Frictions in Internet Auctions with Many Traders: a Counterexample

Peters and Severinov (2006) (PS henceforth) characterize a perfect Bayesian equilibrium (PBE) in a competing auctions environment, where all buyers are linked to all the sellers. PS characterize a PBE using a simple bidding rule, whereby buyers select in which auction to bid. In this note we show that when buyers are linked with a subset of the sellers (i.e. when there are search frictions), the PS bidding rule is no longer guaranteed to be efficient nor a PBE of the competing auctions game of PS. Our results indicate that researchers should be cautious when using the PS bidding rule to make inference about the behavior of buyers and sellers in a market where frictions are present such as eBay.