The Eeckhout Condition and the Subgame Perfect Implementation of Stable Matching

We investigate an extensive form sequential matching game of perfect information. We show that the subgame perfect equilibrium of the sequential matching game leads to the unique stable matching when the Eeckhout Condition (2000) for existence of a unique stable matching holds, regardless of the sequence of agents. This result does not extend to preferences that violate the Eeckhout Condition, even if there is a unique stable matching.Matching; unique stable matching; subgame perfect equilibrium

Sequential decisions in the college admissions problem.

This paper studies sequential mechanisms which mimic a matching procedures for many-to-one real life matching markets. We provide a family of mechanisms implementing the students' optimal allocation in Subgame Perfect Equilibrium.Matching markets; College admission problems; Mechanism design;

Decentralized Job Matching

This paper studies a decentralized job market model where firms (academic departments) propose sequentially a (unique) position to some workers (Ph.D. candidates). Successful candidates then decide whether to accept the offers, and departments whose positions remain unfilled propose to other candidates. We distinguish between several cases, depending on whether agents’ actions are simultaneous and/or irreversible (if a worker accepts an offer he is immediately matched, and both the worker and the firm to which she is matched go out of the market). For all these cases, we provide a complete characterization of the Nash equilibrium outcomes and the Subgame Perfect equilibria. While the set of Nash equilibria outcomes contain all individually rational matchings, it turns out that in most cases considered all subgame perfect equilibria yield a unique outcome, the worker-optimal matching.Two-sided matching ; job market ; subgame perfect equilibrium ; irreversibilities

Decentralised Job Matching

This paper studies a decentralised job market model where firms (academic departments) propose sequentially a (unique) position to some workers (Ph.D. candidates). Successful candidates then decide whether to accept the offers, and departments whose positions remain unfilled propose to other candidates. We distinguish between several cases, depending on whether agents’ actions are simultaneous and/or irreversible (if a worker accepts an offer he is immediately matched, and both the worker and the firm to which she is matched go out of the market). For all these cases, we provide a complete characterization of the Nash equilibrium outcomes and the Subgame Perfect equilibria. While the set of Nash equilibria outcomes contain all individually rational matchings, it turns out that in most cases considered all subgame perfect equilibria yield a unique outcome, the worker-optimal matching.Two-sided matching, Job market, Subgame perfect equilibrium, irreversibilities

Application Costs in Sequential Admission Mechanisms

This paper considers a realistic family of admission mechanisms, with multiple applications and application costs. Multiple applications impose serious coordination problems to colleges, but application costs restore stability. Without application costs and under incomplete information unstable allocations emerge.Application Costs; Matching Markets; Implementation.

A Simple Selling and Buying Procedure

For the assignment game, we analyze the following mechanism: sellers, simultaneously, fix their prices first; then buyers, sequentially, decide which object to buy, if any, among the remaining objects. The first phase of the game determines the potential prices, while the second phase determines the actual matching. We prove that the set of subgame perfect equilibria in pure strategies in the strong sense of the mechanism coincides with the set of sellers' optimal stable outcomes when buyers use maximal strategies. That is, the mechanism leads to the maximum equilibrium prices and to an optimal matching.

Ramón y Cajal: Mediation and Meritocracy

The Ramón y Cajal Program promotes the hiring of top researchers in Spanish R&D centers and academic institutions. The centralized mechanism associated to the Program is analyzed. The paper models it as a two-sided matching market and studies if it provides the incentives to increase the quality of the researchers hired. We analyze the mechanism both under complete and incomplete information. The comparison of the theoretical findings with the available data points out that the mechanism provides poor incentives and does not prevent collusion between research departments and candidates in the hiring process.Matching Markets; Preagreements; Implementation.

A new dynamic mechanism to the marriage problem with a variant

We know from Gale and Shapley (1962) that every Two-Sided Matching Game has a stable solution. It is also well-known that the number of stable matchings increases with the number of agents on both sides. In this paper, we propose two mechanisms, one of which is a variant of the other, to the marriage problem. Our original mechanism implements the full set of stable matchings for any preference profile. On the other hand, the variant mechanism parititons the domain of preference profiles into two; for one set, it implements the full set of stable matchings like the original mechanism and for the other, it ends up with a proper subset of the set of stable matchings. Besides, for some profiles with multi stability, it gives one of the optimal stable matchings. Namely, the second mechanism coincides either with the original mechanism or it is an improvement for one side; and in some profiles, the algortihm induces Gale and Shapley's algorithm for some profiles. Thus, it is a "middle" mechanism

Sequential Decisions in the College Admissions Problem

This paper studies sequential mechanisms which mimic matching prodedures for many-to-one real life matching markets. We provide a family of mechanisms implementing the student´optimal allocation in Subgame Perfect Equilibriu

Sequential decisions in the college admissions problem

This paper models a contractual process by a sequential mechanism, which mimics matching procedures for many-to-one real-life matching problems. In this framework, we provide a family of mechanisms implementing the student-optimal matching in Subgame Perfect Equilibrium (SPE).Alcalde’s work is partially supported by the Institut Valencia` d’Investigacions Econo`miques and the Spanish Ministerio de Educacio´n y Cultura under project BEC 2001-0535. Romero-Medina acknowledges financial support from the Spanish Ministerio de Educacio´n y Cultura under project BCE-2002-02194 and Comunidad de Madrid under project 02303.Publicad