Working Papers

This paper studies many-to-one assignment markets, or matching markets with wages. Although it is well-known that the core of this model is non-empty, the structure of the core has not been fully investigated. To the known dissimilarities with the one-to-one assignment game, we add that the bargaining set does not coincide with the core and the kernel may not be included in the core. Besides, not all extreme core allocations can be obtained by means of a lexicographic maximization or a lexicographic minimization procedure, as it is the case in the one-to-one assignment game.

The maximum and minimum competitive salaries are characterized in two ways: axiomatically and by means of easily verifiable properties of an associated directed graph. Regarding the remaining extreme core allocations of the many-to-one assignment game,  we propose a lexicographic procedure that, for each order on the set of workers, sequentially maximizes or minimizes each worker's competitive salary. This procedure provides all extreme vectors of competitive salaries, that is all extreme core allocations.

Keywords: Many-to-one assignment markets · extreme core allocations · side-optimal allocations · kernel · core

JEL Classifications : C71 · C78 · D47

Cooperative game theory aims to study how to divide a joint value created by a set of players. These games are often studied through the characteristic function form with transferable utility, which represents the value obtainable by each coalition. In the presence of externalities, there are many ways to define this value. Various models that account for different levels of player cooperation and the influence of external players on coalition value have been studied. Although there are different approaches, typically, the optimistic and pessimistic approaches provide sufficient insights into strategic interactions. This paper clarifies the interpretation of these approaches by providing a unified framework. We show that making sure that no coalition receives more than their (optimistic) upper bounds is always at least as difficult as guaranteeing their (pessimistic) lower bounds. We also show that if externalities are negative, providing these guarantees is always feasible. Then, we explore applications and show how our findings can be applied to derive results from the existing literature

Keywords: Cooperative games · optimization problems · cost sharing · core · anti-core · externalities

JEL Classifications : C44 · C71 · D61 · D62 · D63 

We investigate the allocation of children to childcare facilities and propose solutions to overcome limitations in the current allocation mechanism. We introduce a natural preference domain and a priority structure that address these setbacks, aiming to enhance the allocation process. To achieve this, we present an adaptation of the Deferred Acceptance mechanism to our problem, which ensures strategy-proofness within our preference domain and yields the student-optimal stable matching. Finally, we provide a maximal domain for the existence of stable matchings using the properties that define our natural preference domain. Our results have practical implications for allocating indivisible bundles with complementarities.

Keywords: Childcare allocation · complementarities · market design · stability · strategy-proofness

JEL Classifications : C78 · D47 · D61 · D63 · I21 

We adopt the notion of the farsighted stable set to determine which matchings are stable when agents are farsighted in matching markets with couples. We show that a singleton matching is a farsighted stable set if and only if the matching is stable. Thus, matchings that are stable with myopic agents remain stable when agents become farsighted. Examples of farsighted stable sets containing multiple non-stable matchings are provided for markets with and without stable matchings. For couples markets where the farsighted stable set does not exist, we propose the DEM farsighted stable set to predict the matchings that are stable when agents are farsighted.

Keywords: Matching with couples · stable sets · farsighted agents

JEL Classifications : C70 · C78 · D47 

We consider priority-based matching problems with limited farsightedness. We show that, once agents are sufficiently farsighted, the matching obtained from the Top Trading Cycles (TTC) algorithm becomes stable: a singleton set consisting of the TTC matching is a horizon-k vNM stable set if the degree of farsightedness is greater than three times the number of agents in the largest cycle of the TTC. On the contrary, the matching obtained from the Deferred Acceptance (DA) algorithm may not belong to any horizon-k vNM stable set for k large enough.

Keywords: Priority-based matching · top trading cycle · stable set · farsightedness

JEL Classifications : C70 · C78 · D47 · D61

We consider priority-based school choice problems with farsighted students. We show that a singleton set consisting of the matching obtained from the Top Trading Cycles (TTC) mechanism is a farsighted stable set. However, the matching obtained from the Deferred Acceptance (DA) mechanism may not belong to any farsighted stable set. Hence, the TTC mechanism provides an assignment that is not only Pareto efficient but also farsightedly stable. Moreover, looking forward three steps ahead is already sufficient for stabilizing the matching obtained from the TTC.

Keywords: School choice · top trading cycle · stable sets · farsighted students

JEL Classifications : C70 · C78