博弈的一个新性质，特别是τ值与沙普利值所分配的差异之间的关系，重点关注大老板与其他玩家之间的差异。此外，我们还在该背景下给出了凸性的新刻画。最后，我们通过统计分析评估PSV分配在核心中的位置，特别是在计算沙普利值存在计算困难的情况下。