Decentralized Matching at Senior-Level: Stability and Incentives

Abstract

We consider senior-level labor markets and study a decentralized game where firms can fire a worker whenever they wish to make an offer to another worker. The game starts with initial matching of firms and workers and proceeds with a random sequence of job offers. The outcome of the game depends on the random sequence according to which firms make offers and therefore is a probability distribution over the set of matchings. We provide theoretical support for the successful functioning of decentralized matching markets in a setup with myopic workers. We then identify a lower bound on outcomes that are achievable through strategic behavior. We find that in equilibrium either any sequence of offers leads to the same matching or workers (firms) do not agree on what matching is the worst (best) among all possible realizations of the outcome. This implies that workers can always act to avoid a possible realization that they unanimously find undesirable. Hence, a well-known result for centralized matching at the entrylevel carries over to matching at the senior-level albeit without the intervention of a mediator.