Weakest Bidder Types and New Core-Selecting Combinatorial Auctions

TL;DR

This work introduces a new class of core-selecting combinatorial auctions that leverage bidder information available to the auction designer and devise a new family of core-selecting combinatorial auctions that minimize the sum of bidders' incentives to deviate from truthful bidding.

Abstract

Core-selecting combinatorial auctions are popular auction designs that constrain prices to eliminate the incentive for any group of bidders -- with the seller -- to renegotiate for a better deal. They help overcome the low-revenue issues of classical combinatorial auctions. We introduce a new class of core-selecting combinatorial auctions that leverage bidder information available to the auction designer. We model such information through constraints on the joint type space of the bidders -- these are constraints on bidders' private valuations that are known to hold by the auction designer before bids are elicited. First, we show that type space information can overcome the well-known impossibility of incentive-compatible core-selecting combinatorial auctions. We present a revised and generalized version of that impossibility result that depends on how much information is conveyed by the type spaces. We then devise a new family of core-selecting combinatorial auctions and show that they minimize the sum of bidders' incentives to deviate from truthful bidding. We develop new constraint generation techniques -- and build upon existing quadratic programming techniques -- to compute core prices, and conduct experiments to evaluate the incentive, revenue, fairness, and computational merits of our new auctions. Our new core-selecting auctions directly improve upon existing designs that have been used in many high-stakes auctions around the world. We envision that they will be a useful addition to any auction designer's toolkit.

Figures (4)

• Figure 1: Price vectors $\bm{p}^{\texttt{VCG}}$ and $\bm{p}^{\texttt{WT}}$ (in red) and their nearest respective minimum-revenue core points (in yellow, connected by a green line) as derived in Example \ref{['example:core']}. $\mathsf{MRC}(\bm{p}^{\texttt{WT}})$ lies on a different face of the core than $\mathsf{MRC}(\bm{p}^{\texttt{VCG}})$ and is of higher revenue.
• Figure 2: Incentive effects as type spaces convey more information (by varying the number of constraints $K\in\{1,2,4,8,16\}$, with number of goods varying in $\{64,128\}$ and number of bids varying in $\{250,500,1000\}$, averaged over 100 instances for each $K$ and each setting of goods/bids.
• Figure 3: Revenue effects as type spaces convey more information (by varying the number of constraints $K\in\{1,2,4,8,16\}$, with number of goods varying in $\{64,128\}$ and number of bids varying in $\{250,500,1000\}$, averaged over 100 instances for each $K$ and each setting of goods/bids.
• Figure 4: Core burdens shouldered by the lower and upper halves of bidders (measured by winning bid value). For the three $\mathsf{MRC}(\bm{p}^{\texttt{WT}})$-selecting rules, the left bar displays the core burden split relative to WT, and the right bar displays the core burden split relative to VCG. For the two vanilla MRC-selecting rules, the bar displays the core burden split relative to VCG.

Theorems & Definitions (10)

• Theorem 3.1
• proof
• Lemma 4.1
• proof
• Theorem 4.2
• proof
• Theorem 4.3
• proof
• Corollary 4.4
• Example 4.5