Price Formation by Bargaining and Posted Prices

We study markets with two types of agents. Sellers have an indivisible good for sale, and their reservation value is zero. Buyers are randomly matched with sellers, and they value the good at unity. Sellers may be matched with any positive number of buyers, and they may choose to determine the price of the good either by bargaining or by posting prices. These choices are relevant only when a seller meets exactly one buyer. If two or more buyers are matched to a seller the buyers engage in an auction. The agents may choose whether to go to markets with bargaining or posted prices. We show that both market structures are equilibria but that they do not co-exist. Markets with posted prices are shown to be the unique evolutionary stable equilibrium