Download presentation

Presentation is loading. Please wait.

Published byTate Huett Modified over 2 years ago

1
Super solutions for combinatorial auctions Alan Holland & Barry O’Sullivan {a.holland, b.osullivan}@cs.ucc.ie

2
Overview Combinatorial Auctions (CA’s) – Motivation – Auction scenarios – Implications of unreliable bidders Super solutions (SS) – Solution robustness – simple example SS & CA’s – SS for different types of auctions – Experimental Results – Extensions to framework

3
Combinatorial Auctions Motivation – Multiple distinguishable items – Bidders have preferences over combinations of items Facilitates expression of complementarities / substitutabilities – Improves economic efficiency Removes ‘exposure problem’ from multiple single-item auctions

4
Combinatorial Auction Example Two parcels of land for sale – Three bidders valuations AB BidderABAB 1$1m$0 2 $½m$0 3 $2m

5
Exposure Problem Single-item auctions Consider previous example – Two items (A,B) are sold in two separate auctions – Bidder 3 values the pair AB @ $2m – But either X or Y on its own is valueless ($0) – If she bids $1m for each and wins only one item she has lost $1m – This induces depressed bidding Solution: Allow bids on XY – ‘combinatorial bids’

6
Combinatorial Auctions Bids on all combinations of items are allowed Forward Auction – selling items – Maximize revenue – Weighted Set Packing problem Reverse Auction – buying items – Minimize cost – Set Covering Problem – No Free Disposal => Set Partitioning Problem Gaining in popularity – FCC spectrum auctions – Mars, Home-Base, London Transport Authority

7
Complexity Potentially 2 #items bids to consider Winner Determination – NP-Complete [Rothkopf ‘98] – Inapproximable – State of the art algorithms work well in practice CABOB - 1,000’s of bids for 100’s of items in seconds [Sandholm ‘03]

8
Full commitment contracts Auction solutions assume binding contracts (full commitment) – ‘…a contract might be profitable to an agent when viewed ex ante, it need not be profitable when viewed ex post’ [Sandholm&Lesser02] – The converse is also true De-committing – Bidders receive better offers/renege on unprofitable agreements/go bankrupt/disqualified – Levelled-commitment contracts offer de-commitment penalties

9
De-commitment in auctions Single item auction – A winning bid is withdrawn => give the item to 2 nd highest bidder Combinatorial auction – A winning bid is withdrawn => next best solution may require changing all winning bids – Highly undesirable in many circumstances (e.g. SCM) – Auctioneer may be left with a bundle of items that are valueless (Auctioneer’s exposure problem) ‘Prevention is better than cure’ – Robust solutions => a small break can be repaired with a small number of changes

10
CA solution robustness Solution robustness – Unreliable bidders are present – Solution stability paramount – E.g. Supply chain formation Bid withdrawal/disqualification – Next best solution may require changing all winning bids (infeasible in many situations) – Potentially severe implications for revenue

11
(a,b)-super solutions [Hebrard,Hnich&Walsh 04] An (a,b)-super solution – Guarantees that when ‘a’ variables are broken in a solution, only ‘b’ other changes are required to find a new solution – Thus providing solution robustness Example – Solutions to a CSP are – is a (1,0)-super solution – & are (1,1)-super solutions

12
(1,b)-super solution algorithm – MAC-based repair algorithm [Hebrard et al ECAI04] Value assigned to the k th variable AC & Repairability check on the first k-1 variables If more than b changes are required => unrepairable assignment – Our approach Solve the problem optimally using any ILP solver (CPLEX etc…) & optimal revenue = R opt Add a sum constraint s.t. revenue > R opt X k%

13
(1,b)-super solutions for CA’s Zero values may be considered ‘robust’ – Withdrawal of losing bids is immaterial (when a=1) Example CA – valid solutions – : (1,1)-super solution: $1.2m – : (1,0)-super solution: $1.15m – : (1,0)-super solution: $1.1m

