Jan 1, 1975
An economic model of trading in commodities that are inherently indivisible is investigated from a game-theoretic point of view. The report offers an elementary introduction to [n]-person games, balanced sets, and the core, applying them to a simple but nontrivial trading model. It also presents a new perspective on the difficulties that upset the smooth functioning of an economy due to the presence of commodities that come in large, discrete units. The concepts of balanced game and core are developed, and a general theorem is applied to prove that the market in question has a nonempty core — that is, at least one outcome that no subset of traders can improve on. The report discusses a number of examples and reviews a series of other models involving indivisible commodities, with references to the literature.