On Pure Strategy Equilibria in Simultaneous Auctions for Complementary Goods

Abstract

We explore existence and properties of Bayesian Nash equilibrium in simultaneous first-price auctions for complementary goods. We introduce a novel partial order on bidder types and apply methodology in Athey (2001), McAdams (2003) and Reny (2011) to demonstrate existence of monotone equilibria in these auctions when the bid space is finite. We then apply this finding to demonstrate two new results on monotone equilibria in continuous bid spaces. The first of these establishes existence of monotone equilibria in a setting similar to Krishna and Rosenthal (1996), in which a single global bidder bids for multiple objects against a set of local bidders who bid for single objects only. The second considers equilibria with communication as in Jackson, Simon, Swinkels and Zame (2002), showing that in our setting their statements on distributional strategies can be refined to be monotone. Finally, we discuss conditions under which these results can be extended to all-pay, second-price and other standard simultaneous auctions.