Valuing Inputs Under Supply Uncertainty: The Bayesian Shapley Value

Uncertainty of the Shapley Value

This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player’s marginal contribution during the bargaining process. The measure is symmetric with respect to exchangeable substitutions in the players, equal to zero for dummy...

On Shapley Value for Measuring Importance of Dependent Inputs

This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables are dependent. Our main goal here is to show that Shapley value removes the conceptual problems. We do this with some simple examples where Shapley value lea...

Responsive pricing under supply uncertainty

Capacity reservation under supply uncertainty

Shortages of input materials and components used in the production process often adversely influence sales of manufacturing firms. Manufacturers can guarantee delivery of the inputs by initiating capacity reservation arrangements with their suppliers. We study a multi-period capacity reservation contract between a manufacturer and a long-term supplier when there is uncertainty about the quantit...

The Shapley group value

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a priori evaluation of the prospects of a group of players in a coalitional game when acting as a unit. We study its properties and we give an axiomatic charact...