The Aumann-Shapley prices: a survey

Abstract

Introduction The theory of values of nonatomic games as developed by Aumann and Shapley was first applied by Billera, Heath, and Raanan (1978) to set equitable telephone billing rates that share the cost of service among users. Billera and Heath (1982) and Mirman and Tauman (1982a) “translated” the axiomatic approach of Aumann and Shapley from values of nonatom games to a price mechanism on the class of differentiable cost functions and hence provided a normative justification, using economic terms only, for the application of the theory of nonatomic games to cost allocation problems. New developments in the theory of games inspired parallel developments to cost allocation applications. For instance, the theory of semi-values by Dubey, Neyman, and Weber (1981) inspired the work of Samet and Tauman (1982), which characterized the class of all “semi-price” mechanisms (i.e., price mechanisms that do not necessarily satisfy the break-even requirement) and led to an axiomatic characterization of the marginal cost prices. The theory of Dubey and Neyman (1984) of nonatomic economies inspired the work by Mirman and Neyman (1983) in which they characterized the marginal cost prices on the class of cost functions that arise from long-run production technologies. Young's (1984) characterization of the Shapley value by the monotonicity axiom inspired his characterization (Young 1985a) of the Aumann—Shapley price mechanism on the class of differentiable cost functions.