14
(1,b)-super solutions for CA’s Zero values may be considered ‘robust’ – Withdrawal of losing bids is immaterial (when a=1) Example CA – Valid solutions – : (1,1)-super solution: $1.2m – : (1,0)-super solution: $1.15m – : (1,0)-super solution: $1.1m 2 nd & 3 rd solutions are more robust – Less revenue however – 2 nd solution dominates 3 rd – Trade-off ensues between 1 st & 2 nd solution

15
Experiments Aim – Examine trade-off between revenue & robustness – Different economically motivated scenarios Auctions – Generated by bid simulation tool (CATS) [Leyton- Brown et al] – Scenarios exhibit differing complementarity effects

16
Bid distributions arbitrary – arbitrary complementarity between items for different bidders, (Simulates electronic component auctions) regions – complementarity between items in 2-D space (e.g. spectrum auctions, property) scheduling – Auctions for airport landing/take-off slots

17
Bid distributions arbitrary – Random synergies => more varied series of items in bids => more overlap constraints – More pruning => lower search times regions – More mutually exclusive bids – Less pruning => higher search times scheduling – Bids contain few items => less constraints – More pruning => longer search times

18
Constraint Satisfaction Is a super solution possible? – (given b & min revenue) – – Sample auctions - 20 items & 100 bids (v. small) Robust solutions – – arbitrary: super soln’s unlikely - unless min revenue 2 – regions: super soln’s more likely than for arbitrary- unless tolerable revenue ~ 85% of optimum – scheduling: super soln’s likely - unless min revenue > 95% of optimum or b=0 (See paper for full set of results)

19
Constraint Satisfaction Running times – Distributions least likely to have a super soln are quickest to solve – Dense solution space implies deeper tree search

20
Constraint Optimization If no (1,b)-super solution – Optimize robustness & maintain revenue constraint – Minimize number of variables that do not have a repair Else if many (1,b)-super solutions – Find super soln with optimal revenue

21
Constraint Optimization Optimizing Robustness – BnB search – Find a solution with the minimum number of irreparable bids Results – For sched. distribution, no repairs are allowed (b=0), min revenue for a solution is 86% of opt, on average 2.2 bids are irreparable in the most robust solution – Scheduling distribution most difficult to find repairs for all bids (more bids in solution)

22
Constraint Optimization Optimizing Revenue – Many super solutions – find revenue maximizing SS Guarantees a robust solution with maximum revenue – Optimal/Near optimal solutions achievable for scheduling – Computationally expensive (esp. scheduling) – Pure CP approach needs to be augmented with hybrid techniques to improve performance – Continuous (LP) relaxation provides tighter bounds

23
Proposed Extensions to Super Solutions More flexibility required – True cost of repair may not just be measured by number of variables changed E.g. Changing a winning bid to a losing one is more costly than vice versa Introduce a metric for the cost of repair – Break-dependant cost of repair E.g. If an agent withdraws a bid, changing his other winning bids may be considered a cheap operation – Variable values may have degrees of brittleness E.g. Various bidders may have differing probabilities of failure

24
Conclusion Combinatorial Auctions – Improve economic efficiency – NP-complete (although very efficient tailored algorithms exist in practise) – Application domains are expanding Some applications require robustness – Potential exposure problem for the auctioneer Super solutions for CA’s – Framework for establishing robust solutions – CA’s motivate useful extensions to the framework

Similar presentations

OK

Rule-based Price Discovery Methods in Transportation Procurement Auctions Jiongjiong Song Amelia Regan Institute of Transportation Studies University of.

Rule-based Price Discovery Methods in Transportation Procurement Auctions Jiongjiong Song Amelia Regan Institute of Transportation Studies University of.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on history of badminton in the olympics Ppt on duty roster samples Mba ppt on job satisfaction Ppt on content management system Slideshare ppt on marketing Ppt on ufo and aliens today Ppt on red planet mars Ppt on radio station Ppt on electricity generation from municipal solid waste Can you run ppt on ipad