Learning by matching

Abstract

This paper studies a stability notion and matching processes in the job market with incomplete information on the workers' side. Each worker is associated with a type, and each firm cares about the type of her employee under a match. Moreover, firms' information structure is described by partitions over possible worker type profiles. With this firm-specific information, we propose a stability notion which, in addition to requiring individual rationality and no blocking pairs, captures the idea that the absence of rematching conveys no further information. When an allocation is not stable under the status quo information structure, a new pair of an allocation and an information structure will be derived. We show that starting from an arbitrary allocation and an arbitrary information structure, the process of allowing randomly chosen blocking pairs to rematch, accompanied by information updating, will converge with probability one to an allocation that is stable under the updated information structure. Our results are robust with respect to various alternative learning patterns.

Stability and Bayesian Consistency in Two-Sided Markets

“…The notion of stability can be permissive if no further restriction on beliefs is imposed. 9 Although there is no invincible argument for any refinement of beliefs, and off-path beliefs in particular, some restrictions are arguably "desirable" or "intuitive." We propose the following two principles and derive their implications:…”

Stable matching under forward‐induction reasoning

“…This notion presupposes a common prior over types. Chen and Hu (2019) provide an alternative foundation for incomplete-information stability. They adopt a partitional model, and assume that agents optimize according to a max-min criterion.…”