The assignment game is a model for a two-sided market in which a product that comes in large, indivisible units (e.g., houses, cars, etc.) is exchanged for money, and in which each participant either supplies or demands exactly one unit. The units need not be alike, and the same unit may have different values to different participants. It is shown here that the outcomes in the core of such a gamei.e., those that cannot be improved upon by any subset of players -are the solutions of a certain linear programming problem dual to the optimal assignment problem, and that these outcomes correspond exactly to the price-lists that competitively balance supply and demand. The geometric structure of the core is then described and interpreted in economic terms, with explicit attention given to the special case (familiar in the classic literature) in which there is no product differentiationi.e., in which the units are interchangeable. Finally, a critique of the core solution reveals an insensitivity to some of the bargaining possibilities inherent in the situation, and indicates that further analysis would be desirable using other game-theoretic solution concepts. l. Introduction Two-Sided Market GamesTwo-sided market models are important, as COURNOT, EDGEWORTH, BOHM-BAWERK, and others have observed ~), not only for the insights they may give into more general economic situations with many types of traders, consumers, and producers, but also for the simple reason that in real life many markets and most actual transactions are in fact bilateral -i.e., bring together a buyer and a seller of a single commodity. Modern game-theoretic concepts, when applied to even the most elementary economic models, have often yielded suggestive results, sometimes reinforcing and sometimes challenging the more traditional doctrines based on behavioristic theories of the individual 5). The present study, of which this paper is the first part, will concern a class of simple, two-sided market "games" whose distinctive feature is the indivisibility and the ability to satiate of the goods for sale, e.g. houses or automobiles, so that the primary object of the game is simply to find suitable "assignments" of buyers to sellers 6). SHUBIK. 6) This model was first treated by SHAPLEY in 1955; the present account has been extracted from the manuscript of a book in preparation. A short, nongame-theoric account will be found in . L.S. SHAPLEY and M. SHUB1KWe intend to explore the properties of such assignment games from several different solutional viewpoints. In this first part we shall concentrate on the core of the game -i.e., the set of outcomes that no coalition can improve upon1). The Underlying Economic AssumptionsThe assumptions of our model, though restrictive in many respects, do permit considerable latitude in size and structure. There may be many or few traders on either side of the market, there may be product differentiation, and the traders themselves may be quite dissimilar in their likes and dislikes. Thus, a wide range of specific models,...

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We extend the standard model of general equilibrium with incomplete markets to allow for default and punishment by thinking of assets as pools. The equilibrating variables include expected delivery rates, along with the usual prices of assets and commodities. By reinterpreting the variables, our model encompasses a broad range of adverse selection and signalling phenomena in a perfectly competitive, general equilibrium framework.Perfect competition eliminates the need for lenders to compute how the size of their loan or the price they quote might affect default rates. It also makes for a simple equilibrium refinement, which we propose in order to rule out irrational pessimism about deliveries of untraded assets.We show that refined equilibrium always exists in our model, and that default, in conjunction with refinement, opens the door to a theory of endogenous assets. The market chooses the promises, default penalties, and quantity constraints of actively traded assets.

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices.In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between "rational" traders whose behavior is derived from fundamental analysis of the stock, including dividends, and "noise traders", whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, "bubbles" often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is larger, the market price is generally locked within the price range they define.