Matching with Frictions and Entry with Poisson Distributed Buyers and Sellers

I consider a directed search model with population uncertainty. Buyers and sellers are randomly drawn from independent Poisson distributions. This provides a simple justification for the usual equilibrium selection where only symmetric randomizations by buyers are considered, because any equilibrium is payoff equivalent to the symmetric continuation equilibrium. The Poisson assumption also makes the model more tractable, making it possible to handle entry, which is difficult with a fixed finite set of sellers. I also demonstrate that the Poisson model belongs to a more general class of models in which prices are strategic complements and equilibria are unique.