Signaling through entry in auctions with sequential and costly participation

This paper analyzes a scenario in which two bidders compete for two objects sold at two second-price auctions. Each bidder’s valuations of the two objects are affiliated, and participating in each auction is costly. Bidders make their participation decisions for the two auctions sequentially, in that they decide whether to enter the second auction after observing their entry decisions for the first auction. After making their participation decisions for the two auctions, bidders choose their bids in any auction they participate in. We derive the properties of equilibria and provide a sufficient condition for their existence. Due to affiliation and the presence of participation costs, a bidder’s entry into the first auction signals his strong interest in the object sold at the second auction. Hence, a bidder with a higher valuation of the second object is more likely to participate in the first auction in order to deter his opponent from entering the second auction. We then compare the models of sequential and simultaneous participation decisions in terms of equilibrium cutoffs and the equilibrium probability of entry into the two auctions. Lastly, we discuss the effects of the order of entry decisions on the revenues in the two auctions as well as the total revenue.