匹配与学习：一种贝叶斯指派博弈方法

摘要

We study two-sided matching with transferable utility in which each match generates a surplus composed of a commonly known observable component and an initially unknown idiosyncratic component. The idiosyncratic component is revealed gradually through a sequence of publicly observed signals, one per worker firm pair per period. The paper examines a benchmark in which signals are produced externally and are observed regardless of the realized matching. This benchmark is motivated by markets with verifiable and portable evaluation such as standardized tests, certifications, platform ratings, and publication records. Under risk neutrality and common posteriors, each date’s market reduces to a standard Shapley-Shubik assignment game on posterior expected surpluses, and stability is defined as membership in the core of that game. We provide closed-form Normal-Normal Bayesian updating, proving existence of core outcomes at every date, and derive comparative statics in signal precision and in the strength of industry specific comparative advantage. The main long run result is that, under a unique efficient matching margin condition, the matching that maximizes posterior expected total surplus coincides with the efficient matching after a finite random time almost surely, and the probability of selecting an inefficient matching at date t admits an explicit exponential upper bound. Simulations illustrate how information accumulation generates early turnover and how industry specific comparative advantage reshapes the decomposition of worker payoff dispersion into within- and between-industry components. This framework gives a clear starting point to study more complex situations where information comes from actual matches or is kept private.