SBBA:
a Strongly-Budget-Balanced
Double-Auction Mechanism
Erel Segal-Halevi
with
Avinatan Hassidim
Yonatan Aumann
Goal: Gain-from-Trade
Value
Buyers:
Sellers:
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
Goal: Gain-from-Trade
Buyers:
Value
k=5 efficient deals
Gain from trade:
Sellers:
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
VCG Mechanism
 Maximum gain
 Prior-free
 Truthful
 Two prices –
Budget deficit
k=5 efficient deals
Seller price
Buyer price
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
McAfee (1992)
 Gain: (1 - 1/k)
of maximum
 Prior-free
 Truthful
 Two prices –
Budget surplus
k=5 efficient deals
Buyer price
Seller price
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
VCG – Deficit
 Good for traders
 May be very bad
for auctioneer
Seller price
Auctioneer
Deficit
Buyer price
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
McAfee – Surplus
Buyer price
 Good for auctioneer
 May be very bad for
traders
Auctioneer
Surplus
Seller price
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
Our Goal




Gain: (1 - 1/k) of maximum
Prior-free
Truthful
Budget Balance:
good for both traders and auctioneer.
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
Previous Balance Attempts
1. Baliga & Vohra (2003): random sampling.
• Gain: 1 − 𝐶
ln 𝑘
𝑘
of maximum.
2. Babaioff & Nisan (2004): mix VCG + McAfee.
• Requires prior on valuations.
• Budget-balanced in expectation.
3. Colini-Baldeschi & de-Keijzer & Leonardi &
Turchetta (2016): sequential-posted-pricing.
• Requires prior on valuations.
• Welfare: 1/4 of maximum.
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
Our Goal




Gain: (1 - 1/k) of maximum
Prior-free
Truthful
Budget Balance:
good for both traders and auctioneer.
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
Our Solution: SBBA
• Set price to:
min(𝑏𝑘 , 𝑠𝑘+1 )
• If price is 𝒃𝒌 𝑘 − 1 high-value
buyers buy from
𝑘 − 1 random
low-value sellers.
• Expected gain:
(1 - 1/k) of max
𝒔𝒌+𝟏
𝒃𝒌
price
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
Our Solution: SBBA: Case #2
• Set price to:
min(𝑏𝑘 , 𝑠𝑘+1 )
• If price is 𝒔𝒌+𝟏 𝑘 high-value buyers
buy from
𝑘 low-value sellers.
• Maximum gain
• Prior-free
• Budget-balanced
𝒃𝒌
𝒔𝒌+𝟏
price
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
SBBA: Double-Clock Auction
•
•
•
•
Initialize: 𝑝𝑏 = 0, 𝑝𝑠 = ∞
#buyers>#sellers? Increase 𝑝𝑏 until buyers exit.
#sellers>#buyers? Decrease 𝑝𝑠 until sellers exit.
Repeat:
1. Increase 𝑝𝑏 until a buyer exits OR 𝑝𝑏 = 𝑝𝑠 .
2. Decrease 𝑝𝑠 until a seller exits OR 𝑝𝑏 = 𝑝𝑠 .
• 𝑝𝑏 = 𝑝𝑠 at 1.? #buyers=#sellers: all trade.
𝑝𝑏 = 𝑝𝑠 at 2.? #buyers=#sellers-1: randomize.
 Obviously truthful.
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
SBBA: Extensions
1. Spatial distribution & transaction costs:
Babaioff & Nisan & Pavlov (2009):
deficit or surplus.
Our paper:
balance.
2. Constraints on trader-sets:
Duetting&Roughgarden&Talgam-Cohen(2014):
deficit or surplus.
Can we achieve balance without prior?
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction
SBBA: Open Question
• VCG and McAfee are deterministic.
• SBBA is randomized.
• Is there a deterministic mechanism
with the properties of SBBA:




Gain: 1 – o(1) of maximum
Truthful
Prior-free
Strong Budget Balance
Segal-Halevi & Hassidim & Aumann: SBBA: Strongly-Budget-Balanced double-Auction