Design of Combinatorial Auctions for
Allocation and Procurement
Processes
Michael Schwind
JWG-University Frankfurt
CEC-2005
21.7.2005 Technical University of Munich
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Basics of the Combinatorial Auction
Design of an Auction Framework
Economic Validation of Auction Design
Summary and Outlook
Literature
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Combinatorial Auction
Basics
• Bidders` Valuations for Bundles of Goods:
– Substitutionalities  Subadditivity
– Complementarities  Superadditivity
• Winner Determination Problem (WDP):
– Allocation Auction  Weighted Set Packing Problem
– Procurement Auction  Weighted Set Covering Problem
• Procurement Auction:
min
  x (S ) p (S )
i
xi ( S ) S Bi
i
i
s.t.c.
  x (S ) 1  j
SBi ,S  j i
xi ( s)

i
0;1 i, S
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Combinatorial Auction
Variants
• Multidimensional Auction:
– Exchange of complex preference information
– Various dimensions: e.g. quality, delivery time
• Multi-attributive Auction:
– Impact of attributes on W2P is determined by valuation
functions
• Multi-item Auction:
– Single items of different goods are bundled in bids
• Multi-unit Auction:
– Multiple items of a good type are bundled in bids
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Combinatorial Auction
Advantages / Problems
• Advantages:
– Higher efficiency in final allocation
– Lower transaction costs
– Higher transparency
• Problems:
– NP-hardness of WDP:
• Exact solutions: Integer programming, branch-and-bound
• Heuristics: Simulated annealing, genetic algorithms
– Pricing Problem:
• Linear prices / Non-linear prices (anonymous / personalized)
– Preference Elicitation Problem:
• 2j-1 combinations of bids in worst case
– Incentive Compatibility / Stability of Mechanism:
• Vickrey-Clarke-Groves (n+1 * NP-hard)
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Combinatorial Auction
Process Design
• Modeling of the pre and post auction phase:
– Organization of the auction preparation and post processing phase
– E.g. publication of auction rules, transaction management
• Design of the main auction phase:
– Major impact on the auction outcome
– Design of the allocation mechanism
• Modeling of the auction process flow control:
– Timing of bidding sequence, closing, clearing time
• Legal, security and system stability issues:
– Transaction management protocol, etc.
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Basics of the Combinatorial Auction
Design of an Auction Framework
Economic Validation of Auction Design
Summary and Outlook
Literature
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Combinatorial Auction
Decision Support
Ascending /
Descending
Auction
• Fundamental Decisions:
Price feedback
–
–
One-shot: sealed-bid VCG
usable, only acceptance
Iterative: price feedback,
anonymous pricing, usage
of sealed bid proxy agents,
clock auction
Bid formation
–
Bid valuation: multiattributive, manual /
automated bid
construction (logistics),
preference elicitation by
questions, bid withdrawal
(leveled-commitment)
allowed in connection with
proxy agents
Open-Outcry
Clock-Auction
Quality
Quantity
anonymous
non-linear
pricing
allowed
only bid
acceptance
notification
required
Iterative
Auction
anonymous
linear
pricing
required
Time
other
individual
non-linear
pricing
allowed
Proxy-Agent
Sealed-Bidding
CA Price
Feedback
Bid-Valuation
Module
SealedBidding
leveled
commitment
alllowed
CA Bid
Formation
One-Shot
Auction
bidwithdrawal
allowed
manual
valuation
allowed
automated
bidgeneration
required
multiattributive
valuation
required
OR
OR-of-XOR
AND-OR
Bidding Language
Constraints
AND
Vickrey-ClarkeGroves
fast result
calculation
required
Integer-Programming
Solver
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
min. Provider
exact result
calculation
required
CA Winner
Determination
Quantity
Turnover
approximate
result
calculation
allowed
allocation
result
constraints
required
GA / SA / Greedy Solver
other
Winner-Determination
Constraints
Combinatorial Auction
Decision Support
• Fundamental Decisions:
Bid formation (contd.)
–
Bidding language
constraints: Logic (AND /
OR, XOR, OR-of XOR),
expressiveness vs. simplicity
Ascending /
Descending
Auction
–
–
Integer programming: small
problem size, exact, slow,
VCG
GA / SA / Greedy:
big problem size,
approximate, fast
computational speed vs.
