matching with waiting times the german entry level labor market for lawyers abstract we study the allocation of german lawyers to regional courts for legal trainee ships because of excess demand in some regions lawyers often have to wait before being allocated the currently used berlin mechanism is not weakly pareto efficient does not eliminate justified envy and does not respect improvements we introduce a mechanism based on the matching with contracts literature using waiting time as the contractual term the resulting mechanism is strategy proof weakly pareto efficient eliminates justified envy and respects improvements we extend our proposed mechanism to allow for a more flexible allocation of positions over time

walrasian equilibrium with gross substitutes in this paper we study the problem of efficient production and allocation of indivisible objects among a set of consumers we assume that the agents preferences depend on the bundle of objects and the quantity of money they consume furthermore we assume that preferences are quasilinear in money and that agents have a large endowment of money with indivisibilities it is well known that many familiar properties of the utility functions fail to ensure existence in their striking analysis of the matching problem kelso and crawford 5 introduce the gross substitutes gs condition which ensures the non emptiness of the core we propose two new conditions and show that with quasilinearity they are equivalent article id jeth 1999 2531 available online at http www idealibrary com on

collateral in credit rationing in markets with imperfect information note in their 1981 article joseph stiglitz and andrew weiss analyze adverse selection and incentive effects in the loan market the models considered are based on two crucial assumptions borrowers are subject to limited liability and lenders cannot distinguish borrowers projects of different risk stiglitz and weiss show that a bank that raises its interest rate may suffer adverse selection because only risky borrowers will be willing to borrow at the higher rate thus lenders may choose not to raise the interest rate to eliminate excess demand resulting in the possibility of a credit rationing equilibrium stiglitz and weiss also consider briefly the role of collateral in such credit rationing models they conclude that lenders may choose not to use collateral requirements as a rationing device an increase in collateral requirements like an increase in the interest rate potentially leads to a decrease in the lender s expected return on loans because of resulting adverse incentive and selection effects the purpose of this note is to further investigate the role of collateral in these models stiglitz and weiss discussion in section iii establishes that adverse selection effects can result from increases in collateral when borrowers are risk averse i will show by returning to a model they discussed earlier in section i that the adverse selection effects can also occur when borrowers are risk neutral stiglitz and weiss outline a model to consider the use of collateral as a rationing device section iii in that model all potential borrowers face the same array of risky projects each potential borrower chooses at most one of those projects to undertake the individuals are by assumption risk averse with decreasing absolute risk aversion and possess different amounts of initial wealth thus choice of project if any to undertake and the method of finance selffinance from initial wealth or loan finance will differ from one individual to the next stiglitz and weiss show that among those who undertake risky projects and who choose borrowing as the method of finance wealthier individuals undertake riskier projects an increase in collateral has two effects on the market for loans those individuals who remain in the market will choose to undertake less risky projects and those individuals who drop out of the market are less wealthy low risk borrowers if the second effect is sufficiently strong then increased collateral requirements will mean decreased expected returns for the lender thus a credit rationing equilibrium may occur since lenders may not choose to use collateral requirements or the interest rate to eliminate excess demand the adverse selection effect just described does not occur in this model if the individuals are risk neutral consequently the potential for a credit rationing equilibrium is limited to cases where borrowers are risk averse to see that increases in collateral requirements can also result in adverse selection if borrowers are risk neutral consider the model stiglitz and weiss used to analyze the adverse selection effects of increases in the interest rate section i pp 395 99 it differs from the section iii model discussed above in three ways first borrowers are risk neutral second all projects ar loan financed the analogy to the section iii model is that no individuals have sufficient wealth to self finance projects third in the section

