1 / 225

Online Algorithms for Market Clearing

Online Algorithms for Market Clearing. Martin Zinkevich Joint Work with Avrim Blum and Tuomas Sandholm (SODA 2002). Introduction. E-Bay: Single Auction. Buy Bids: people wanting to buy Sell Bids: people wanting to sell. E-Bay: Single Auction. Buy Bids: people wanting to buy

nita-coffey
Download Presentation

Online Algorithms for Market Clearing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Online Algorithms for Market Clearing Martin Zinkevich Joint Work with Avrim Blum and Tuomas Sandholm (SODA 2002)

  2. Introduction

  3. E-Bay: Single Auction Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  4. E-Bay: Single Auction Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  5. E-Bay: Single Auction Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  6. Improvement #1: Double Auction Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  7. Graphical Version Price Profit Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  8. Improvement #2:Bidding For Different Intervals

  9. Jane Toy’s R Us Mark Temporal Bidding Problem Introduction Time Expiration Time Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  10. How to Make Money • Buy the PS2 from one person for some money, and sell it to someone else for more than you bought it. • Keep no inventory, have sellers mail PS2 directly to buyers.

  11. Types of Algorithms • One can imagine two types of algorithms: • Offline: An algorithm which knows the whole sequence before making decisions. • Online: An algorithm which finds the type, price, and expiration time of a bid as it is introduced, and must act on a bid before it expires.

  12. Formalizing the Goal • Find a matching of concurrent buy and sell bids that maximizes profit

  13. The Maximal Matching Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  14. The Offline Problem Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  15. Convert to a Graph Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  16. Convert to a Graph Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  17. Convert to a Weighted Graph 5 Price 1 5 5 2 Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  18. Convert to a Weighted Graph 5 1 5 5 2

  19. Find a Matching of Maximum Weight 5 1 5 5 A matching for a graph is a set of edges which do not share any vertices 2

  20. Find a Matching of Maximum Weight 5 1 5 5 A matching for a graph is a set of edges which do not share any vertices 2

  21. Find a Matching of Maximum Weight 5 1 5 5 2 Algorithms exist to solve this in polynomial time

  22. Find a Matching of Maximum Weight

  23. Find a Matching of Maximum Weight Price Matching of maximal weight maximizes profit! Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  24. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  25. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  26. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  27. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  28. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  29. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  30. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  31. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  32. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  33. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  34. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  35. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  36. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  37. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  38. What Online Sees… Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  39. Two Online Difficulties Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  40. Getting the Most Matches Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  41. Getting the Most Per Match Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  42. Two Small Problems • Maximizing Liquidity: maximizing the number of matches • The Ice Cream Problem: maximizing profit of one trade

  43. Outline • Introduction • Small Problem #1:Maximizing Liquidity • Small Problem #2:The Ice Cream Problem • Putting it Together • Conclusion • New Results

  44. Maximizing Liquidity

  45. Simplified Matching • Let’s try to maximize the number of trades with positive profit on each trade.

  46. A Maximal Numeric Matching Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  47. Also Maximal Numerically Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  48. Offline: Convert to a Graph No weights needed Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  49. Convert to a Graph No edge here Price Time Buy Bids: people wanting to buy Sell Bids: people wanting to sell

  50. Convert to a Graph

More Related