Strategic Bidding for Multiple Units in Simultaneous and Sequential Auctions Stéphane Airiau & Sandip Sen Department of Mathematical and Computer Sciences The University of Tulsa 1 DAI Hards - University of Tulsa
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 2 DAI Hards - University of Tulsa
Auctions Standardized procedures for allocating goods/tasks Artificial societies Real world 3 DAI Hards - University of Tulsa
Bundle bidding scenario ((Computer, television, cd player $1000), (television, music system, console, $600), (cd player, console, music system $400)) 4 DAI Hards - University of Tulsa
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 5 DAI Hards - University of Tulsa
Valuation Function 6 DAI Hards - University of Tulsa
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 n Goal: maximize v ( n ) c ( i ) � � i 1 = humans typically make sub-rational decisions ideal agent application 7 DAI Hards - University of Tulsa
Experimental setup 5 days 5 auctions/day selling different number of 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 8 DAI Hards - University of Tulsa
Price Expectations 9 DAI Hards - University of Tulsa
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 degree SRA RA RN RS SRS Closing µ+2 σ µ+ σ µ µ- σ µ-2 σ price 10 DAI Hards - University of Tulsa
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 AP ( m 1 ) Additional cost + + � m ( AP ( m 1 ) AP ( i )) � + + + � � i 1 = For one item, select auction with lowest cost For many items, repeat calculations 11 DAI Hards - University of Tulsa
Lookahead Vs. Dummy agents Utility # Units purchased 1-day Vs 642 32 Dummies 2-day Vs 736.7 37.4 Dummies 3-day Vs. 803.5 39.3 Dummies Single strategic agent Vs. dummy agents: agents with further lookahead dominate 12 DAI Hards - University of Tulsa
Multiple strategic agents Utility % loss Utility % loss 1 Vs 2 Avg 666.9 1 Vs 1 473.5 26.2 1day 618.5 3.7 2 Vs 2 640.2 13.1 2day 715.1 3 1 Vs 3 Avg 698.3 3 Vs 3 647.8 19.4 1day 606.4 5.4 Multiple strategic 3day 790.2 1.7 2 Vs 3 Avg 765 agents competing 2day 731 0.7 against dummy 3day 799.5 0.5 1 Vs 2 Vs 3 Avg 680.5 bidders: 1day 609.3 5.1 Agent with further 2day 647.1 12.2 lookahead dominates 3day 785 2.3 13 DAI Hards - University of Tulsa
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 other risk attitudes Risk seeking attitudes perform better than risk averse attitudes Strategic agents may gain more if they are farther apart in risk attitude. 14 DAI Hards - University of Tulsa
Future Work Use probability distribution of valuations of other bidders Learning and modeling to estimate bidder valuations Multi-item auctions Other auction types 15 DAI Hards - University of Tulsa
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