Bilateral search and vertical heterogeneity

Just like perfect (frictionless) matching models, a search model is propose d that is characterized by bilateral search and vertical heterogeneity. It allows for a generally specified utility function. The equilibrium allocati on is unique and exists in iterated strict dominance. Tnt model is robust w ith the perfect matching model as frictions disappear. Nonetheless, the equ ilibrium allocations are surprisingly odd. For multiplicatively separable p references, the distributions are partitioned endogenously. And for a wide range of preferences, matching sets are naturally disconnected.