Strategyproof matching with regional minimum and maximum quotas

This paper considers matching problems with individual/regional minimum/maximum quotas. Although such quotas are relevant in many real-world settings, there is a lack of strategyproof mechanisms that take such quotas into account. We first show that without any restrictions on the regional structure, checking the existence of a feasible matching that satisfies all quotas is NP-complete. Then, assuming that regions have a hierarchical structure (i.e., a tree), we show that checking the existence of a feasible matching can be done in time linear in the number of regions. We develop two strategyproof matching mechanisms based on the Deferred Acceptance mechanism (DA), which we call Priority List based Deferred Acceptance with Regional minimum and maximum Quotas (PLDA-RQ) and Round-robin Selection Deferred Acceptance with Regional minimum and maximum Quotas (RSDA-RQ). When regional quotas are imposed, a stable matching may no longer exist since fairness and nonwastefulness, which compose stability, are incompatible. We show that both mechanisms are fair. As a result, they are inevitably wasteful. We show that the two mechanisms satisfy different versions of nonwastefulness respectively; each is weaker than the original nonwastefulness. Moreover, we compare our mechanisms with an artificial cap mechanism via simulation experiments, which illustrate that they have a clear advantage in terms of nonwastefulness and student welfare

Strategyproof and fair matching mechanism for ratio constraints

We introduce a new type of distributional constraints called ratio constraints, which explicitly specify the required balance among schools in two-sided matching. Since ratio constraints do not belong to the known well-behaved class of constraints called M-convex set, developing a fair and strategyproof mechanism that can handle them is challenging. We develop a novel mechanism called quota reduction deferred acceptance (QRDA), which repeatedly applies the standard DA by sequentially reducing artificially introduced maximum quotas. As well as being fair and strategyproof, QRDA always yields a weakly better matching for students compared to a baseline mechanism called artificial cap deferred acceptance (ACDA), which uses predetermined artificial maximum quotas. Finally, we experimentally show that, in terms of student welfare and nonwastefulness, QRDA outperforms ACDA and another fair and strategyproof mechanism called Extended Seat Deferred Acceptance (ESDA), in which ratio constraints are transformed into minimum and maximum quotas

Towards a fair distribution mechanism for asylum

It has been suggested that the distribution of refugees over host countries can be made more fair or efficient if policy makers take into account not only numbers of refugees to be distributed but also the goodness of the matches between refugees and their possible host countries. There are different ways to design distribution mechanisms that incorporate this practice, which opens up a space for normative considerations. In particular, if the mechanism takes countries’ or refugees’ preferences into account, there may be trade-offs between satisfying their preferences and the number of refugees distributed. This article argues that, in such cases, it is not a reasonable policy to satisfy preferences. Moreover, conditions are given which, if satisfied, prevent the trade-off from occurring. Finally, it is argued that countries should not express preferences over refugees, but rather that priorities for refugees should be imposed, and that fairness beats efficiency in the context of distributing asylum. The framework of matching theory is used to make the arguments precise, but the results are general and relevant for other distribution mechanisms such as the relocations currently in effect in the European Unio

Weighted Matching Markets with Budget Constraints

We investigate markets with a set of students on one side and a set of colleges on the other. A student and college can be linked by a weighted contract that defines the student's wage, while a college's budget for hiring students is limited. Stability is a crucial requirement for matching mechanisms to be applied in the real world. A standard stability requirement is coalitional stability, i.e., no pair of a college and group of students has any incentive to deviate. We find that a coalitionally stable matching is not guaranteed to exist, verifying the coalitional stability for a given matching is coNP-complete, and the problem of finding whether a coalitionally stable matching exists in a given market, is Sigma(P)(2)-complete: NPNP -complete. Other negative results also hold when blocking coalitions contain at most two students and one college. Given these computational hardness results, we pursue a weaker stability requirement called pairwise stability, where no pair of a college and single student has an incentive to deviate. Unfortunately, a pairwise stable matching is not guaranteed to exist either. Thus, we consider a restricted market called a typed weighted market, in which students are partitioned into types that induce their possible wages. We then design a strategy-proof and Pareto efficient mechanism that works in polynomial-time for computing a pairwise stable matching in typed weighted markets

Affirmative Action through Minority Reserves: An Experimental Study on School Choice

Presentado en: Seminar 3, Departamento de Fundamentos de Análisis Económico de la Universidad de Alicante el 26 de mayo de 2014Comunicación presentada el 26 de junio de 2014 en las 13th Journées Louis-André Gérard-Varet, celebrdas del 23 al 26 de junio de 2014 en Aix-en-Provence (Francia) y organizadas por el IDEP, Institut d'éconjomie publiquePresentado también el 16 de abril de 2015 en el Meeting of COST Action IC1205 on Computational Social Choice, COST European Cooperation in Science and Technology, celebrado del 14 al 16 de abril de 2015 en Glasgow (Reino Unido)Publicado como: Barcelona GSE Working Paper Series nº 752. Barcelona: Barcelona Graduate School of Economics, february 2014 (version September 2014)Minority reserves are an affirmative action policy proposed by Hafalir et al. (2013) in the context of school choice. We study in the laboratory the effect of minority reserves on the outcomes of two prominent matching mechanisms, the Gale-Shapley and the Top Trading Cycles mechanisms. Our first experimental result is that the introduction of minority reserves enhances truth-telling of some minority students under the Gale-Shapley but not under the Top Trading Cycles mechanism. Secondly, for the Gale-Shapley mechanism we also find that the stable matchings that are more beneficial to students are obtained more often relative to the other stable matchings when minority reserves are introduced. Finally, the overall expected payoff increases under the Gale-Shapley but decreases under the Top Trading Cycles mechanism if minority reserves are introduced. However, the minority group benefits and the majority group is harmed under both mechanismsPeer Reviewe