Measuring individual productivity (or equivalently distributing the overall productivity) in a network structure of workers displaying peer effects has been a subject of ongoing interest in many areas ranging from academia to industry. In this paper, we propose a novel approach based on cooperative game theory that takes into account the peer effects of worker productivity represented by a complete bipartite network of interactions. More specifically, we construct a series of cooperative games where the characteristic function of each coalition of workers is equal to the sum of each worker intrinsic productivity as well as the productivity of other workers within a distance discounted by an attenuation factor. We show that these (truncated) games are balanced and converge to a balanced game when the distance of influence grows large. We then provide an explicit formula for the Shapley value and propose an alternative coalitionally stable distribution of productivity which is computationally much more tractable than the Shapley value. Lastly, we characterize this alternative distribution based on three sensible properties of a logistic network. This analysis enhances our understanding of game-theoretic analysis within logistics networks, offering valuable insights into the peer effects' impact when assessing the overall productivity and its distribution among workers.

翻译：在存在同伴效应的工人网络结构中度量个体生产率（或等价地分配整体生产率）一直是学术界和工业界等多个领域持续关注的问题。本文提出一种基于合作博弈论的新方法，该方法考虑了由完全二分交互网络所表征的工人生产率的同伴效应。具体而言，我们构建了一系列合作博弈，其中每个工人联盟的特征函数等于各工人内在生产率之和，以及由衰减因子折减的距离内其他工人的生产率之和。我们证明这些（截断）博弈是平衡的，且当影响距离趋于无穷时收敛于一个平衡博弈。随后我们给出夏普利值的显式公式，并提出一种替代性的联盟稳定生产率分配方案，其计算复杂度远低于夏普利值。最后，我们基于物流网络的三个合理性质对该替代分配方案进行刻画。该分析深化了对物流网络中博弈论分析的理解，为评估整体生产率及其在工人间分配时同伴效应的影响提供了重要见解。