Information Asymmetry, Job Switching Mobility, and Screening of Abilities : A Tale of Two Sectors

How does information asymmetry between firms regarding the quality (ability) of workers, determine the distribution of workers' qualities in those firms? We build a game theoretic model of information asymmetry between 2 representative firms competing in the labor market for labor inputs. In the benchmark model where one firm is perfectly informed about the quality of workers, while the other firm is fully uninformed, we show the existence and uniqueness of the equilibrium in which the informed firm obtains the high quality workers, while the uninformed firm obtains the low quality workers. We then consider an extension of the model where the uninformed firm is partially informed, in that high quality workers are distinguishable, while low quality workers are not. In equilibrium, the partially informed firm obtains both the highest and lowest quality workers, while the fully informed firm obtains the middle quality workers. We also consider a version of the baseline model with worker mobility friction, finding that in equilibrium, the results are similar to the model with the partially informed firm. For welfare concern, a higher technology level of the partially informed sectior, an wider screening range, or a lower job switching friction level, will all lead to a higher level of the social surplus. While firms are able to work on the improvement of the first two factors, reducing labor market rigidity may have to heavily reply on the government policy. Our results have particular applications to the interactions between the state-owned and private firms in China's labor market, as well as the interactions between foreign and domestic firms competing in the labor market in general