entrepreneurship and organization design we model entrepreneurship and the emergence of firms as an outcome of simultaneous bidding for labor services among heterogeneous agents what distinguishes our approach from prior work is that occupational choice and job matching are determined simultaneously so that the opportunity costs of entrepreneurs are accounted for those who are relatively unmanageable while possibly excellent managers themselves become entrepreneurs entrepreneurs compete and create value by building efficient organizations and offering potentially well paid jobs to others while the entry of an additional entrepreneur typically reduces some individual wages we show that it always raises the average wage and depresses the average income of incumbent entrepreneurs this result may help explain the empirically low returns to entrepreneurship

substitutes and stability for matching with contracts we consider the matching problem with contracts of hatfield and milgrom 2005 and we introduce new concepts of bilateral and unilateral substitutes we show that bilateral substitutes is a sucient condition for the existence of a stable allocation in this framework however the set of stable allocations does not form a lattice under this condition and there does not necessarily exist a doctor optimal stable allocation under a slightly stronger condition unilateral substitutes the set of stable allocations still does not necessarily form a lattice with respect to doctors preferences but there does exist a doctor optimal stable allocation and other key results such as incentive compatibility and the rural hospitals theorem are recovered

efficient resource allocation under multi unit demand abstract we study resource allocation with multi unit demand such as the allocation of courses to students in contrast to the case of single unit demand no stable mechanism not even the student proposing deferred acceptance algorithm achieves desirable properties it is not strategy proof and the resulting allocation is not even weakly efficient under submitted preferences we characterize the priority structure of courses over students under which stability is consistent with strategy proofness or efficiency we show that stability is compatible with strategy proofness or efficiency if and only if the priority structure is essentially homogeneous this result suggests that efficient allocation under multi unit demand is difficult and that the use of stable mechanisms may not deliver desirable outcomes

matching with couples stability and incentives in large markets accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists because couples view pairs of jobs as complements a stable matching may not exist when couples are present this paper s main result is that a stable matching exists when there are relatively few couples and preference lists are suciently short relative to market size we also discuss incentives in markets with couples we relate these theoretical results to the job market for psychologists in which stable matchings exist for all years of the data despite the presence of couples

matching with contracts comment the theory of two sided matching markets has interested researchers for its theoretical appeal and its relevance to the design of real world institutions the medical residency matching mecha nism in the united states the national resident matching program nrmp and student assign ment systems in new york city and boston are important mechanisms designed by economists using the theory 1 hatfield and paul r milgrom 2005 present a unified framework of matching with contracts which includes the two sided matching and package auction models as well as a simplified version of a labor market model of alexander kelso and vincent p crawford 1982 as special cases they introduce the substitutes condition of contracts which is an adaptation of the substitutability condition in the matching literature roth and marilda a oliveira sotomayor 1990 to matching with contracts they show that there exists a stable allocation if contracts are substitutes for hospitals and that a number of other results in matching generalize to problems with contracts they further claim that the substitutes condition on individual hospitals prefer ences is necessary to guarantee the existence of a stable allocation for all possible singleton preferences of others that is if contracts are not substitutes for a hospital then there exists a preference profile of other hospitals with single job openings and doctors such that there exists no stable allocation we show that this last claim of hatfield and milgrom 2005 does not hold in general the counterexample we present involves a hospital which has two different kinds of positions and the preferences of the hospital are a combination of preferences of these two positions while the substitutes condition does not hold for that hospital we adopt a technique developed by bettina klaus and flip klijn 2005 and show that there exists a stable allocation we then present the weak substitutes condition which we show is necessary to guarantee existence of stable allocations the modified result we present as well as the original contribu tion of hatfield and milgrom 2005 suggest a connection between the substitutes condition and stability 2

credit markets with imperfect information risk aversion versus pessimism abstract stiglitz and weiss 1981 credit rationing is embedded within rank dependent expected utility theory our results show that sufficient pessimism or sufficient risk aversion by borrowers may eliminate adverse selection moreover lender optimism may eliminate credit rationing even when adverse selection exists

stability and competitive equilibrium in trading networks we 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

