A general strategy-proof fair allocation mechanism revisited

This paper revisits the fair and optimal allocation mechanism (Sun and Yang, Economics Letters 81:73-79, 2003) and demonstrates that it is coalitionally strategy-proof. The proof is valid for general preferences, it is simple and it is short.assignment game, fairness, strategy-proofness

An Introduction to Fair and Non-Manipulable Allocations of Indivisible Objects

This paper analyzes a way of allocating primarily three indivisible objects to the same number of individuals. We define an allocation rule that, given the preferences of the individuals, distributes an amount of money together with exactly one indivisible object to each of the individuals in a fair and optimal way. The monetary distributions are foremost interpreted as compensations and are regulated by an exogenously given upper limit. We examine some of the rule's properties, with the most important one being that the rule is coalitionally strategy-proof

Sets in Excess Demand in Ascending Auctions with Unit-Demand Bidders

This paper analyzes the problem of selling a number of indivisible items to a set of unitdemand bidders. An ascending auction mechanism called the Excess Demand Ascending Auction (EDAA) is defined. The main results demonstrate that EDAA terminates in a finite number of iterations and that the exact auction mechanism in Demange, Gale and Sotomayor (J. Polit. Economy 94: 863–872, 1986) and its modification based on the Ford- Fulkerson method, proposed by Sankaran (Math. Soc. Sci. 28: 143–150, 1994), reduce to special cases of EDAA.Multi-item auction;Unit-demand bidders;Excess demand;Algorithms

College admissions as a market design problem

Opiskelijavalintojen suunnittelu on herättänyt Suomessa paljon keskustelua, kun viimeaikaiset poliittiset päätökset ovat muuttaneet valintajärjestelmää keskitetympään suuntaan. Jotkut antaisivat korkeakoulujen itse päättää opiskelijavalinnoistaan, kun taas toiset uskovat keskitetyn ja ylioppilastutkinnon arvosanoja hyödyntävän valintajärjestelmän olevan entistä, hajautettua järjestelmää kustannustehokkaampi. Tarkastellen sekä keskitettyjen että hajautettujen pariutumismarkkinoiden teoriaa että myös kouluvalintoja ja pääsykokeita koskevaa empiiristä kirjallisuutta, tämä tutkielma pyrkii kuvaamaan niitä lukuisia tekijöitä, joita politiikantekijän täytyy huomioida opiskelijavalintoja kehittäessä. Todellisten mekanismien suunnitteluun hyvin soveltuvana kaksisuuntaisten pariutumismarkkinoiden kirjallisuuteen perehdytään syvällisesti. Niin sanottu student-proposing deferred acceptance –algoritmi osoittautuu parhaaksi valinnaksi, jos politiikantekijä kokee erityisen tärkeäksi, että mekanismi kannustaa hakijoita totuudenpuhumiseen, ja toisaalta valintakriteerinä käytettävää pisteytystä noudatetaan. Näin ainakin, jos korkeakoulujen ei uskota manipuloivan mekanismia. Käytännön mekanismit kuitenkin usein jättävät hakijoille joitain kannustimia raportoida todellisista eroavia preferensseja, hakijat saattavat raportoida epätosia preferensseja itselleen epäedullisesti, ja student-proposing deferred acceptance –algoritmissakin kaikkien mahdollisten hakukohteiden asettaminen preferenssijärjestykseen on vain heikosti dominanttia. Siksi ilmoitettuja preferenssejä ei tulisi ajatella suoraksi todistusaineistoksi hakijoiden preferensseistä. Korkeakouluille yhteiset pääsykokeet ylioppilastutkinnon muodossa voivat olla hajautettua järjestelmää kustannustehokkaampia, kun korkeakoulujen ei tarvitse kuluttaa resursseja erillisten pääsykokeiden järjestämiseen. Opiskelijoilla on kuitenkin sitten korkeammat kannustimet menestyä ylioppilaskokeissa, ja on jo näyttöä siitä, että ylioppilastutkinnon arvosanoja pyritään korottamaan entistä enemmän. Kokonaisvaikutus kustannuksiin jää siis epävarmaksi empiiriseksi kysymykseksi. Valmennuskurssien tärkeys vähentynee, mikä säästää yhteiskunnan resursseja ja lisää sosioekonomista tasa-arvoa. Toisaalta aikaisemmin elämässä tehtyjen valintojen merkitys korostuu, mikä saattaa heikentää sosioekonomista tasa-arvoa. Ylioppilastutkinnon tärkeyden korostuminen parantaa kannustimia ahkeraan opiskeluun jo lukio-opintojen aikana, minkä politiikantekijä voi nähdä hyödylliseksi. Vaikka yhteisiin pääsykokeisiin perustuva valintajärjestelmä parantaa huomattavasti opiskelijan mahdollisuuksia tulla valituksi toissijaiseen hakukohteeseen tultuaan hylätyksi ensisijaisesta hakukohteesta, jää empiiriseksi kysymykseksi, kuinka paljolti tämä vähentää uudelleenhakemista kilpailtuihin opiskelupaikkoihin. Tiettyihin korkeakouluihin kohdistuva ylikysyntä on suora seuraus hakijoiden preferensseistä, eikä ratkaistavissa millään mekanismilla, mikä antaa korkean arvon hakijoiden preferenssien tyydyttämiselle.The design of college admissions has been a heatedly discussed topic in Finland, as recent government initiatives have led to a more centralized system. Some argue for letting colleges decide on their admissions procedures, while others believe that a centralized matchmaking procedure with priorities determined by the matriculation examination would be more cost-effective. This thesis aims to characterize various factors that the policy maker must take into account when designing a college admissions procedure, in light of existing theoretical research on both centralized and decentralized matching markets and empirical studies on social determinants of college choice and the capacity of entrance examinations to elicit information on student ability and motivation. The two-sided matching literature is discussed extensively because of its usefulness for designing centralized clearinghouses for matching markets. The student-proposing deferred acceptance algorithm emerges as the best choice for a policy maker who regards strategy-proofness and respecting of priorities as especially important, at least if manipulation by colleges is implausible. However, strategy-proofness is fragile in practical applications, applicants may try to manipulate also strategy-proof mechanisms and reporting the whole preference relation is still only weakly dominant. Consequently, satisfaction of reported preferences should not be taken as evidence of welfare properties of a matching without qualifications. The use of a common entrance examination may be more cost effective than a system based on college-specific entrance examinations, as colleges do not then need to spend resources on organizing the examinations. However, students have then stronger incentives to perform in the common entrance examination, and there is already evidence that more students retake the matriculation examination in Finland. The overall effect on the costs of organizing entrance examinations is an uncertain empirical matter. The importance of preparation courses is likely to decrease, which saves resources and contributes to socioeconomic equity. On the other hand, making students choose on their study paths earlier in life may erode socioeconomic equity. A larger role for the matriculation examination provides stronger incentives for showing effort in high school, which the policy maker may see as beneficial. While a system with a common entrance examination makes it possible for a student to get admitted to a second preference when she is rejected by her first preference, it remains an empirical question to what extent this reduces the propensity to apply again to competitive colleges. The excess demand for certain colleges is a result of student preferences and is not solvable by any mechanism that gives a strong priority to satisfying student preferences

