On monotone strategy equilibria in simultaneous auctions for complementary goods (Q2283142)

This paper analyzes existence and properties of equilibrium when \(N\ge 2\) bidders compete for \(L\ge 2\) objects via simultaneous but separate auctions. It is assumed that the bidders have independent private valuations over combinations of objects, where objects are complements in the sense that bidders' valuations are supermodular in sets of objects won; auctions are simultaneous in the sense that bidders may bid on each object individually but may not submit contingent or combinatorial bids. The authors examine the monotonous equilibrium with the endogenous destructive building of \textit{M. O. Jackson} et al. [Econometrica 70, No. 5, 1711--1740 (2002; Zbl 1106.91348)] and demonstrate that they exist as a whole. Existence results apply to many auction formats, including first bid, second bid and all-pay. Section 6 contains several numerical examples of bidding behavior in simultaneous auctions for complementarities, which illustrate the authors' theoretical results. Proofs of all propositions and lemmas are collected in Appendix. Investigations are of particular interest to researchers of this topic.