Coordination Frictions and Heterogeneity in Markets with Bidding

Abstract Two heterogeneous buyers with commonly known preferences must choose which one of two di¤erent goods-a high value good and a low value good-to bid on when the goods are sold through simultaneously held …rst-price auctions. We …nd that e¢ ciency of equilibrium allocation depends on allowing sellers to announce and commit to reservation prices before the auctions are held. This is achieved by …rst characterizing a unique buyer equilibrium for a generic subset of the parameter space when reservation prices are exogenously set to zero. This equilibrium exhibits coordination frictions and results in a potentially ine¢ cient allocation of the goods. The high value good is sold for sure, though it could be to either buyer and could even be at the reservation price. The low value good is either not sold or sold exactly at the reservation price to the buyer with a lower marginal valuation for the high value good. We then characterize buyer equilibria for all reservation prices. Endogenizing seller behavior by allowing sellers to announce and commit to reservation prices results in a unique market equilibrium of the game in which buyers perfectly coordinate, the e¢ cient allocation is achieved, and both allocation and payo¤s are equivalent to that of the price-posting case. The contrasting results between exogenous and endogenous reservation prices stems from the following: when the same side that searches (here, the buyer side) is responsible for price formation, coordination frictions are still present because buyers have incentive to compete over the higher value good and hence could both bid on it. However, when the passive side of the market (here, the seller side) is in e¤ect responsible (here, by setting binding reservation prices), the two-sided heterogeneity results in perfect coordination by the buyers in choosing their goods. JEL classi…cation: C78, D44