标题： 测量组织结构中的领导力和生产率 显示英文标题

标题： Measuring leadership and productivity in an organisational structure

摘要： 本文开发了一种新颖的方法论框架，用于评估由有向图表示的组织结构中的领导潜力和生产率。 在此背景下，个体被建模为节点，不对称的监督或报告关系被建模为有向边。 利用可转移效用合作博弈理论，我们引入了平均森林（AF）度量，这是一种基于最大生成森林枚举的边际主义领导度量，其中团队以树状结构层次化。 AF度量在底层博弈的超加性假设下，捕捉每个代理在所有可行团队配置中的期望贡献。 我们进一步定义了一个组织生产率的度量，即从这些配置中得出的期望总价值。 本文研究了AF度量的关键理论性质——如线性、组件可行性和单调性——并分析了其对底层有向图结构修改的敏感性。 为了解决大规模网络中的计算挑战，提出了一种蒙特卡洛模拟算法用于实际估计。 该框架能够识别结构最优的领导者，并增强对网络设计如何影响集体表现的理解。 显示英文摘要

摘要： This paper develops a novel methodological framework for assessing leadership potential and productivity within organisational structure represented by directed graphs. In this setting, individuals are modeled as nodes and asymmetric supervisory or reporting relationships as directed edges. Leveraging the theory of transferable utility cooperative games, we introduce the Average Forest (AF) measure, a marginalist leadership measure grounded in the enumeration of maximal spanning forests, where teams are hierarchically structured as arborescences. The AF measure captures each agent`s expected contribution across all feasible team configurations under the assumption of superadditivity of the underlying game. We further define a measure of organisational productivity as the expected aggregate value derived from these configurations. The paper investigates key theoretical properties of the AF measure -- such as linearity, component feasibility, and monotonicity -- and analyzes its sensitivity to structural modifications in the underlying digraph. To address computational challenges in large networks, a Monte Carlo simulation algorithm is proposed for practical estimation. This framework enables the identification of structurally optimal leaders and enhances understanding of how network design impacts collective performance.