The core of a transferable utility game as the solution to a public good market demand problem

The core of a monotonic transferable utility (TU) game is shown to be the set of prices that incentivize each individual to demand the grand coalition in a market demand problem in which the goods being demanded are coalitions viewed as excluable public goods. It is also shown that the core is the intersection of superdifferentials evaluated at the grand coalition of the covers of person-specific TU games derived from the original game. These characterizations of the core demonstrate how a market demand approach to coalition formation in the spirit of Baldwin and Klemperer (Tropical geometry to analyze demand, University of Oxford, 2014; Econometrica, 87: 867–932, 2019) is related to the approach to the core using the cover of a TU game and it superdifferential at the grand coalition developed by Shapley and Shubik (J Econ Theory, 1: 9–25, 1969), Aubin (Math Oper Res, 6:1–13, 1981), and Danilov and Koshevoy (J Math Anal Appl, 247: 1–14, 2000).