On the manipulability of competitive equilibrium rules in many-to-many buyer-seller markets

We thank participants of seminars at the Universities of Salamanca, Valencia, Osaka, Waseda, East Anglia, and Seoul National, at the workshop on Game Theory in Rio de Janeiro, MOVE-Jerusalem, and ASSET meeting in Aix Marseille, as well as two reviewers and an Associate Editor for very helpful comments for very helpful comments. Marilda Sotomayor acknowledges financial support from CNPq-Brazil. David Pérez-Castrillo is a fellow of MOVE. He acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2012-31962 and ECO2015-63679-P), Generalitat de Catalunya (2014SGR-142), the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563) and ICREA Academia. Previous versions of this paper, analyzing one-to-one matching models only, circulated under the titles "Two Folk Manipulability Theorems in One-to-one Two-sided Matching Markets with Money as a Continuous Variable" and "Two Folk Manipulability Theorems in the General One-to-one Two-sided Matching Markets with Money".We analyze the manipulability of competitive equilibrium allocation rules for the simplest many-to-many extension of Shapley and Shubik's (Int J Game Theory 1:111-130, 1972) assignment game. First, we show that if an agent has a quota of one, then she does not have an incentive to manipulate any competitive equilibrium rule that gives her her most preferred competitive equilibrium payoff when she reports truthfully. In particular, this result extends to the one-to-many (respectively, many-to-one) models the Non-Manipulability Theorem of the buyers (respectively, sellers), proven by Demange (Strategyproofness in the assignment market game. École Polytechnique, Laboratoire d'Économetrie, Paris, 1982), Leonard (J Polit Econ 91:461-479, 1983), and Demange and Gale (Econometrica 55:873-888, 1985) for the assignment game. Second, we prove a "General Manipulability Theorem" that implies and generalizes two "folk theorems" for the assignment game, the Manipulability Theorem and the General Impossibility Theorem, never proven before. For the one-to-one case, this result provides a sort of converse of the Non-Manipulability Theorem

Essays on Matching and Market Design.

