\input zb-basic \input zb-ioport \iteman{io-port 05732060} \itemau{Lentz, Rasmus} \itemti{Sorting by search intensity.} \itemso{J. Econ. Theory 145, No. 4, 1436-1452 (2010).} \itemab Summary: I characterize matching in an on-the-job search model with endogenous search intensity, heterogeneous workers and firms, and match surplus is shared between workers and firms through bargaining. I provide proof of existence and uniqueness of steady state equilibrium. Given equally efficient matched and unmatched search, the worker skill conditional distribution of firm productivity over matches is stochastically increasing (decreasing) in worker skill if the production function is supermodular (submodular). I also show that this strong notion of sorting does not obtain everywhere for the firm productivity conditional match distribution. \itemrv{~} \itemcc{} \itemut{assortative matching; supermodularity; search friction; endogenous search intensity} \itemli{doi:10.1016/j.jet.2010.02.013} \end