Valuing Inputs Under Supply Uncertainty: The Bayesian Shapley Value

Roland Pongou and Jean-Baptiste Tondji ()
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Jean-Baptiste Tondji: Department of Economics, University of Ottawa, Ottawa, ON

No 1617E, Working Papers from University of Ottawa, Department of Economics

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 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 wage function. 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 existence of a pure strategy Nash equilibrium. We present several applications of our theory to real-life situations.

Keywords: Input valuation; uncertainty; a priori Shapley value; Bayesian Shapley value; rationalizability (search for similar items in EconPapers)
JEL-codes: C70 D20 D80 J30 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2016
New Economics Papers: this item is included in nep-gth
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Related works:
Journal Article: Valuing inputs under supply uncertainty: The Bayesian Shapley value (2018)
Working Paper: Valuing Inputs Under Supply Uncertainty: The Bayesian Shapley Value (2016)
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