Seminar on "Search with Private Information: Sorting, Price Formation, and Convergence to Perfect Competition"

We consider a dynamic market where heterogeneous buyers and sellers are randomly paired in each period, with match values being supermodular in both types and production costs depending on seller's type. Within each match, the seller type becomes observable while the buyer type remains private, and the seller makes a take-it-or-leave-it offer. We first highlight sellers' trade-off between a higher price and a higher selling probability under extremely large search frictions when agents completely disregard future payoffs. Log-supermodularity of the gains from trade, which equals the match value minus the production cost, is necessary and sufficient for positive assortative matching (PAM). This means that when the gains from trade is decreasing (increasing) in seller's type, supermodularity is not necessary (not sufficient) for PAM. When search frictions vanish, the condition for PAM returns to supermodularity, as sellers' incentive to secure trade in any given period becomes inconsequential. We then demonstrate that the steady state equilibrium exists and converges to the competitive limit as search frictions vanish.