Valuing inputs under supply uncertainty: The Bayesian Shapley value

• 成果类型: Article
• 署名作者: Pongou, Roland; Tondji, Jean-Baptiste
• 署名单位: University of Ottawa; Harvard University; Harvard T.H. Chan School of Public Health
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.08.005
• 发表日期: 2018
• 页码: 206-224
• 关键词: Input valuation; uncertainty; A priori Shapley value; Bayesian Shapley value; rationalizability; Fidelity networks

摘要

We consider the problem of valuing inputs in a production environment in which input supply is uncertain. Inputs can be workers in a firm, risk factors for a disease, securities in a financial market, or nodes in a networked economy. Each input takes its values from a finite set and uncertainty is modeled as a probability distribution over this set. First, we provide an axiomatic solution to this problem, uniquely characterizing a valuation scheme called the a priori Shapley value. Second, we solve the problem of valuing inputs a posteriori that is, after observing output, obtaining the Bayesian Shapley value. Third, we address the question of rationalizing uncertainty in labor supply in a non-cooperative production game where payoffs are given by the Shapley wage function. We also provide an intuitive condition for the existence of a pure strategy Nash equilibrium. Illustrations of the theory include an application to fidelity networks. 2017 Elsevier Inc. All rights reserved.