Non-revelation mechanisms in many-to-one markets

This paper presents a sequential admission mechanism where students are allowed to send multiple applications to colleges and colleges sequentially decide the applicants to enroll. The irreversibility of agents decisions and the sequential structure of the enrollments make truthful behavior a dominant strategy for colleges. Due to these features, the mechanism implements the set of stable matchings in Subgame Perfect Nash equilibrium. We extend the analysis to a mechanism where colleges make proposals to potential students and students decide sequentially. We show that this mechanism implements the stable set as well

Non-revelation mechanisms in many-to-one markets

This paper presents a sequential admission mechanism where students are allowed to send multiple applications to colleges and colleges sequentially decide the applicants to enroll. The irreversibility of agents decisions and the sequential structure of the enrollments make truthful behavior a dominant strategy for colleges. Due to these features, the mechanism implements the set of stable matchings in Subgame Perfect Nash equilibrium. We extend the analysis to a mechanism where colleges make proposals to potential students and students decide sequentially. We show that this mechanism implements the stable set as well.Stable matching, Subgame perfect Nash equilibrium

Games with capacity manipulation : incentives and Nash equilibria

Studying the interaction between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized capacity manipulations games where hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introducedStable matching, Capacity, Nash equilibrium, Cycles

Pareto Dominance of Deferred Acceptance through Early Decision

An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance

The iterative deferred acceptance mechanism

Lately, there has been an increase in the use of sequential mechanisms, instead of the traditional direct counterparts, in college admissions in many countries, including Germany, Brazil, and China. We describe these mechanisms and identify their shortcomings in terms of incentives and outcome properties. We introduce a new mechanism, which improves upon these shortcomings. Unlike direct mechanisms, which ask students for a full preference ranking over colleges, our mechanism asks students to sequentially make choices or submit partial rankings from sets of colleges. These are used to produce a tentative allocation at each step. If at some point it is determined that a student can no longer be accepted into previous choice, then she is asked to make another choice among colleges that would tentatively accept her. Participants following the simple strategy of choosing the most-preferred college in each step is an ex-post equilibrium that yields the Student-Optimal Stable Matching

Games with capacity manipulation: Incentives and Nash equilibria

Studying the interactions between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized games of manipulation in which hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced

Non-revelation mechanisms in many-to-one markets

In this study we present a simple mechanism in a many-to-one matching market where multiple costless applications are allowed. The mechanism is based on the principles of eligibility and priority and it implements the set of stable matchings in Subgame Perfect Nash Equilibrium. We extend the analysis to a symmetric mechanism where colleges and students interchange their roles. This mechanism also implements the set of stable matchings

Non-revelation Mechanisms in Many-to-One Markets

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