Working Papers

We study the structure of the core in many-to-one assignment games, where firms with limited capacity hire workers in a transferable utility framework. While the core in such games is known to be non-empty and admits side-optimal elements, less is known about its full geometry, particularly the characterization and enumeration of its extreme points. We provide a graph-theoretic criterion for core vertices: a salary vector is a vertex of the core if and only if its associated tight digraph is connected. Building on this, we develop a lexicographic procedure that generates all core vertices as they are supported by a max-min salary vector.

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

JEL Classifications : C71 · C78 · D47

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