On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods

Matthew Gentry, Tatiana Komarova, Pasquale Schiraldi, Wiroy Shin

Research output: Contribution to journalArticlepeer-review


We explore existence and properties of equilibrium when bidders compete for objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for objects against many local bidders who bid for single objects only. We then consider monotone equilibrium with endogenous tiebreaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that these exist in general. These existence results apply to many auction formats, including first-price, second-price, and all-pay.
Original languageEnglish
Pages (from-to)109-128
Number of pages20
JournalJournal of Mathematical Economics
Early online date19 Sept 2019
Publication statusPublished - Dec 2019


  • simultaneous auctions
  • complementarities
  • synergies
  • equilibria existence
  • multi-object auctions
  • monotone strategies


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