Working Paper: CEPR ID: DP12483
Authors: Matthew Gentry; Tatiana Komarova; Pasquale Schiraldi; Wiroy Shin
Abstract: We explore existence and properties of equilibrium when N>1 bidders compete for L>1 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 L objects against many local bidders who bid for single objects only, highlighting the step in this extension which fails with multiple global bidders. We therefore instead consider an alternative equilibrium with endogenous tie-breaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that this exists in general. Finally, we explore efficiency in simultaneous auctions with symmetric bidders, establishing novel sufficient conditions under which inefficiency in expectation approaches zero as the number of bidders increases.
Keywords: simultaneous auctions; complementarities; synergies; equilibria; existence; efficiency; multi-object auctions; monotone strategies
JEL Codes: D44; C72
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| bidder valuations (supermodularity) (D44) | existence of monotone Bayesian Nash equilibria (C73) |
| structure of the auction (D44) | bidder behavior (D44) |
| number of bidders (D44) | auction efficiency (D44) |