economic efficiency
Winner determination
constraints: quantity /
turnover share, no. provider
Quality
Quantity
anonymous
non-linear
pricing
allowed
only bid
acceptance
notification
required
Iterative
Auction
anonymous
linear
pricing
required
Time
other
individual
non-linear
pricing
allowed
Proxy-Agent
Sealed-Bidding
CA Price
Feedback
Bid-Valuation
Module
SealedBidding
Winner determination:
–
Open-Outcry
Clock-Auction
leveled
commitment
alllowed
CA Bid
Formation
One-Shot
Auction
bidwithdrawal
allowed
manual
valuation
allowed
automated
bidgeneration
required
multiattributive
valuation
required
OR
OR-of-XOR
AND-OR
Bidding Language
Constraints
AND
Vickrey-ClarkeGroves
fast result
calculation
required
Integer-Programming
Solver
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
min. Provider
exact result
calculation
required
CA Winner
Determination
Quantity
Turnover
approximate
result
calculation
allowed
allocation
result
constraints
required
GA / SA / Greedy Solver
other
Winner-Determination
Constraints
Basics of the Combinatorial Auction
Design of an Auction Framework
Economic Validation of Auction Design
Summary and Outlook
Literature
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Combinatorial Auction
Economic Validation
• Analysis and Prototype Design:
–
Properties of procurement / allocation
process
• Experimental Game Theory:
–
–
–
Field implementation of prototype
Small scale experimental field evaluation
Iterative redesign
• Automated Mechanism Design:
–
–
–
Simulation implementation
Evaluation using benchmark
Iterative parameter optimization
• Evaluation:
–
Mechanism evaluation using benchmark
• Meta language description:
–
Analysis of procurement and allocation process
properties and design of auction prototype
according to process properties
Field implementation of auction prototype
Small scale experimental field evaluation
Sufficient
allocation quality
reached ?
no
yes
Implementation of auction prototype in
mechanism design optimizer
Simulative evaluation of auction using
benchmark
Optimal
allocation quality
reached ?
no
yes
Evaluation of mechanism using benchmark
Auction description using XML-based CAMeL
Description in auction meta language
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
auction redesign
auction parameter
optimization
Basics of the Combinatorial Auction
Design of an Auction Framework
Economic Validation of Auction Design
Summary and Outlook
Literature
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Combinatorial Auction
Summary & Outlook
• Advantages of the approach:
– Enables trade off in practical environments
– Two-step validation of economic properties
• Development of a Combinatorial Auction Meta Language (CAMeL):
– Enables description of auction in all phases of design process
– CAMeL integrates:
• Bidding Language description
• Auction constraints and admission rules
• Auction process control
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Basics of the Combinatorial Auction
Design of an Auction Framework
Economic Validation of Auction Design
Summary and Outlook
Literature
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Literatur
– Ausubel, L. M., Cramton, P. and Milgrom, P. (2005) The Clock-Proxy
Auction: A Practical Combinatorial Auction Design. In Combinatorial
Auctions.(Eds, Cramton, P., Shoham, Y. and Steinberg, R.) MIT Press.
– Bichler, M., Pikovsky, A., Setzer T. (2005) Kombinatorische Auktionen in
der betrieblichen Beschaffung - Eine Analyse grundlegender
Entwurfsprobleme. Wirtschaftsinformatik.
– Hohner, G., Rich, J., Ng, E., Reid, G., Davenport, A. J., Kalagnanam, J.,
Lee, H. S. and Chae, A. (2003) Combinatorial and Quantity-Discount
Procurement Auctions Benefit Mars, Incorporated and its Suppliers.
Interfaces, 33, 23-35.
– Kalagnanam, J. and Parkes, D. C. (2003) Auctions, Bidding and Exchange
Design. In Supply Chain Analysis in the eBusiness Area.(Eds, Simchi-Levi,
D., Wu, S. D. and Shen, M. Z.) Kluwer Academic Publishers.
– Kameshwaran, S. and Narahari, Y. (2001) Auction Algorithms for
Achieving Efficiencies in Logistics Marketplaces. Proceedings of the
International Conference on Energy, Automation and Information
Technology.
– McAfee, P. and McMillan, J. (1987) Auctions and Bidding. Journal of
Economic Literature, 25, 699-738.
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie
Literatur
– McMillan, J. (1995) Why Auction the Spectrum? Telecommunications
Policy, 19, 191-199.
– Nisan, N. (2005) Bidding Languages. In Combinatorial Auctions.(Eds,
Cramton, P., Shoham, Y. and Steinberg, R.) MIT Press.
– Porter, D., Rassenti, S. J., Smith, V. L. and Roopnarine, A. (2003)
Combinatorial Auction Design. Interdisciplinary Center for Economic
Science, George Mason University.
– Sandholm, T. (2002a) Algorithm for optimal winner determination in
combinatorial auctions. Artificial Intelligence, 135, 1-54.
– Schwind, M., Stockheim, T. and Rothlauf, F. (2003) Optimization
Heuristics for the Combinatorial Auction Problem. Proceedings of the
Congress on Evolutionary Computation CEC 2003, Canberra, Australia,
pp. 1588-1595.
– Schwind, M., Weiss, K. and Stockheim, T. (2004) CAMeL - Eine MetaSprache für Kombinatorische Auktionen. 2004-111, Institut für
Wirtschaftsinformatik, Johann Wolfgang Goethe-Universität.
– Smith, V. L. (1994) Economics in Laboratory. The Journal of Economic
Perspectives, 8, 113-131.
– Vickrey, W. (1963) Counterspeculation, Auctions, and Competitive Sealed
Tenders. Journal of Finance, 16, 8-37.
Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie