Computing Bayes-Nash Equilibria in Combinatorial Auctions with Verification

Abstract

We present a new algorithm for computing pure-strategy ε-Bayes-Nash equilibria (ε-BNEs) in combinatorial auctions. The main innovation of our algorithm is to separate the algorithm’s search phase (for finding the ε-BNE) from the verification phase (for computing the ε). Using this approach, we obtain an algorithm that is both very fast and provides theoretical guarantees on the ε it finds. Our main contribution is a verification method which, surprisingly, allows us to upper bound the ε across the whole continuous value space without making assumptions about the mechanism. Using our algorithm, we can now compute ε-BNEs in multi-minded domains that are significantly more complex than what was previously possible to solve. We release our code under an open-source license to enable researchers to perform algorithmic analyses of auctions, to enable bidders to analyze different strategies, and many other applications.

Shapley-Based Core-Selecting Payment Rules

“…In this note, we do not consider the possibility of the local bidders engaging in complex bidding, i.e., making an additional bundle bid on the global bundle {1, 2}, even though such manipulations have shown to be beneficial [Beck andOtt, 2013, Bosshard andSeuken, 2020]. Instead, we assume that each bidder only bids on their bundle of interest.…”

The Cost of Simple Bidding in Combinatorial Auctions

“…Similarly, Cramton [2013] writes: "For the most part, the bidder can focus simply on determining its true preferences for packages that it can realistically expect to win." In fact, prior theoretical and algorithmic work analyzing Bayes-Nash equilibria of CA payment rules has often assumed (explicitly or implicitly) that bidders only bid on their bundles of interest [Ausubel and Baranov, 2019, Bosshard et al, 2020, Rabinovich et al, 2013, with the notable exception of Beck and Ott [2013]. In this paper, we show that assuming that bidders only bid on their bundles of interest is a very significant restriction of the game-theoretic analysis, because bidder's best responses may no longer be optimal when the full strategy space (of bidding on all bundles) is considered.…”

Competing Combinatorial Auctions

“…The free-rider problem in this context is often referred to as the threshold problem.3 The use of LLG models goes back at least toKrishna and Rosenthal (1996). Other papers employing an LLG model includeErdil and Klemperer (2010),Beck and Ott (2013),Goeree and Lien (2016),Baisa and Burkett (2018),Ausubel and Baranov (2020),Bosshard et al (2020), Finster (2020.…”

“…For combinatorial pay-as-bid auctions, seeBaranov (2010),Bosshard et al (2020); for combinatorial coreselecting auctions, seeSano (2012),Goeree and Lien (2016),Ausubel and Baranov (2020). For the magnitude of the free-rider problem in various auctions see Section 5.…”