Fictitious students creation incentives in school choice problems

We address the question of whether schools can manipulate the student-optimal stable mechanism by creating fictitious students in school choice problems. To this end, we introduce two different manipulation concepts, where one of them is stronger. We first demonstrate that the student-optimal stable mechanism is not even weakly fictitious student-proof under general priority structures. Then, we investigate the same question under acyclic priority structures. We prove that, while the student-optimal stable mechanism is not strongly fictitious student-proof even under the acyclicity condition, weak fictitious student-proofness is achieved under acyclicity. This paper, hence, shows a way to avoid the welfare detrimental fictitious students creation (in the weak sense) in terms of priority structures

Alternative characterizations of Boston mechanism

Kojima and Ünver (2011) are the first to characterize the class of mechanisms coinciding with the Boston mechanism for some priority order. By mildly strengthening their central axiom, we are able to pin down the Boston mechanism outcome for every priority order. Our main result shows that a mechanism is outcome equivalent to the Boston mechanism at every priority if and only if it respects both preference rankings and priorities and satisfies individual rationality for schools. In environments where each student is acceptable to every school, respecting both preference rankings and priorities is enough to characterize the Boston mechanism

Filling position incentives in matching markets

One of the main problems in the hospital-doctor matching is the maldistribution of doctor assignments across hospitals. Namely, many hospitals in rural areas are matched with far fewer doctors than what they need. The so called "Rural Hospital Theorem" (Roth (1984)) reveals that it is unavoidable under stable assignments. On the other hand, the counterpart of the problem in the school choice context|low enrollments at schools| has important consequences for schools as well. In the current study, we approach the problem from a different point of view and investigate whether hospitals can increase their filled positions by misreporting their preferences under well-known Boston, Top Trading Cycles, and stable rules. It turns out that while it is impossible under Boston and stable mechanisms, Top Trading Cycles rule is manipulable in that sense

On the "group non-bossiness" property

We extend the concept of non-bossiness to groups of agents and say that a mechanism is group non-bossy if no group of agents can change the assignment of someone else while theirs being unaffected by misreporting their preferences. First, we show that they are not equivalent properties. We, then, prove that group strategy-proofness is sufficient for group non-bossiness. While this result implies that the top trading cycles mechanism is group non-bossy, it also provides a characterization of the market structures in which the deferred acceptance algorithm is group non-bossy

Cooperation cannot be sustained in a discounted repeated prisoners' dilemma with patient short and long run players

This study presents a modified version of the repeated discounted prisoners' dilemma with long and short-run players. In our setting a short-run player does not observe the history that has occurred before he was born, and survives into next phases of the game with a probability given by the current action profile in the stage game. Thus, even though it is improbable, a short-run player may live and interact with the long-run player for infinitely long amounts of time. In this model we prove that under a mild incentive condition on the stage game payoffs, the cooperative outcome path is not subgame perfect no matter how patient the players are. Moreover with an additional technical assumption aimed to provide a tractable analysis, we also show that payoffs arbitrarily close to that of the cooperative outcome path, cannot be obtained in equilibrium even with patient players

When manipulations are harm[less]ful?

We say that a mechanism is harmless if no student can ever misreport his preferences so that he does not hurt but someone else. We consider a large class of rules which includes the Boston, the agent-proposing deferred acceptance, and the school-proposing deferred acceptance mechanisms (sDA). In this large class, the sDA happens to the unique harmless mechanism. We next provide two axiomatic characterizations of the sDA. First, the sDA is the unique stable, non-bossy, and independent of irrelevant student mechanism. The last axiom is a weak variant of consistency. As harmlessness implies non bossiness, the sDA is also the unique stable, harmless, and independent of irrelevant student mechanism

A non-cooperation result in a repeated discounted prisoners' dilemma with long and short run players

This study presents a modified version of the repeated discounted prisoners' dilemma with long and short-run players. In our setting a short-run player does not observe the history that has occurred before he was born, and survives into next phases of the game with a probability given by the current action profile in the stage game. Thus, even though it is improbable, a short-run player may live and interact with the long-run player for infinitely long amounts of time. In this model we prove that under a mild incentive condition on the stage game payoffs, the cooperative outcome path is not subgame perfect no matter how patient the players are. Moreover with an additional technical assumption aimed to provide a tractable analysis, we also show that payoffs arbitrarily close to that of the cooperative outcome path, cannot be obtained in equilibrium even with patient players

Enrollment manipulations in school choice

In the United States, schools with more students receive more federal funds. Yet a harsher consequence of the low enrollment is school closure. Schools, therefore, have a strong incentive to have as many students as possible. This might lead them to engage in strategic behavior to increase their enrollment. This paper studies one such kind of manipulative behavior by schools in the school choice setting. Specifically, we study whether schools can increase their enrollment levels through first concealing their capacity and then rematching for their available seats under the well-known Boston (BM), Top Trading Cycles (TTC), and stable mechanisms (Gale and Shapley, 1962). All of the mechanisms turn out to be manipulable by schools in this way whenever students can freely rematch after the centralized match. Nevertheless, if only unassigned students are allowed to rematch, then schools cannot manipulate the BM and stable mechanisms. TTC, on the other hand, continues to be manipulable

Characterizations of the cumulative offer process

In the matching with contracts setting, we provide new axiomatic characterizations of the “cumulative offer process” ( COPCOP ) in the domain of hospital choice functions that satisfy “unilateral substitutes” and “irrelevance of rejected contracts.” We say that a mechanism is truncation-proof if no doctor can ever benefit from truncating his preferences. Our first result shows that the COPCOP is the unique stable and truncation-proof mechanism. Next, we say that a mechanism is invariant to lower-tail preference change if no doctor’s assignment changes after he changes his preferences over the contracts that are worse than his assignment. Our second result shows that a mechanism is stable and invariant to lower-tail preference change if and only if it is the COPCOP . Lastly, by extending Kojima and Manea’s (Econometrica 78:633–653, 2010) result, we show that the COPCOP is the unique stable and weakly Maskin monotonic mechanism. I am grateful to the associate editor and the anonymous referee for their through comments and suggestions. I thank Bertan Turhan for his comments. The author gratefully acknowledges the Marie Curie International Reintegration Grant (No: 618263) within the European Community Framework Programme and TÜBİTAK (The Scientific and Technological Research Council of Turkey) Grant (No: 113K763) within the National Career Development Program

Graduate admission with financial support

We formulate a graduate admission problem, which features different financial support options, in a matching with contracts setting. We introduce an algorithm, called "Minimum-Need Adjusted Cumulative Offer Process" (MCOP). Under certain mild assumptions on students' preferences, MCOP is stable, fair, strategy-proof, and respects improvements. Moreover, it limitedly respects departments' minimum number of teaching and research assistant (TA/RA) needs in the sense that no other stable mechanism honors those needs more than MCOP. It is also efficient within the class of stable mechanisms that limitedly respect the TA/RA needs. Lastly, we offer an axiomatic characterization: A mechanism is stable and strategy-proof, and limitedly respects the TA/RA needs if and only if it is MCOP