Many game-theoretic solution notions have been defined or can be defined not only with reference to the all-player coalition, but also with reference to an arbitrary coalition structure. In this paper, theorems are established that connect a given solution notion, defined for a coalition structure with the same solution notion applied to appropriately defined games on each of the coalitions in ~'. This is done for the kernel, nucleolus, bargaining set, value, core, and the YON NEUMAYN-MORGEN-STERN solution. It turns out that there is a single function that plays the central role in five out of the six solution notions in question, though each of these five notions is entirely different. This is an unusual instance of a game theoretic phenomenon that does not depend on a particular solution notion but holds across a wide class of such notions.

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 128.235.251.160 on Sun, IN THIS PAPER, we study an exchange economy where allocation of resources is guided by a price mechanism, but prices are subject to inequality constraints, An equilibrium is obtained by introducing quantity constraints on the net trades of those commodities for which the price constraints are binding. The set of admissible quantity constraints is defined in a way which avoids trivial equilibria.Two kinds of price rigidities are considered in turn, namely constraints on nominal prices in an economy with a numeraire (Sections 4 and 5) and constraints on relative or real prices in an economy without a numeraire (Section 6). The two kinds are then considered simultaneously (Section 7). In each case, we find that inequality constraints on net trades may be substituted for price adjustments, one-to-one, as devices to equate supply and demand. (Clearly, this is a statement about feasibility, not about efficiency). Some background remarks on price rigidities and quantity rationing (Section 2) precede the description of the model (Section 3). The results are so organized that the basic technique of proof is introduced first on a simple problem (constraints on all nominal prices); the technique is then extended in two directions (constraints on some but not all nominal prices, constraints on all real prices); these extensions are combined in a final theorem, of which the first three are special cases (constraints on some nominal and/or some real prices). 2The phenomenon of price rigidity, i.e., the persistence of prices at which supply and demand are not equal, is frequently observed, and plays an important role in some macro-economic models, Downwards wage rigidity in the presence of underemployment, with or without minimum wage laws, is the foremost example.2 Rent controls, price controls aimed at curbing inflationary pressures, usury laws, price uniformity over time or space, provide other examples.In most cases, price rigidities may be described as inequality constraints on * for interesting discussions and helpful suggestions; I am particularly grateful to Pierre Dehez and Dieter Sondermann who discovered mistakes in earlier versions of this paper; responsibility for remaining errors is mine. 2 The present note was motivated by research in progress on the rational aspects of wage rigidities and unemployment compensation, viewed as a form of income insurance for which market opportunities offer no substitute. 301This content downloaded from 128.235.251.160 on Sun,