A Pooling Analysis of Two Simultaneous Online Auctions

Motivated by the ease with which online customers can bid simultaneously in multiple auctions, we analyze a system with two competing auctioneers and three types of bidders: those dedicated to either of the two auctions and those that participate simultaneously in both auctions. Bidding behavior is specified and proven to induce a Bayesian Nash equilibrium, and a closed-form expression for the expected revenue of each auctioneer is derived. For auctioneers selling a single item, partial pooling--i.e., the presence of some cross-auction bidders--is beneficial to both auctioneers as long as neither one dominates the market (e.g., possesses more than 60%-65% of the market share). For multi-item auctions, pooling is mutually beneficial only if both auctioneers have nearly identical ratios of bidders per items for sale; otherwise, only the auctioneer with the smaller ratio benefits from pooling. Pooling's impact on revenue decreases with the number of bidders, suggesting that popular auction sites need not be overly concerned with mitigating bidding across auctions.