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

This paper analyzes the extent to which well-known results on the relationship between the bargaining set, the core, and the kernel in one-to-one assignment games generalize to many-to-one assignment markets, and by extension, many-tomany markets. Using a minimal counterexample, we show that the bargaining set does not necessarily coincide with the core and that the kernel may not be contained within the core. Notably, to the best of our knowledge, among cooperative games arising from network optimization problems in the literature, the many-toone assignment market is the first to exhibit such a failure in these relationships.

Keywords: Many-to-one assignment markets · bargaining set ·  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