Clubs, Commonality, and the Core: An Integration of Game Theory and the Theory of Public Goods

One of proposed conditions for equilibrium in a non-zero-stum, many-person game is that outcomes lie in the core. The concept of core seems to have numerous applicationis to economics, but up to present almost its sole application has been demonstration that competitive market equilibrium is in core.2 This article will attempt to apply same concept to theory of clubs-voluntary organizations for mutual benefit-of which a special case is provision of public goods. The results inidicate further possibilities for development of this concept in political economy. This should not suggest, however, that core concept is a silmiple one and its application without difficulty. At best notion is complex and at times analysis is difficult to manipulate.3 In most general terms, a position in core is supposed to represent a stable allocation or outcome of a game, one from which there is no tendency to movement caused by coalition formationi and dissolution. In specific terms, core is set of undominated imputations; an allocation in core is one for which there exists no blocking coalition. A mathematical definition of core, due to Luce and Raiffa, may be given: If set of payments to n players in a game is denoted as x=(x1, x2, ..., x.), then an imnputation belongs to core if it satisfies this requiremenit: