Your SlideShare is downloading. ×
0
Multiple auctions Lecture Series 06 David Yuen
Overview <ul><li>Multiple auctions </li></ul><ul><ul><li>Multiunit or multiple single-unit </li></ul></ul><ul><ul><li>Char...
Multiunit or multiple single unit <ul><li>Multiunit auction </li></ul><ul><ul><li>Allow to bid for multiple units  </li></...
Multiunit or multiple single unit <ul><li>Similar items are being sold in many auctions </li></ul><ul><ul><li>Second hand ...
Multiunit or multiple single unit 1332 450 Car Auction eBay Auction
Why there still exists local bidders <ul><li>Local bidders bid in a single auction: bid true valuation </li></ul><ul><ul><...
Characteristics of multiple auctions  <ul><li>Demand from bidder </li></ul><ul><ul><li>One unit or more </li></ul></ul><ul...
Timing structure <ul><li>Sequential  </li></ul><ul><ul><li>Start after last auction finishes </li></ul></ul><ul><ul><li>Au...
Timing structure <ul><li>Simultaneous </li></ul><ul><ul><li>Start at the same time </li></ul></ul><ul><ul><li>Decision mad...
What can be (have been) done? <ul><li>Simultaneous auctions </li></ul><ul><ul><li>2 nd  price auctions </li></ul></ul><ul>...
Simultaneous second price auctions  <ul><li>Settings </li></ul><ul><ul><li>Second-price (Vickrey) auctions  (no reserve pr...
Global Bidder Expected Utility <ul><li>Static local bidders: exactly N bidders per auction  </li></ul><ul><li>Dynamic loca...
Bidding in Multiple Auctions <ul><li>Optimal to bid strictly positive in all available auctions, even if only 1 item is re...
Finding Optimal Bid <ul><li>Arduous task in large settings using numerical methods </li></ul><ul><li>Reduction of search s...
Optimal Bidding Strategy (cont) <ul><li>Single global bidder </li></ul><ul><li>Static local bidders (N=5) in M auctions </...
Optimal Bidding Strategy
Multiple Global Bidders <ul><li>Computational simulation approach </li></ul><ul><li>A mix of global and local bidders </li...
Multiple Global Bidders (cont) <ul><li>Global bidders only </li></ul><ul><ul><li>No stable state is found </li></ul></ul><...
Multiple Global Bidders (cont) 3 global bidders in 2 auctions 3 global bidders + 10 local bidders  in 2 auctions
Market Efficiency (cont) <ul><li>Market efficiency reduces if </li></ul><ul><ul><li>All local bidders:  Highest valuation ...
Market Efficiency
Unrestricted auction heuristics <ul><li>Settings </li></ul><ul><ul><li>Standard single unit auction formats </li></ul></ul...
Unrestricted auction <ul><li>Degree of Overlap </li></ul><ul><li>% of progressive auctions </li></ul>
Why use heuristics? <ul><li>Long prediction horizon </li></ul><ul><li>Practical time constraints  </li></ul><ul><li>Modell...
Existing benchmarks <ul><li>Random (RND) </li></ul><ul><ul><li>Randomly pick k auctions </li></ul></ul><ul><ul><li>Bid as ...
Two-stage heuristics <ul><li>Aim: to reduce the search space </li></ul><ul><li>Threshold heuristics </li></ul><ul><ul><li>...
Threshold strategies <ul><li>Single auction dominant heuristics (DOM) </li></ul><ul><ul><li>True value for second price me...
Auction selection heuristics <ul><li>Exhaustive search selection (ES) (Byde 02) </li></ul><ul><li>Knapsack utility approxi...
Auction selection heuristics (cont) <ul><li>Knapsack utility approximation (cont) </li></ul><ul><ul><li>Estimate the optim...
Scenario 1: simultaneous auction <ul><li>For a set of 8 simultaneous Vickrey auctions </li></ul><ul><li>Compare with optim...
Scenario 2: unrestricted auction <ul><li>Increasingly better than benchmarks when </li></ul><ul><ul><li>degree of overlap ...