sorting through search and matching models in economics toward understanding assortative matching this is a self contained introduction to research on search and matching we first explore the nontransferable and perfectly transferable utility matching paradigms and then a unifying imperfectly transferable utility matching model motivated by some unrealistic predictions of frictionless matching we flesh out the foundational economics of search theory we then revisit the original matching paradigms with search frictions we finally allow informational frictions that often arise such as in college student sorting

a theory of anticipated utility abstract a new theory of cardinal utility with an associated set of axioms is presented it is a generalization of the von neumann morgenstern expected utility theory which permits the analysis of phenomena associated with the distortion of subjective probability

unilateral substitutability implies substitutable completability in many to one matching with contracts abstract we prove that the unilateral substitutability property introduced in hatfield and kojima 2010 implies the substitutable completability property from hatfield and kominers 2014 this paper provides a novel linkage between these two sufficient conditions for the existence of a stable matching in many to one matching markets with contracts a substitutable completion of a preference is a substitutable preference created by adding some sets of contracts to the original preference order we provide an algorithm which when operated on the unilaterally substitutable preferences produces such a substitutable completion thus it provides a constructive proof of the connection between the two properties

matching with contracts we develop a model of matching with contracts which incorporates as special cases the college admissions problem the kelso crawford labor market matching model and ascending package auctions we introduce a new law of aggregate demand for the case of discrete heterogeneous workers and show that when workers are substitutes this law is satisfied by profit maximizing firms when workers are substitutes and the law is satisfied truthful reporting is a dominant strategy for workers in a worker offering auction matching algorithm we also parameterize a large class of preferences satisfying the two conditions

matching and price competition we develop a model in which firms set impersonal salary levels before matching with workers wages fall relative to any competitive equilibrium while profits rise almost as much implying little inefficiency furthermore the best firms gain the most from the system while wages become compressed in light of our results we discuss the performance of alternative institutions and the recent antitrust case against the national resident matching program

matching with branch of choice contracts at the united states military academy branch selection is a key decision in a cadet s military career cadets at usma can increase their branch priorities at a fraction of slots by extending their service agreement this real life matching problem lls an important gap in market design literature although priorities fail a key substitutes condition the agent optimal stable mechanism is well dened and in contrast to the current usma mechanism it is fair stable and strategy proof adoption of this mechanism benets cadets and the army this new

on the possibility of credit rationing in the stiglitz weiss model contrary to what is consistently assumed in the literature the return function cannot be hump shaped in the stiglitz weiss 1981 model this has important consequences for the possible occurrence of credit rationing and redlining with a single class of borrowers banks offer credit in two stages demand possibly exceeds supply in stage one but not in stage two with several observationally distinguishable borrower classes the firms in a borrower class are redlined only under circumstances which imply that they would not get credit in a perfect capital market either die rendite funktion kann im stiglitz weiss 1981 modell nicht so wie das in der literatur durchgangig angenommen wird hugelformig sein das hat wichtige implikationen fur die moglichkeit von kreditrationierung einerseits und fur die moglichkeit des ausschlusses ganzer kreditnehmergruppen vom kapitalmarkt andererseits mit nur einer klasse von kreditnehmern erfolgt die kreditvergabe in zwei stufen wahrend auf der ersten stufe eine ubernachfrage vorliegen kann herrscht auf der zweiten stufe marktraumung bei mehreren unterscheidbaren kreditnehmerklassen wird eine klasse nur unter den bedingungen vom kreditmarkt ausgeschlossen bei deren vorliegen sie auch in einem vollkommenen kreditmarkt keinen kredit erhalten wurde

