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Page count: 28

Burdett, Shi and Wright (2001) offer a directed search model where the buyers decide which seller to visit after observing the price each seller posts, and showed that there exists a unique symmetric equilibrium. Coles and Eeckhout (2003) showed that there is a continuum of symmetric equilibria, if the sellers are allowed to post general mechanisms and not only fixed prices. I show that many of the equilibria that Coles and Eeckhout identify, including the fixed price equilibria suggested by Burdett, Shi and Wright (2001), are not robust to introducing heterogeneous buyers with two possible types. In this case only ex-post efficient equilibria exist, i.e. a buyer with a lower valuation can never win against a buyer with a higher valuation if they visit the same seller. This suggests that mechanisms like auctions that utilize buyer competition in an efficient manner may endogenously arise when sellers post competing mechanisms. When the type space is continuous instead of having two possible types, the ex-post efficiency result is not maintained. If the sellers' strategy space is unrestricted, then any allocation respecting sequential rationality of the buyers, can be implemented in equilibrium. However, posting simple fixed price mechanisms never constitute an equilibrium, while posting (second-price or first-price) auctions does if the distribution function is convex.