# School choice, university admissions, and entry-level labor markets

Hafalir, Isa E./Hakimov, Rustamdjan/Kübler, Dorothea/Kurino, Morimitsu (2014): **College Admissions with Entrance Exams: Centralized versus Decentralized. **Discussion** **Paper SP II 2014-208. Berlin: WZB.

We theoretically and experimentally study a college admissions problem in which colleges accept students by ranking students’ efforts in entrance exams. Students hold private information regarding their ability level that affects the cost of their efforts. We assume that student preferences are homogeneous over colleges. By modeling college admissions as contests, we solve and compare the equilibria of “centralized college admissions” (CCA) in which students apply to all colleges, and “decentralized college admissions” (DCA) in which students can only apply to one college. We show that lower ability students prefer DCA whereas higher ability students prefer CCA. The main qualitative predictions of the theory are supported by the experimental data, yet we find a number of behavioral differences between the mechanisms that render DCA less attractive than CCA compared to the equilibrium benchmark.

Hakimov, Rustamdjan/Kesten, Onur (2014): **The Equitable Top Trading Cycles Mechanism for School Choice. **Discussion** **Paper SP II 2014-210. Berlin: WZB.

A particular adaptation of Gale's top trading cycles procedure to school choice, the so-called TTC mechanism, has attracted much attention both in theory and practice due to its superior efficiency and incentive features. We discuss and introduce alternative adaptations of Gale’s original procedure that can offer improvements over TTC in terms of equity along with various other distributional considerations. Instead of giving all the trading power to those students with the highest priority for a school, we argue for the distribution of the trading rights of all slots of each school among those who are entitled to a slot at that school, allowing them to trade in a thick market where additional constraints can be accommodated. We propose a particular mechanism of this kind, the Equitable Top Trading Cycles (ETTC) mechanism, which is also Pareto efficient and strategy-proof just like TTC and eliminates justified envy due to pairwise exchanges. Both in simulations and in the lab, ETTC generates significantly fewer number of justified envy situations than TTC.

Guillen, Pablo/Hakimov, Rustamdjan (2014): **Monkey see, monkey do: truth-telling in matching algorithms and the manipulation of others. **Discussion Paper SP II 2014-202. Berlin: WZB.

We test the effect of the amount of information on the strategies played by others in the theoretically strategy-proof Top Trading Cycles (TTC) mechanism. We find that providing limited information on the strategies played by others has a negative and significant effect in truth-telling rates relative to full or no information about others’ strategies. Subjects report truthfully more often when either full information or no information on the strategies played by others is available. Our results have potentially important implications for the design of markets based on strategy-proof matching algorithms.

Anno, Hidekazu/Kurino, Morimitsu (2014): **Second-best incentive compatible allocation rules for multiple-type indivisible objects. **Discussion Paper SP II 2014-201. Berlin: WZB.** **

We consider the problem of allocating several types of indivisible goods when preferences are separable and monetary transfers are not allowed. Our finding is that the coordinate-wise application of strategy-proof and non-wasteful rules yields a strategy-proof rule with the following efficiency property: no strategy-proof rule Pareto-dominates the rule. Such rules are abundant as they include the coordinate-wise use of the two well-known priority-based rules of the top trading cycles (TTC) and the deferred acceptance (DA). Moreover, our result supports the current practice in Market Design that separately treats each type of market for its design.

Kesten, Onur/Kurino, Morimitsu (2012): **On the (im)possibility of improving upon the student-proposing deferred acceptance mechanism.** WZB Discussion Paper SP II 2012-202. Berlin: WZB.

This paper studies a general school choice problem with or without outside options. The Gale-Shapley student-proposing deferred acceptance mechanism (DA) has played a central role not only in theory but also in important practical applications. We show that in problems where some students cannot credibly submit a single school as the only acceptable option, it is possible to improve upon DA without sacrificing strategyproofness. On the other hand, in unrestricted problems where no outside options necessarily exist, it is not possible to improve upon DA via a strategy-proof mechanism.

Braun, Sebastian/Dwenger, Nadja/Kübler, Dorothea/Westkamp, Alexander (2012):** Implementing quotas in university admissions.** An Experimental Analysis. In: *Games and Economic Behavior*, Vol. 85, No. May, S. 232–251.

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.

Hugh-Jones, David/Kurino, Morimitsu/Vanberg, Christoph (2014):** An experimental study on the incentives of the probabilistic serial mechanism.** In: *Games and Economic Behavior*, Vol. 87, S. 367–380.

We report an experiment on the Probabilistic Serial (PS) mechanism for allocating indivisible goods. The PS mechanism, a recently discovered alternative to the widely used Random Serial Dictatorship mechanism, has attractive fairness and efficiency properties if people report their preferences truthfully. However, the mechanism is not strategy-proof, so participants may not truthfully report their preferences. We investigate misreporting in a set of simple applications of the PS mechanism. We confront subjects with situations in which the theory suggests that there is an incentive or no incentive to misreport. We find little misreporting in situations where misreporting is a Nash equilibrium. However, we also find a significant degree of misreporting in situations where there is actually no benefit to doing so. These findings suggest that the PS mechanism may have problems in terms of truthful elicitation.

Kurino, Morimitsu (2014):** House allocation with overlapping generations.** In: *American Economic Journal*, Vol. 6(1), S. 258–289.

Many real-life applications of house allocation problems are dynamic. For example, each year college freshmen move in and seniors move out of on-campus housing. Each student stays on campus for only a few years. A student is a "newcomer" in the beginning and then becomes an "existing tenant". Motivated by this observation, we introduce a model of house allocation with overlapping generations. In terms of a dynamic rule without monetary transfers, we examine two static rules of serial dictatorship and top trading cycles. We support these seniority-based rules in terms of their dynamic Pareto efficiency and incentive compatibility.

Hashimoto, Tadashi/Hirata, Daisuke/Kesten, Onur/Kurino, Morimitsu/Ünver, Utku (2014):** Two axiomatic approaches to the probabilistic serial mechanism.** In: *Theoretical Economics*, Vol. 9, S. 253–277.

This paper studies the problem of assigning a set of indivisible objects to a set of agents when monetary transfers are not allowed and agents reveal only ordinal preferences, but random assignments are possible. We offer two characterizations of the probabilistic serial mechanism, which assigns lotteries over objects. We show that it is the only mechanism that satisfies non-wastefulness and ordinal fairness, and the only mechanism that satisfies sd-efficiency, sd-envy-freeness, and weak invariance or weak truncation robustness (where “sd” stands for first-order stochastic dominance).