Strategic Bidding for Multiple Units in Simultaneous and Sequential - - PowerPoint PPT Presentation

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Strategic Bidding for Multiple Units in Simultaneous and Sequential Auctions

Stéphane Airiau & Sandip Sen

Department of Mathematical and Computer Sciences The University of Tulsa

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Agent Based Systems

 Multiagent Systems

 Cooperative groups

 machines on a factory floor, network of workstations,

robot teams

 Self-interested agents

 bidders in an auction, organizations in a supply chain,

competing manufacturers/suppliers/vendors

 Personal assistant agents

 assisting users with information processing needs,

e.g., email filtering, web browsing assistant, recommender agents

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Auctions

 Standardized procedures for allocating

goods/tasks

 Artificial societies  Real world

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Bundle bidding scenario

((Computer, television, cd player $1000), (television, music system, console, $600), (cd player, console, music system $400))

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Multiple-item auctions

 Auction of multiple, distinguishable items  Bidders have preferences over item

combinations

 Combinatorial auctions

 Bids can be submitted over item bundles  Winner selection: combinatorial optimization

 NP-complete

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Valuation Function

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Reduced bundle bidding problem

 Multiple (concurrent and sequential)

single and multi-unit auctions

 User has a valuation function v.  Problem: deciding on how many items to

bid for in each auction and at what value

 Goal: maximize  humans typically make sub-rational decisions  ideal agent application

• =
• n

i

i c n v

1

) ( ) (

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Experimental setup

 5 days  5 auctions/day selling different number

• f items

 Bidders

 one or few strategic bidders  dummy bidders

 All strategic bidders have same

valuation function and are given the same expecting closing price distribution

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Price Expectations

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Agent behaviors

 Lookahead: 1,2,3-days  Risk attitudes

 Risk neutral(RN): believe the expected

closing price is correct

 Risk averse(RA): overestimate  Risk seeking(RS): underestimate  Degrees of risk averseness and risk seeking

µ-2σ µ-σ µ µ+σ µ+2σ Closing price SRS RS RN RA SRA degree

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Bid calculation

 Obtaining one more item in an auction

 No active bids in auction: AP(1)+δ  m active bids in auction: place (m+1) bids each at

AP(m+1)+δ

 Additional cost

 For one item, select auction with lowest cost  For many items, repeat calculations

• =
• +

+ + + +

m i

i AP m AP m AP

1

)) ( ) 1 ( ( ) 1 (

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Lookahead Vs. Dummy agents

Utility # Units purchased 1-day Vs Dummies 642 32 2-day Vs Dummies 736.7 37.4 3-day Vs. Dummies 803.5 39.3

Single strategic agent Vs. dummy agents: agents with further lookahead dominate

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Multiple strategic agents

Utility % loss 1 Vs 1 473.5 26.2 2 Vs 2 640.2 13.1 3 Vs 3 647.8 19.4

Utility % loss 1 Vs 2 Avg 666.9 1day 618.5 2day 715.1 3.7 3 1 Vs 3 Avg 698.3 1day 606.4 3day 790.2 5.4 1.7 2 Vs 3 Avg 765 2day 731 3day 799.5 0.7 0.5 1 Vs 2 Vs 3 Avg 680.5 1day 609.3 2day 647.1 3day 785 5.1 12.2 2.3

Multiple strategic agents competing against dummy bidders: Agent with further lookahead dominates

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Difference in Risk attitude

 A single strategic agent competing with

dummy buyers: RN is the maximally profitable risk attitude

 Two strategic agents competing with dummy

buyers:

 RN attitude perform better against player with all

• ther risk attitudes

 Risk seeking attitudes perform better than risk

averse attitudes

 Strategic agents may gain more if they are farther

apart in risk attitude.

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Future Work

 Use probability distribution of valuations

• f other bidders

 Learning and modeling to estimate

bidder valuations

 Multi-item auctions  Other auction types