Bilateral search and vertical heterogeneity

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