Complexity <ul><li>Acceptable speed at least > 200 auctions </li></ul>
Any Questions? <ul><li>Thank You! </li></ul>
Upcoming SlideShare
Loading in...5
×

Bidding Strategies for Simultaneous Auctions

1,072

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
1,072
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
20
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript of "Bidding Strategies for Simultaneous Auctions"

  1. 1. Multiple auctions Lecture Series 06 David Yuen
  2. 2. Overview <ul><li>Multiple auctions </li></ul><ul><ul><li>Multiunit or multiple single-unit </li></ul></ul><ul><ul><li>Characteristics of multiple single-unit auctions </li></ul></ul><ul><li>Simultaneous second price auctions </li></ul><ul><ul><li>Theoretical analysis </li></ul></ul><ul><ul><li>With Enrico Gerding and Raj Dash </li></ul></ul><ul><li>Unrestricted auction heuristics </li></ul><ul><ul><li>Auction format and timing </li></ul></ul><ul><ul><li>Simulation results </li></ul></ul><ul><ul><li>With Andrew Byde (HP) </li></ul></ul>
  3. 3. Multiunit or multiple single unit <ul><li>Multiunit auction </li></ul><ul><ul><li>Allow to bid for multiple units </li></ul></ul><ul><ul><li>US Treasury Bill auction </li></ul></ul><ul><li>Format </li></ul><ul><ul><li>Discriminatory (Paid you own bid) </li></ul></ul><ul><ul><li>Uniform-Price </li></ul></ul><ul><li>Strategic behaviour </li></ul><ul><ul><li>Demand reduction </li></ul></ul><ul><ul><li>Tacit collusion </li></ul></ul><ul><li>Not the focus of this presentation </li></ul>
  4. 4. Multiunit or multiple single unit <ul><li>Similar items are being sold in many auctions </li></ul><ul><ul><li>Second hand car auction </li></ul></ul><ul><ul><ul><li>Tens of cars in each auction session </li></ul></ul></ul><ul><ul><li>Popular items in eBay </li></ul></ul><ul><ul><ul><li>More than 1000 auctions for iPod nano at any moment </li></ul></ul></ul><ul><li>Participate in multiple single auctions </li></ul><ul><ul><li>Global bidder: participate in all available auctions </li></ul></ul><ul><ul><li>Improved expected profit </li></ul></ul><ul><ul><li>Possibility to hunt for bargain </li></ul></ul>
  5. 5. Multiunit or multiple single unit 1332 450 Car Auction eBay Auction
  6. 6. Why there still exists local bidders <ul><li>Local bidders bid in a single auction: bid true valuation </li></ul><ul><ul><li>Participation costs </li></ul></ul><ul><ul><li>Information </li></ul></ul><ul><ul><li>Budget constraint </li></ul></ul><ul><ul><li>Risk attitude </li></ul></ul><ul><ul><li>Bounded rationality </li></ul></ul>
  7. 7. Characteristics of multiple auctions <ul><li>Demand from bidder </li></ul><ul><ul><li>One unit or more </li></ul></ul><ul><ul><li>Disposal assumption </li></ul></ul><ul><li>Nature of the goods </li></ul><ul><ul><li>Substitute: internet broadband contracts </li></ul></ul><ul><ul><li>Complementary: game console and games </li></ul></ul><ul><li>Timing structure </li></ul><ul><ul><li>Sequential </li></ul></ul><ul><ul><li>Simultaneous </li></ul></ul><ul><ul><li>Unrestricted </li></ul></ul>
  8. 8. Timing structure <ul><li>Sequential </li></ul><ul><ul><li>Start after last auction finishes </li></ul></ul><ul><ul><li>Auction outcomes provides extra info </li></ul></ul><ul><ul><li>Impossible to exceed purchase quota </li></ul></ul><ul><ul><li>Example: second hand car auction </li></ul></ul><ul><li>Optimal bidding strategy </li></ul><ul><ul><li>Second price auction </li></ul></ul><ul><ul><li>Winner leaves (N=10) </li></ul></ul><ul><ul><li>No bidder replacement </li></ul></ul><ul><ul><li>Increasing optimal bid </li></ul></ul>“ Auction Theory”, Ch 15, Vijay Krishna Bid fraction Auction#
  9. 9. Timing structure <ul><li>Simultaneous </li></ul><ul><ul><li>Start at the same time </li></ul></ul><ul><ul><li>Decision made based on little info </li></ul></ul><ul><ul><li>Risk of exceeding purchase quota </li></ul></ul><ul><ul><li>Example: FCC spectrum auction </li></ul></ul><ul><li>Unrestricted </li></ul><ul><ul><li>The most general case </li></ul></ul><ul><ul><li>Start/ finish at any time </li></ul></ul><ul><ul><li>Example: online auction sites </li></ul></ul>
  10. 10. What can be (have been) done? <ul><li>Simultaneous auctions </li></ul><ul><ul><li>2 nd price auctions </li></ul></ul><ul><ul><li>Bidder wants only 1 unit </li></ul></ul><ul><ul><li>Complete substitute </li></ul></ul><ul><ul><li>Optimal and bidding strategy </li></ul></ul><ul><ul><li>Theoretical analysis with simulation results </li></ul></ul><ul><li>Unrestricted auctions </li></ul><ul><ul><li>Any standard single unit auction format </li></ul></ul><ul><ul><li>Bidder wants 1 or more units </li></ul></ul><ul><ul><li>Complete substitute </li></ul></ul><ul><ul><li>Heuristic approach </li></ul></ul>
  11. 11. Simultaneous second price auctions <ul><li>Settings </li></ul><ul><ul><li>Second-price (Vickrey) auctions (no reserve price) </li></ul></ul><ul><ul><li>Each seller/auction sells 1 item </li></ul></ul><ul><ul><li>Each buyer wants 1 item </li></ul></ul><ul><ul><li>Free disposal </li></ul></ul><ul><ul><li>Risk neutral buyers </li></ul></ul>
  12. 12. Global Bidder Expected Utility <ul><li>Static local bidders: exactly N bidders per auction </li></ul><ul><li>Dynamic local bidders model: bidders determined by Poisson with average N </li></ul>v Bidder valuation G(b) Probability of winning auction given bid b g(b) = d G(b)/ d b
  13. 13. Bidding in Multiple Auctions <ul><li>Optimal to bid strictly positive in all available auctions, even if only 1 item is required: </li></ul><ul><li>Better to participate in all available auctions </li></ul>
  14. 14. Finding Optimal Bid <ul><li>Arduous task in large settings using numerical methods </li></ul><ul><li>Reduction of search space : </li></ul><ul><ul><li>In most cases, optimal set of bids consists either of two different bid values (a high bid and a low bid) or all bids are equal </li></ul></ul><ul><ul><li>Proof for non-decreasing bidder density functions (e.g. uniform and logarithmic) </li></ul></ul><ul><ul><li>Holds empirically for most common distributions </li></ul></ul><ul><li>Bids are below the true valuation </li></ul>
  15. 15. Optimal Bidding Strategy (cont) <ul><li>Single global bidder </li></ul><ul><li>Static local bidders (N=5) in M auctions </li></ul><ul><li>Empirical observation </li></ul><ul><ul><li>Low valuation: equal bids </li></ul></ul><ul><ul><li>High valuation: 1 high bid, (M-1) low bids </li></ul></ul><ul><li>Bifurcation phenomenon </li></ul><ul><li>Expected utility increases w.r.t. M </li></ul><ul><ul><li>Most beneficent for midrange valuation </li></ul></ul>
  16. 16. Optimal Bidding Strategy
  17. 17. Multiple Global Bidders <ul><li>Computational simulation approach </li></ul><ul><li>A mix of global and local bidders </li></ul><ul><li>Iteratively finding best response </li></ul><ul><ul><li>Discretize bid space initially </li></ul></ul><ul><ul><li>Utility maximisation for each bidder type </li></ul></ul><ul><ul><li>Next iteration based on latest bid distribution </li></ul></ul><ul><ul><li>Stable solution  symmetric Nash equilibrium </li></ul></ul>
  18. 18. Multiple Global Bidders (cont) <ul><li>Global bidders only </li></ul><ul><ul><li>No stable state is found </li></ul></ul><ul><ul><li>Low valuations: stable </li></ul></ul><ul><ul><li>High valuations: fluctuating between 2 states </li></ul></ul><ul><li>Global + local bidders </li></ul><ul><ul><li>Very stable solution </li></ul></ul><ul><ul><li>Bifurcation also occurs </li></ul></ul><ul><li>Best strategy is also to bid in all auctions </li></ul>
  19. 19. Multiple Global Bidders (cont) 3 global bidders in 2 auctions 3 global bidders + 10 local bidders in 2 auctions
  20. 20. Market Efficiency (cont) <ul><li>Market efficiency reduces if </li></ul><ul><ul><li>All local bidders: Highest valuation individuals bid in the same auction </li></ul></ul><ul><ul><li>Dynamic local bidders: items may remain unsold </li></ul></ul><ul><ul><li>Global bidders: win more than 1 item </li></ul></ul><ul><li>Against static local bidders </li></ul><ul><ul><li>Always improves efficiency </li></ul></ul><ul><li>Against dynamic local bidders </li></ul><ul><ul><li>Improves efficiency when M is small </li></ul></ul><ul><ul><li>Reduces efficiency when M is large </li></ul></ul>
  21. 21. Market Efficiency
