Directed search and optimal production

I consider a model of directed search in which strategic sellers advertise general trading mechanisms. A mechanism determines the number of buyers that will get served and the side payments as a function of ex post realized demand. After observing these advertisements buyers simultaneously visit exactly one seller. Each buyer’s expected utility depends on the visiting decisions of other buyers. This dependence becomes especially interesting since the buyers cannot coordinate their visiting strategies. Despite the presence of strategic interaction among the sellers all symmetric equilibria are constrained efficient but not payoff equivalent. Therefore, authorities should intervene in this type of market to redistribute surplus and not to improve efficiency. As markets grow infinitely large all equilibria yield the same profit. For the large market case I provide conditions under which only a very simple class of mechanisms is posted in equilibrium.