Games of capacity allocation in many-to-one matching with an aftermarket

In this paper, we study many-to-one matching (hospital-intern markets) with an aftermarket. We analyze the Nash equilibria of capacity allocation games, in which preferences of hospitals and interns are common knowledge and every hospital determines a quota for the regular market given its total capacity for the two matching periods. Under the intern-optimal stable matching system, we show that a pure-strategy Nash equilibrium may not exist. Common preferences for hospitals ensure the existence of equilibrium in weakly dominant strategies whereas unlike in games of capacity manipulation strong monotonicity of population is not a sufficient restriction on preferences to avoid the nonexistence problem. Besides, in games of capacity allocation, it is not true either that every hospital weakly prefers a mixed-strategy Nash equilibrium to any larger regular market quota profiles

Games of capacities : a (close) look to Nash Equilibria

The paper studies two games of capacity manipulation in hospital-intern markets. The focus is on the stability of Nash equilibrium outcomes. We provide minimal necessary and sufficient conditions guaranteeing the existence of pure strategy Nash Equilibria and the stability of outcomes

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

Games of capacities : a (close) look to Nash Equilibria

The paper studies two games of capacity manipulation in hospital-intern markets. The focus is on the stability of Nash equilibrium outcomes. We provide minimal necessary and sufficient conditions guaranteeing the existence of pure strategy Nash Equilibria and the stability of outcomes.

Games of Capacities: A (Close) Look to Nash Equilibria

The paper studies two games of capacity manipulation in hospital-intern markets. The focus is on the stability of Nash equilibrium outcomes. We provide minimal necessary and sufficient conditions guaranteeing the existence of pure strategy Nash Equilibria and the stability of outcomes.Stable Matchings, Capacity, Nash Equilibrium, Cycles.

Manipulation via Capacities Revisited

This paper revisits manipulation via capacities in centralized two-sided matching markets. Sönmez (1997) showed that no stable mechanism is nonmanipulable via capacities. We show that non-manipulability via capacities can be equivalently described by two types of non-manipulation via capacities: non-Type-I-manipulability meaning that no college with vacant positions can manipulate by dropping some of its empty positions; and non-Type-II-manipulability meaning that no college with no vacant positions can manipulate by dropping some of its filled positions. Our main result shows that the student-optimal stable mechanism is the unique stable mechanism which is non-Type-I-manipulable via capacities and independent of truncations. Our characterization supports the use of the student-optimal stable mechanism in these matching markets because of its limited manipulability via capacities by colleges

Imperfect Competition in Two-sided Matching Markets

This paper considers a simple equilibrium model of an imperfectly competitive two-sided matching market. Firms and workers may have heterogeneous preferences over matches on the other side, and the model allows for both uniform and personalized wages or contracts. To make the model tractable, I use the Azevedo and Leshno (2013) framework, in which a finite number of firms is matched to a continuum of workers. In equilibrium, even if wages are exogenous and fixed, firms have incentives to strategically reduce their capacity, to increase the quality of their worker pool. The intensity of incentives to reduce capacity is given by a simple formula, analogous to the classic Cournot model, but depends on different moments of the distribution of preferences. I compare markets with uniform and personalized wages. For fixed quantities, markets with personalized wages always yield higher efficiency than markets with uniform wages, but may be less efficient if firms reduce capacity to avoid bidding too much for star workers

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