Knowledge that Transforms

the positions they do fill are filled by foreign medical school graduates. It has been suggested that changes in the manner in which the clearinghouse treats hospitals and students might alter this situation.3 However it was shown in Roth [4] that any two outcomes that are stable-the relevant equilibrium notion4 for this kind of market-fill the same number of positions at any hospital. Since that paper also showed that the clearinghouse procedure yields a stable outcome, any change in procedure that preserves this property would thus have no effect on the perceived numerical maldistribution of physicians among hospitals. Here it is shown that any hospital that fails to fill all of its positions at some stable outcome will not only fill the same number of positions at any other stable outcome, but will fill them with exactly the same residents. Thus, while the staffs of other hospitals are determined by which of the multiple equilibria of such a market is reached, the situation of hospitals whose positions are not all filled remains unaffected. The maldistribution of phvsicians, and particularly of American educated physicians, is therefore a property of equilibria of this kind of market, and not an artifact of the particular equilibrium presently selected. The formal model:5 The agents in the hospital-intern market consist of two disjoint

Two costlessly mobile firms are to be located in a market region, a subset of the plane. The firms compete by setting locations and delivered price schedules. To study this competitive stiuation an appropriate extensive form game is defined, along with an appropri- ate noncooperative solution concept. Existence and general properties of the equilibrium are demonstrated. Among the results are: Each firm increases its profit by locating so as to decrease total cost to both firms of serving the market. Firms will never locate coinciden- tally if they have identical production costs and transport cost rates, or if these are different and the firms are located in a circular market region having a uniform demand distribution. THIS PAPER STUDIES competition between two profit maximizing firms in space who are costlessly mobile and may discriminate in price. We will allow the firms to set locations and delivered price schedules and we will be concerned with the existence- and properties of equilibria in location and price. Starting with Hotelling (9), the spatial competition literature has focused on location on bounded linear markets by two or more firms. Hotelling assumed identical firms that produced a single good with constant cost of production and considered consumers to be uniformly distributed and to have inelastic demand. He also assumed that the consumers pay transport cost and purchase the good from the cheapest source. Hotelling claimed that a Nash equilibrium in locations for the two firm market existed and yielded back-to-back locations at the center of the market. Many authors, most recently, D'Aspremont, Gabszewicz, and Thisse (2) have noted that an equilbrium in prices and location does not exist for Hotelling's model. However, if the firms employ identical exogeneously specified prices, Hotelling's conclusions hold. Subsequent work by Smithies (14), Hartwick and Hartwick (7), and Eaton (3) claimed to show that a Nash equi- librium in f.o.b. prices and locations can exist in markets with a uniform distribu- tion of consumers each of whom have identical elastic demand functions for the two and three firm problems. The work of D'Aspremont et al. casts doubt on these conclusions without the adoption of restrictive conditions. Our work contrasts with these works and related research which has dealt with linear markets, with uniform distributions of customers and with identical firms. Our work will involve markets that are subsets of the plane having nonuniform distributions of customers. Our firms will be allowed to be different, that is, have differences in production and transport costs. However, the fundamental difference in our approach is that our firms will set discriminatory prices and not price f.o.b. In many ways our work will represent the discriminatory pricing

The encompassing principle is used to develop a testing framework which unifies the literature on non-nested testing, allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist, as well as embracing nested hypothesis testing. The concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest, and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative. The analysis is illustrated by an application to two non-nested linear regression models, and it is shown that the conventional F test, as well as all the one degree of freedom non-nested tests, has an encompassing interpretation, and that the F test is a complete parametric encompassing test.

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at

[We extend the principal-agent framework with risk-neutral principals to situations in which several principals simultaneously and independently attempt to influence a common agent. We show that implementation is, in the aggregate, always efficient (cost-minimizing), and that noncooperative behavior induces an efficient (potentially second-best) action choice if and only if collusion among the principals would implement the first-best action at the first-best level of cost. We also investigate the existence of equilibria, the distribution of net rewards among principals, the characteristics of actions chosen in inefficient equilibria, and potential institutional remedies for welfare losses induced by noncooperative behavior.]

We develop a duopoly model in which exit occurs because of the existence of fixed costs or opportunity costs. Each firm enters the market knowing its own cost, but not that of its opponent. As times goes on, each firm becomes increasingly pessimistic about the cost of its remaining rival. The time of exit is the only strategic variable, so that our model is a of attrition. In contrast to the classic war of attrition, however, we assume that with positive probability each firm's costs may be low enough that staying in forever is a dominant strategy. Thus our model, unlike the classic one, has a unique equilibrium.

On montre comment le test de Wald s'applique a des ensembles de restrictions d'egalite et d'inegalite et on presente la distribution, pour de grands echantillons, du test sous l'hypothese nulle

Stochastic equilibria under uncertainty with continuous-time security trading and consumption are demonstrated in a general setting. A common question is whether the current price of a security is an unbiased predictor of the future price of the security plus intermediate dividends. This is the hypothesis of expected financial gains from trade. The relevance of this hypothesis in multi-good economies is called into question by the following demonstrated fact. For each set of probability assessments there exists a corresponding equilibrium, one with the original agents, original equilibrium allocations, and no expected financial gains from trade under the given probability assessments. The spanning number of the economy is defined as the fewest number of security markets required to sustain a complete markets equilibrium (in a dynamic sense made precise in the paper). The spanning number is linked directly to agent primitives, in particular the manner in which new information resolves uncertainty over time. The spanning number is shown to be invariant under bounded changes in expectations. Several examples are given in which the spanning number is finite even though the number of potential states of the world is infinite.

[A model of decentralized exchange and price formation is defined using the bargaining theory of A. Rubinstein. Agents meet at random and bargain over the terms of trade. If there are no transaction costs, every perfect equilibrium of the bargaining game implements a Walrasian equilibrium of the underlying exchange economy.]