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Valuing inputs under supply uncertainty: The Bayesian Shapley value

Roland Pongou () and Jean-Baptiste Tondji

Games and Economic Behavior, 2018, vol. 108, issue C, 206-224

Abstract: 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.

Keywords: Input valuation; Uncertainty; A priori Shapley value; Bayesian Shapley value; Rationalizability; Fidelity networks (search for similar items in EconPapers)
JEL-codes: C70 D20 D80 J30 (search for similar items in EconPapers)
Date: 2018
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Working Paper: Valuing Inputs Under Supply Uncertainty: The Bayesian Shapley Value (2016) Downloads
Working Paper: Valuing Inputs Under Supply Uncertainty: The Bayesian Shapley Value (2016) Downloads
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