matching and price competition comment the theory of two sided matching markets has interested researchers for its theoretical appeal and relevance to real life applications the matching of medical residents and hospitals in the united states has been studied extensively by alvin e roth 1984 and others the national resident matching program nrmp the matching authority in the us hospital resident matching market runs a centralized matching mechanism that is a variant of the deferred acceptance algorithm of david gale and lloyd s shapley 1962 redesigned by roth and elliott peranson 1999 a recent antitrust case against the nrmp charged that the centralized matching mechanism suppressed wages of residents although the lawsuit itself was dismissed it sparked discussion about the effect of centralized matching on wages and efficiency jeremy bulow and jonathan levin 2006 bl henceforth investigate a matching market with price competition where each firm can hire only one worker and show that a the average wage is lower b profit of each firm is higher c wages are more compressed and d the resulting matching is slightly less efficient in the presence of the matching mechanism than in any competitive equilibrium although bl declare we have chosen our assumptions for analytical simplicity and transparency not as the most realistic possible model of the residency match 654 these results were often interpreted as an argument against the nrmp and led to discussion about potential changes of the matching mechanism vincent p crawford forthcoming for instance proposes the flexible salary match in which hospitals are allowed to indicate several levels of possible wages and medical students are allowed to express preferences over pairs of hospitals and wages we show that conclusions a and b above do not necessarily hold when firms may hire more than one worker and the number of workers in different firms are different more specifically we present an example with multiple positions in which the average worker wage is higher in the equilibrium with the matching mechanism than in a competitive equilibrium and profit of each firm is lower in the equilibrium with the matching mechanism than in a competitive equilibrium our findings may explain why some of the results of bl disagree with empirical findings of muriel niederle and roth 2003 2004 who find little or no effect of the centralized matching on wages in some medical matching markets in the united states note that different firms hire different numbers of workers in many labor markets like the nrmp there are other reasons why the conclusions and policy implications of bl may not be applicable to markets like the nrmp for example a competitive equilibrium may not be a

relaxing the substitutes condition in matching markets with contracts in the many to one matching model with contracts i provide new necessary and new sufficient conditions for the existence of a stable allocation these new conditions exploit the fact that one side of the market has strict preferences over individual contracts

equilibria and indivisibilities gross substitutes and complements this paper examines an exchange economy with heterogeneous indivisible objects that can be substitutable or complementary we show that a competitive equilibrium exists in such economies provided that all the objects can be partitioned into two groups and from the viewpoint of each agent objects in the same group are substitutes and objects across the two groups are complements this condition generalizes the well known kelso crawford gross substitutes condition and is called gross substitutes and complements we also provide practical and typical examples from which substitutes and complements are both jointly observed

the structure performance relationship for european banking abstract the relationship between market structure and performance has been studied extensively for american banking in contrast little work has been done to investigate this relationship for european banking two explanations of a positive correlation between profitability and concentration have been advanced the traditional structure performance hypothesis scp and the efficient structure hypothesis previous empirical tests of the alternative hypotheses have yielded mixed results but the tests were not robust because they did not incorporate measures of efficiency directly in the model this study applies a stochastic cost frontier as proposed by aigner et al 1977 to derive measures of x inefficiency and scale inefficiency under the assumption that the errors are distributed half normal we incorporate these measures of inefficiencies directly into the tests as proposed by berger and hannan 1993 we do not find a positive and significant relationship between concentration and profitability for a sample of banks across 11 european countries over a four year period 1988 1991 however we do find evidence to support one of the two versions of the efficient structure hypothesis for banks located in countries with low concentration of banks since little support is found for either of the scp hypotheses a simple policy of strict limitations on cross border acquisitions and growth is not warranted

cumulative offer process is order independent this note shows that in the matching with contracts model the outcome of the cumulative offer process is order independent if every hospital has a choice function that satisfies the bilateral substitutability condition and the irrelevance of rejected contracts condition

bidding for army career specialties improving the rotc branching mechanism motivated by the low retention rates of us military academy and reserve officer training corps graduates the army recently introduced incentives programs in which cadets could bid 3 years of additional service obligation to obtain higher priority for their desired branches the full potential of this incentives program is not utilized because of the rotc s deficient matching mechanism i propose a design that eliminates these shortcomings and mitigates several policy problems the army has identified in contrast to the rotc mechanism my design utilizes market principles more extensively and it is a hybrid between a market mechanism and a priority based allocation mechanism