Add to ORKGAbstract. This paper studies Bayesian equilibrium in a worker firm matching problem in which workers choose their human capi-tal investment and firms choose wages before the matching process occurs. Symmetric equilibrium exists, and supports assortative matching. However, when the number of traders is large, low types tend to invest too much, while higher types invest in a way that is bilaterally efficient. In this sense the upper end of the market be-haves in a manner that is similar to the way they would behave in a competitive (hedonic) equilibrium. The lower end of the market, however, does not. All types end up investing more and being paid higher wages than they are in a simple hedonic equilibrium. In the limit, the Bayesian game supp...