Working Papers
The strong effects of weak externalities on school choice
Eduardo Duque and J.P. Torres-Martínez
In classical school choice contexts there exists a centralized assignment procedure that is stable and strategy-proof: the Gale-Shapley student-optimal stable mechanism. We show that this property is not satisfied when externalities are incorporated into the model, even in scenarios in which students are primarily concerned about their own placement (weak externalities). Indeed, although weak externalities have no effects on stability, there are school choice contexts in which no stable and strategy-proof mechanism exists. Furthermore, we show that stability and strategy-proofness are compatible if and only if schools' priorities are Ergin-acyclic. This strong effect of weak externalities on incentives is related to the incompatibility between stability, strategy-proofness, and non-bossiness in classical school choice problems.
Multi-level matching markets
Gabriela Denis and J.P. Torres-Martínez
In a multi-level matching market, agents participate in two centralized assignment process over time in order to obtain placements at institutions that they consider complementary. In this context, we aim to understand how the interrelationship between the underlying clearinghouses influences agents' behavior. By identifying agents with students, and institutions with high schools or colleges, we analyze the compatibility between strategy-proofness, stability, and efficiency when colleges may prioritize students considering their secondary education and students' preferences for colleges may depend on their high school placement. We show that many multi-level matching markets have no stable mechanism less manipulable than another. Moreover, the stable mechanism that implements the student-optimal deferred acceptance algorithm in each clearinghouse---denoted by DA*---is the only one that can be strategy-proof, but strong assumptions on school priorities are required to ensure this property. However, a student can stop manipulating DA* when a limit is imposed on the number of reporting schools. Although DA* cannot be Pareto dominated by another stable mechanism, its inefficiency might not be mitigated without harming some students.
On housing markets with indecisive agents
Emilio Guamán and J.P. Torres-Martínez
We study the non-monetary exchange of indivisible goods when agents may be unable to compare some of them. Adding incomplete preferences to the Shapley-Scarf housing market model, we introduce two concepts of coalitional stability: the core and the strong core. The core is the set of allocations immune to blocking coalitions that improve the well-being of house-switching members, while the strong core is the set of allocations immune to blocking coalitions that may leave some members with a house incomparable with the original. In the domain of incomplete, transitive, and strict preferences, we characterize a family of group strategy-proof mechanisms that always select allocations in the core. Moreover, in the subdomain in which incomplete preferences induce transitive incomparability relations, we show that there are efficient, individually rational, and weakly group strategy-proof mechanisms that select allocations in the strong core when it is non-empty. We also extend these results to housing allocation problems in which existing tenants and newcomers coexist.
Incentives in three-sided markets
Jorge Arenas and J.P. Torres-Martínez
In a class of three-sided matching problems in which the core is non-empty, we show that no stable mechanism is strategy-proof for those who internalize the trilateral structure of the market in their preferences. This impossibility is related to the incompatibility between stability, one-sided strategy-proofness, and one-sided non-bossiness in two-sided markets. Furthermore, unlike what happens in marriage markets, strong restrictions on preferences are needed to ensure that stability and one-sided strategy-proofness are compatible for each market side.
