Representing Games as Coalition Production Economies with Public Goods

In this paper we introduce a new approach to representing both TU-games and NTU-games as special economic structures. Instead of represent-ing a game as a market – an exchange economy with concave utility functions – as in the extant literature, we represent an arbitrary game as a coalition produc-tion economy with a public good. The economy provides an indirect description of the game. Our model uses the idea of a social planner or arbitrager who, through arbitrage on productive activities, seeks to minimize the net cost of providing the public good subject to the constraint that the society satis…es its reservation welfare level. Note that in constrast to the prior literature on representing games as economic structures, we require neither that the game be balanced nor that there are large numbers of players. Our approach to repre-senting a game as an economic structure uses techniques from consumer demand theory and, in particular, the notion of a compensated demand correspondence. The main results of this paper exhibit a relationship between cooperative game theory and consumer demand theory.