Auctions

Madalina Croitoru, Cornelius Croitoru
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Contents
MADALINA CROITORU
1
Combinatorial Auctions
2
Proposed Model: examples
3
Proposed Model: advantages
4
Discussion
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Contents
MADALINA CROITORU
1
Combinatorial Auctions
2
Proposed Model: examples
3
Proposed Model: advantages
4
Discussion
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Auctions
Who should get the goods and at what prices?
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Auctions: English auction
The auctioneer opens
the auction by
announcing a starting
price for the item on sale
and then accepts
increasingly higher bids
from the floor consisting
of buyers (bidders).
If no competing bidder
challenges the standing bid
within a given time frame, the
item is sold to the highest
bidder at a price equal to his
or her bid.
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Auctions: Dutch auction
The auctioneer begins
with a high asking price
which is lowered until
some participant is
willing to accept the
auctioneer's price
The winning participant
pays the last announced
price.
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Auctions: Vickery auction
Sealed-bid auction
Bidders submit written
bids without knowing
the bid of the other
people in the auction
The highest bidder wins,
but the price paid is the
second-highest bid
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Combinatorial Auctions
Auction where the bidders
can place bids on
combinations of items
(bundles)
First proposed for the
allocation of
airport landing slots
Rassenti, Stephen J., Vernon L. Smith, and Robert L. Bulfin (1982):
"A Combinatorial Auction Mechanism for Airport Time Slot Allocation“
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Combinatorial auctions: background
Employed in a variety of industries:
airport landing slots
truckload transportation
bus routes
allocating spectrum for wireless communication services
Two main problems to be addressed:
The bidding language
Conciseness
Expressivity
Winner Determination algorithms
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Combinatorial auctions: approaches
Atomic offers
Bidders offer (B, p) where B is a bundle (a subset of goods) and p is
the price
The OR language
Bidders offer (B1, p1), (B2, p2), …, (Bn, pn) to bid for as many Bi as
possible paying the sum of respective prices:
The XOR language
Bidders offer (B1, p1), (B2, p2), …, (Bn, pn) to bid for at most one Bi
and, if receiving more than one paying the most expensive of the Bi
included:
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Combinatorial auctions: approaches
TBBL: Tree Based
Bidding Language
Building a tree:
Frontier: the goods
Internal nodes: subsets
that include all the
goods in the respective
subtrees
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
This paper: contribution
Artificial Intelligence
problem
Combinatorial
Auctions
MADALINA CROITORU
Representation
Generalised
Network Flow
Language
for Bid
Specification
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Reasoning
Winner
Determination:
Adequate
Aggregation
Of
Individual
Preferences
Faculty of
COMPUTER SCIENCE
Contents
MADALINA CROITORU
1
Combinatorial Auctions
2
Proposed Model: examples
3
Proposed Model: advantages
4
Discussion
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
How to build your bid: start
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
How to build your bid: goods
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
How to build your bid: bundles
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
How to build your bid: bids
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
How to build your bid: bonus
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Example 1
The bidder is interested in maximum k products
considered equal. The bonus will increase in
function of the number of products and not
surpass k
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Example 2
The bidder is interested in exactly one product
from each set of products (m sets of products).
The bonus is proportional with the number of sets.
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Contents
MADALINA CROITORU
1
Combinatorial Auctions
2
Proposed Model: examples
3
Proposed Model: advantages
4
Discussion
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Proposed model: advantages
Two main problems to be addressed:
The bidding language
Conciseness
Expressivity
Winner Determination algorithms
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Proposed model: advantages
Two main problems to be addressed:
The bidding language
Conciseness
Expressivity
Winner Determination algorithms
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Conciseness
Bundle system:
pair H = (R, B) where R is a
set of resources (goods,
products) and B a family of
subsets of R
A bundle system can be
explicitly represented as
bipartite graph
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Conciseness
We propose representing a bundle implicitly using constructive rules
Result: a potentially exponential bundle system represented polynomially
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Proposed model: advantages
Two main problems to be addressed:
The bidding language
Conciseness
Expressivity
Winner Determination algorithms
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
TBBL
The bidder is interested in in a bundle consistent
of two or three resources of type E, together with
the resource M which adds 10 to the values sum
of the particular resources of type E
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Proposed model: advantages
Two main problems to be addressed:
The bidding language
Conciseness
Expressivity
Winner Determination algorithms
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Winner Determination
The task of finding a maximum value allocation for bidder valuations
NP-hard problem: equivalent to weighted set packing
Translate the winner determination problem as a adequate
aggregation of individual preferences
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Contents
MADALINA CROITORU
1
Combinatorial Auctions
2
Proposed Model: examples
3
Proposed Model: advantages
4
Discussion
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Discussion: work in progress
Representation and reasoning:
Novel algorithms working on the proposed graphical
representation are still to be investigated
Results of proposed algorithms have to be compared
with those provided by existing work and potential
differences justified from a relevance viewpoint
Reasoning and efficiency:
The structure of the represented bids can be used to
characterise interesting complexity classes
MADALINA CROITORU
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE
Questions?
UNIVERSITATEA
ALEXANDRU IOAN CUZA
IASI
Faculty of
COMPUTER SCIENCE