Approximate cores of replica games and economies. Part I: Replica games, externalities, and approximate cores

Abstract

Sufficient conditions are demonstrated for the non-emptiness of approximate cores of sequences of replica games, i.e. for all sufficiently large replications the games have non-empty approximate cores and the approximation can be made arbitrarily ‘good’. The conditions are simply that the games are superadditive and satisfy a non-restrictive ‘per-capita’ boundedness assumption (these properties are satisfied by games derived from well-known models of replica economies). It is argued that the results can be applied to a broad class of games derived from economic models, including ones with external economies and diseconomies, indivisibilities, and non-convexities. To support this claim, in Part I applications to an economy with local public goods are provided, and in Part II, to a general model of a coalition production economy with few restrictions on production technology sets and with (possibly) indivisibilities in consumption. Additional examples in Part I illustrate the generality of the result.