Comparison of auctions and posted prices in a finite random matching model

I determine the steady state equilibrium in a random matching model with a finite number of buyers and sellers. Two trading mechanisms, namely, auctions and posted prices are compared. Auctions depict a situation where the sellers are unable to commit to a reserve price, whereas posted prices depict a situation where the sellers commit to a publicly announced price. In the corresponding infinite agent model the two mechanisms are equivalent, while in the finite case posted prices are preferred by sellers and auctions by buyers.