Mini-Lecture: Choice, Stability, and Strategy-Proofness in Matching Markets
The aim of this lecture is to characterize the conditions under which stable and strategy-proof mechanisms exist in many-to-one matching models with contracts. The classical sufficient conditions — substitutability and size monotonicity of choice functions on the “many” side of the market — are violated in a number of economically relevant environments in which stable and strategy-proof matching is nevertheless possible.
A more permissive set of conditions guarantees that the worker-proposing deferred acceptance mechanism remains stable and strategy-proof. These weaker conditions are also necessary for the guaranteed existence of a stable and strategy-proof mechanism in many-to-one matching with contracts.
Finally, the open problem of characterizing the maximal domain on which stable matchings exist in these models will be discussed.