The Core of a Public Goods Economy

Abstract

THE CORE, an n person game solution concept, has proved to be very useful in analyzing economic allocations in a private goods economy (see, e.g., [1]). Viewed as an n person game, such an economy requires the specification of production and distribution activities open to an arbitrary coalition of economic agents. We say a coalition can improve upon a proposed vector of utility levels which stems from an allocation which is collectively feasible for all of the economic agents if it can achieve levels of utility for all of its members which are higher than the corresponding levels in the proposed vector. The core consists of all utility vectors feasible for the whole economy which cannot be improved upon by any coalition. The crucial issue is how to formulate what a coalition can achieve for itself. In a private goods economy there is a natural formulation-we simply allow a coalition to produce its own outputs from its own inputs, and look at the utility levels resulting from a distribution of these outputs among the group. In public goods economies, or more generally in economies involving externalities, the formulation of what a coalition can achieve for itself is not so transparent. The problem is that agents not in a given coalition can modify the distribution of utilities within the coalition. Unlike the situation in a private goods economy, we cannot specify a set of utility levels attainable by a coalition independently of the activities of the complementary coalition, i.e., agents not in the coalition. Consider anl economy with pure public goods. By the definition of pure public goods, the mlembers of a coalitiotn would be able to consume the public goods produced by the complementary coalition. Thus it is natural to say that a coalition can achieve for itself utility levels associated with the distribution of both public anid private goods which it produces using its own resources, together with the consumption of the public goods produced by the complementary coalition. In order to determine the quantity of public goods produced by the complementary coalition we must define a set of permissible activities for it. Suppose we allow it to produce any amount of public and private goods consistent with its endowment of resources. Then, in order to deter the given coalition from forming and objecting to the status quo, it would threaten to produce no public goods, since this would nullify any free consumption of its public goods by the