Using a combination of experimental, theoretical, computational and empirical methods, my dissertation studies matching and market design with applications to education policy including school choice and college admissions. I tackle three problems: the effect of standardized tests on matching mechanisms (Chapter 2); experimental evidence of matching in a large market (Chapter 3); and quasi-experimental evidence of the theoretical properties of matching mechanisms (Chapter 4). In Chapter 2, I investigate the matching of college admissions, where students' admission priorities and colleges' preferences over students are misaligned, due the imperfect measure of student aptitudes by standardized entrance tests. I show that in this case any matching mechanism that is stable with regard to priority is not stable with regard to preference. The resulting instability leads to market unraveling. However, a manipulable mechanism, combined with limited information about priorities, may succeed in mending this market failure. A laboratory experiment confirms this theoretical prediction. In Chapter 3, we study the role market size plays in school choice. We evaluate the performance of the Boston and the Deferred Acceptance (DA) mechanism in laboratory with different market sizes. The results show that increasing the market size from 4 to 40 students per match increases participant truth-telling under the DA but decreases it under the Boston mechanism, leading to a decrease in efficiency but no change in the large stability advantage of the DA over the Boston mechanism. Furthermore, increasing the scale to 4,000 students per match has no effect on either individual behavior or mechanism performance. Our results indicate that "large market" in practice is smaller than in theory. In Chapter 4, we evaluate the Immediate Acceptance (Boston) mechanism and the parallel mechanism in college admissions, both in the laboratory and with naturally-occurring data. Through both channels, we find that the more emphasis a mechanism put on the first choice, the more likely students rely on their rankings in the test to manipulate their reported preferences, which confirms the theoretical predictions. Although in the laboratory, the parallel mechanism proves to be more stable, we do not observe economically significant difference in stability in the field.PhDInformationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113391/1/mjng_1.pd

Entitlement theory of justice and end-state fairness in the allocation of goods

Robert Nozick allegedly introduced his liberal theory of private ownership as an objection to theories of end-state justice. Nevertheless, we show that, in a stylized framework for the allocation of goods in joint ventures, both approaches can be seen as complementary. More precisely, in such a context, self-ownership (the basis for Nozick’s entitlement theory of justice) followed by voluntary transfer (Nozick’s principle of just transfer) can lead to end-state fairness (as well as Pareto efficiency). Furthermore, under a certain solidarity condition, the only way to achieve end-state fairness, following Nozick’s procedure, is to endorse an egalitarian rule for the initial assignment of rights

Proposal For a Study of Commonsense Physical Reasoning

This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-80-C-0505.Our common sense views of physics are the first coin in our intellectual capital; understanding precisely what they contain could be very important both for understanding ourselves and for making machines more like us. This proposal describes a domain that has been designed for studying reasoning about constrained motion and describes my theories about performing such reasoning. The issues examined include qualitative reasoning about shape and physical processes, as well as ways of using knowledge about motion other than "envisioning". Being a proposal, the treatment of these issues is necessarily cursory and incomplete.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

Design Principles for Signal Detection in Modern Job Application Systems: Identifying Fabricated Qualifications

Hiring a new employee is traditionally thought to be an uncertain investment. This uncertainty is lessened by the presence of signals that indicate job fitness. Ideally, job applicants objectively signal their qualifications, and those signals are correctly assessed by the hiring team. In reality, signal manipulation is pervasive in the hiring process, mitigating the reliability of signals used to make hiring decisions. To combat these inefficiencies, we propose and evaluate SIGHT, a theoretical class of systems affording more robust signal evaluation during the job application process. A prototypical implementation of the SIGHT framework was evaluated using a mock-interview paradigm. Results provide initial evidence that SIGHT systems can elicit and capture qualification signals beyond what can be traditionally obtained from a typical application and that SIGHT systems can assess signals more effectively than unaided decision-making. SIGHT principles may extend to domains such as audit and security interviews