Ascending multi-item auctions

• Increase prices until each item is demanded only once • Item prices vs. bundle prices – E.g. where there exist no appropriate item prices Bundle Bidder 1’s valuation Bidder 2’s valuation {1} {2} {1,2} $0 $0 $3 $2 $2 $2 • Discriminatory vs. nondiscriminatory prices

Automated bid elicitation

in combinatorial auctions [Conen & Sandholm IJCAI-01 workshop; ACM Ecommerce-01; AAAI-02; Hudson & Sandholm -02]

Another complex problem in combinatorial auctions:

“The revelation problem”

• Bidders may need to bid on all 2 #items combinations – Need to compute the valuation for each combination • Each valuation computation can be NP-complete • For example if a carrier company bids on trucking tasks: TRACONET [Sandholm AAAI-93] – Need to communicate the bids – Need to reveal the bids • Loss of privacy & strategic info

Approaches for tackling the revelation problem • Classic single-shot full revelation mechanims (Vickrey Clarke-Groves) – Exponentially many valuations revealed • Ascending mechanisms with price feedback (iBundle, [Parkes et al 1999] , akBa [Wurman et al. 2000] , etc.) – Can save revelation – Need exponential revelation in worst case [Nisan 2001] • Our new approach: an

elicitor “agent”

– Knows things that individual bidders don’t (others’ bids so far) – Asks non-redundant questions from bidders to focus their revelation – Can save revelation – Exponential revelation in worst case [Nisan 2001] – Could be combined with price feedback mechanisms

Our Query Types for Elicitation •

Value information

: What is your valuation for bundle A? (Answer: Exact or Bounds) – Extensions: • More and more refined answers over times • Bounds in the queries

Order information

: Which bundle do you prefer, A or B?

• •

Rank information

: – What is the rank of bundle

b

? – What bundle is at rank

x

? – Given bundle

b

, what is the next lower (higher) ranked bundle?

• We designed a host of elicitation algorithms that use these query types in different combinations and with different query policies

Example elicitation experiment with random non-redundant value queries only With free disposal Number of bundle values asked / number of bundles Random (nonredundant) elicitor Best elicitor developed so far Advantage of elicitation also holds as the number of agents grows

Incentive compatibility

– Elicitor’s questions leak information about others’ preferences – Can be made incentive compatible in weaker equilibrium notions • Ask enough questions to determine Clarke tax prices (#agents+1 “elicitors”) • Could interleave these “extra” questions with real questions – To avoid lazyness; Not necessary from an incentive perspective • Agents don’t have to answer the questions & may answer questions that were not asked – Unlike in ascending “price feedback” auction mechanisms