  22. 22. Unrestricted auction heuristics <ul><li>Settings </li></ul><ul><ul><li>Standard single unit auction formats </li></ul></ul><ul><ul><ul><li>Dutch, English, first and second price </li></ul></ul></ul><ul><ul><ul><li>Any combination </li></ul></ul></ul><ul><ul><li>Each seller/auction sells 1 item </li></ul></ul><ul><ul><li>Each buyer wants 1 or more item (k ≥ 1) </li></ul></ul><ul><ul><li>Free disposal </li></ul></ul><ul><ul><li>Risk neutral buyers </li></ul></ul>
  23. 23. Unrestricted auction <ul><li>Degree of Overlap </li></ul><ul><li>% of progressive auctions </li></ul>
  24. 24. Why use heuristics? <ul><li>Long prediction horizon </li></ul><ul><li>Practical time constraints </li></ul><ul><li>Modelled as a Markov Decision Process </li></ul><ul><ul><li>Proved to be intractable (Boutilier 99) </li></ul></ul><ul><ul><li>Limited to small number of auctions (M<6) </li></ul></ul><ul><li>Heuristics is prevalent (Anthony 03, Dumas 05) </li></ul><ul><ul><li>Neglect difference between auctions </li></ul></ul><ul><ul><li>Never bid in more than k auctions </li></ul></ul>
  25. 25. Existing benchmarks <ul><li>Random (RND) </li></ul><ul><ul><li>Randomly pick k auctions </li></ul></ul><ul><ul><li>Bid as if it is a local bidder </li></ul></ul><ul><li>Greedy (GRD) </li></ul><ul><ul><li>Calculate extra item required </li></ul></ul><ul><ul><li>nExtra = k – nObtained </li></ul></ul><ul><ul><li>Pick nExtra auctions with least bidders </li></ul></ul><ul><ul><li>No chance to exceed purchase quota </li></ul></ul>
  26. 26. Two-stage heuristics <ul><li>Aim: to reduce the search space </li></ul><ul><li>Threshold heuristics </li></ul><ul><ul><li>Set the maximum bid for each auction </li></ul></ul><ul><ul><li>Actual bid depends on progress in an auction </li></ul></ul><ul><li>Auction selection heuristics </li></ul><ul><ul><li>Decide whether to participate in an individual auction </li></ul></ul><ul><li>Allows “mix-and-match” </li></ul>
  27. 27. Threshold strategies <ul><li>Single auction dominant heuristics (DOM) </li></ul><ul><ul><li>True value for second price mechanisms </li></ul></ul><ul><ul><li>Affected by nBidder for first price mechanisms </li></ul></ul><ul><li>Equal threshold heuristics (EQT) </li></ul><ul><ul><li>Same threshold for all auctions </li></ul></ul><ul><ul><li>Estimate average nBidder with harmonic mean </li></ul></ul><ul><ul><li>Approximate expected utility by assuming identical auction format </li></ul></ul><ul><ul><li>Find threshold that maximises utility </li></ul></ul>
  28. 28. Auction selection heuristics <ul><li>Exhaustive search selection (ES) (Byde 02) </li></ul><ul><li>Knapsack utility approximation (KS) </li></ul><ul><ul><li>Significant loss if the demand limit is exceeded </li></ul></ul><ul><ul><li>Find best number of auctions to participate in </li></ul></ul><ul><ul><ul><li>With simplified multiple auction model </li></ul></ul></ul><ul><ul><ul><li>Given thresholds are fixed </li></ul></ul></ul>Different subset of possible auctions= 2 |S|
  29. 29. Auction selection heuristics (cont) <ul><li>Knapsack utility approximation (cont) </li></ul><ul><ul><li>Estimate the optimal number of wins, x </li></ul></ul><ul><ul><ul><li>Suppose it is the best to place bid in 3 out of 4 auction and the p win =0.7 each, n Opt =3, x Opt =3  0.7=2.1 </li></ul></ul></ul><ul><ul><li>Apply knapsack algorithm </li></ul></ul><ul><ul><ul><li>Objective: maximise item value, i.e. minimise expected payment </li></ul></ul></ul><ul><ul><ul><li>Sack weight limit: xOpt </li></ul></ul></ul><ul><ul><ul><li>Item weight: p win if placing bid b(a) for auction a </li></ul></ul></ul><ul><ul><ul><li>Item value: (-1)  expected payment for a </li></ul></ul></ul>
  30. 30. Scenario 1: simultaneous auction <ul><li>For a set of 8 simultaneous Vickrey auctions </li></ul><ul><li>Compare with optimal results </li></ul>
  31. 31. Scenario 2: unrestricted auction <ul><li>Increasingly better than benchmarks when </li></ul><ul><ul><li>degree of overlap is high </li></ul></ul><ul><ul><li>% progressive auctions (Dutch, English) is high </li></ul></ul>Deg of overlap %progressive auctions low low low low high high high high
  32. 32. Complexity <ul><li>Acceptable speed at least > 200 auctions </li></ul>
  33. 33. Any Questions? <ul><li>Thank You! </li></ul>
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×