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. Stability and Competitive Equilibrium in Trading Networks John William HatfieldUniversity of Texas at Austin Scott Duke KominersHarvard University and University of Chicago Alexandru Nichifor University of St Andrews Michael OstrovskyStanford University Alexander Westkamp Maastricht UniversityWe introduce a model in which agents in a network can trade via bilateral contracts. We find that when continuous transfers are allowed and utilities are quasi-linear, the full substitutability of preferences is sufficient to guarantee the existence of stable outcomes for any underlying network structure. Furthermore, the set of stable outcomes is essentially equivalent to the set of competitive equilibria, and all stable outcomes are in the core and are efficient. By contrast, for any domain of preferences strictly larger than that of full substitutability, the existence of stable outcomes and competitive equilibria cannot be guaranteed.

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Bonn Graduate School of Economics (BGSE)is gratefully acknowledged.Deutsche Post World Net is a sponsor of the BGSE.An analysis of the German university admissions system * Alexander WestkampChair of Economic Theory II, Economics Department, University of Bonn; e-mail: awest@uni-bonn.de. AbstractThis paper analyzes the sequential admissions procedure for medical subjects at public universities in Germany. Complete information equilibrium outcomes are shown to be characterized by a stability condition that is adapted to the institutional constraints of the German system.I introduce matching problems with complex constraints and the notion of procedural stability. Two simple assumptions guarantee existence of a student optimal procedurally stable matching mechanism that is strategyproof for students. In the context of the German admissions problem, this mechanism weakly Pareto dominates all equilibrium outcomes of the currently employed procedure. Applications to school choice with affirmative action are also discussed.

In many-to-one matching with contracts, agents on one side of the market, e.g., workers, can ful ll at most one contract, while agents on the other side of the market, e.g., rms, may desire multiple contracts. Hat eld and Milgrom [6] showed that when rms' preferences are substitutable and size monotonic, the worker-proposing cumulative o er mechanism is stable and strategy-proof (for workers). 1 Recently, stable and strategy-proof matching has been shown to be possible in a number of real-world se ings in which preferences are not necessarily substitutable (see, e.g., Sönmez and Switzer [13], Sönmez [12], Kamada and Kojima [7], and Aygün and Turhan [1]); this has motivated a search for weakened substitutability conditions that guarantee the existence of stable and strategy-proof mechanisms. Hat eld and Kojima [3] introduced unilateral substitutability and showed that when all rms' preferences are unilaterally substitutable (and size monotonic), the cumulative o er mechanism is stable and strategy-proof. Kominers and Sönmez [9] identi ed a novel class of preferences, called slot-speci c priorities, and showed that if each rm's preferences are in this class, then the cumulative o er mechanism is again stable and strategy-proof. Subsequently, Hat eld and Kominers [4] developed a concept of substitutable completion and showed that when each rm's preferences admit a size monotonic substitutable completion, the cumulative o er mechanism is once more stable and strategy-proof. In this paper, we introduce three novel conditions-observable substitutability, observable size monotonicity, and non-manipulability via contractual terms-and show that when these conditions are satis ed, the cumulative o er mechanism is the unique mechanism that is stable and strategy-proof. Moreover, when the choice function of any rm fails one of our three conditions, we can construct unit-demand choice functions for the other rms such that no stable and strategy-proof mechanism exists.

No abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Copyright remains with the author(s). Terms of use: Documents inDiscussion papers of the WZB serve to disseminate the research results of work in progress prior to publication to encourage the exchange of ideas and academic debate. Inclusion of a paper in the discussion paper series does not constitute publication and should not limit publication in any other venue. The discussion papers published by the WZB represent the views of the respective author(s) and not of the institute as a whole. Quotas for special groups of students often apply in school or university admission procedures. This paper studies the performance of two mechanisms to implement such quotas in a lab experiment. The first mechanism is a simplified version of the mechanism currently employed by the German central clearinghouse for university admissions, which first allocates seats in the quota for top-grade students before allocating all other seats among remaining applicants. The second is a modified version of the student-proposing deferred acceptance (SDA) algorithm, which simultaneously allocates seats in all quotas. Our main result is that the current procedure, designed to give top-grade students an advantage, actually harms them, as students often fail to grasp the strategic issues involved. The modified SDA algorithm significantly improves the matching for top-grade students and could thus be a valuable tool for redesigning university admissions in Germany. Keywords: College admissions; experiment; quotas; matching; Gale-Shapley mechanism;Boston mechanism JEL classification: C78; C92; D78; I20