Reducing Costly Information Acquisition in AuctionsKate Larson, University of

Waterloo

Presented by David Thompson,University of British Columbia

July 10, 2006

Overview

• Deliberative Agents

• Auctions and Deliberative Bidders

• Optimal Search

• Larson’s Auction

• Results

Deliberative Agents

• Can deliberate (to gain information) as well as bidding like a normal agent

Deliberative Agents: Properties

• R: “Resources” dedicated to deliberation on each possible problem

• cost: function mapping resource allocations to cost in utility

• A: “Algorithms” provide solutions to problems

• PP: “Performance profiles” describe how allocating resources to an algorithm affect the quality of solution it returns

Deliberative Agents: Anytime Algorithms

• All algorithms are assumed to have the anytime property (similar to local search):– Can be stopped at anytime (or work with any

amount of resources)– Always return a solution– Increasing time/resources always produces a

weakly better solution

Auctions and Deliberative Bidders

• Agents pay deliberation costs

• Strategy space is expanded to include deliberation actions (equilibria in this space: “deliberation equilibria”)

• Agents may want to deliberate about each others’ valuations (“strategic deliberation”)

Auctions: Desirable Properties

• “Deliberation-proof”: agents have no incentive to strategically deliberate

• “Non-misleading”: agents have no incentive to act inconsistently with their valuation

• “Preference-formation independence”: auction doesn’t depend on cost functions, algorithms or performance profiles

• This combination is impossible (result from a previous paper), drop preference-formation independence

Optimal Search

• An abstract problem from Operations Research:– n boxes, each with contents of different

values

– fi(v), distribution over value of box i

– costi, cost of opening box i

– Agent gets to keep 1 box (after exploring)

Optimal Search: Solution

• Assign each box a cutoff value Ki, where agent is indifferent to opening box i

• Selection Rule: open box with highest cut-off value

• Stopping Rule: stop when the maximum observed reward is greater than cutoff of all unopened boxes

Larson’s Auction

• Using knowledge of agents’ algorithms and performance profiles, calculate cutoffs for each agent and order them

• At stage t, the first t bidders participate in a 2nd price auction with a reserve price– Reserve prices are set to produce a non-

misleading Bayes-Nash equilibrium (acting as a proxy for bidders t+1..n)

Larson’s Auction: Properties

• Non-misleading: by reserve-price design

• Deliberation-proof:– Agents have no incentive to deliberate before

they can bid– Earlier agents have already demonstrated

unexpectedly low valuations (by not buying)– On expectation, later agents won’t affect the

outcome (the auction will close)

Experimental Results: Efficiency(Uniform Costs)

Experimental Results: Efficiency(Informative Costs)

Experimental Results: Cost of Deliberation vs. 2nd Price Auction (Uniform Costs)

Experimental Results: Cost of Deliberation vs. 2nd Price Auction (Informative Costs)

Thank You.