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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 our valuation problem, defining three intuitive axioms which we use to uniquely characterize a valuation scheme that we call the a priori Shapley value.

Second, we solve the problem of valuing inputs a posteriori-that is, after observing output. This leads to the Bayesian Shapley value.

Third, we consider the problem of rationalizing uncertainty when the inputs are rational workers supplying labor in a non-cooperative production game in which payoffs are given by the Shapley wagefunction. We find that probability distributions over labor supply that can be supported as mixed strategy Nash equilibria always exist. We also provide an intuitive condition under which we prove the existenceof a pure strategy Nash equilibrium. We present several applications of our theory to real-life situations.

Item Type: MPRA Paper -

Original Title: Valuing Inputs Under Supply Uncertainty : The Bayesian Shapley Value-

Language: English-

Keywords: Input valuation, uncertainty, a priori Shapley value, Bayesian Shapley value, rationalizability-

Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - GeneralD - Microeconomics > D2 - Production and Organizations > D20 - GeneralD - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - GeneralJ - Labor and Demographic Economics > J3 - Wages, Compensation, and Labor Costs > J30 - General-

Autor: Pongou, Roland


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