On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods

61 Pages Posted: 23 Jul 2015 Last revised: 21 Jul 2018

See all articles by Matthew L. Gentry

Matthew L. Gentry

London School of Economics & Political Science (LSE) - Department of Economics

Tatiana Komarova

London School of Economics & Political Science (LSE)

Pasquale Schiraldi

London School of Economics & Political Science (LSE)

Wiroy Shin

Korea Institute for Industrial Economics & Trade (KIET)

Date Written: June 20, 2018

Abstract

We explore existence and properties of equilibrium when N ≥ 2 bidders compete for L ≥ 2 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 tiebreaking 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 Classification: D44, C72

Suggested Citation

Gentry, Matthew L. and Komarova, Tatiana and Schiraldi, Pasquale and Shin, Wiroy, On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods (June 20, 2018). Available at SSRN: https://ssrn.com/abstract=2634091 or http://dx.doi.org/10.2139/ssrn.2634091

Matthew L. Gentry

London School of Economics & Political Science (LSE) - Department of Economics ( email )

Houghton Street
London WC2A 2AE
United Kingdom
(+44) 020 7955 6213 (Phone)

HOME PAGE: http://econ.lse.ac.uk/staff/gentry_matthew/

Tatiana Komarova (Contact Author)

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

Pasquale Schiraldi

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

Wiroy Shin

Korea Institute for Industrial Economics & Trade (KIET) ( email )

Sejong
Korea, Republic of (South Korea)

HOME PAGE: http://www.wiroy-shin.com

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