Algorithmic Game Theory and Internet Computing

1. Algorithmic Game Theoryand Internet Computing New Market Models and Algorithms Vijay V. Vazirani

2. Markets

3. Stock Markets

4. Internet

5. Revolution in definition of markets

6. Revolution in definition of markets • New markets defined by • Google • Amazon • Yahoo! • Ebay

7. Revolution in definition of markets • Massive computational power available for running these markets in a centralized or distributed manner

8. Revolution in definition of markets • Massive computational power available for running these markets in a centralized or distributed manner • Important to find good models and algorithms for these markets

9. Theory of Algorithms • Powerful tools and techniques developed over last 4 decades.

10. Theory of Algorithms • Powerful tools and techniques developed over last 4 decades. • Recent study of markets has contributed handsomely to this theory as well!

11. Adwords Market • Created by search engine companies • Google • Yahoo! • MSN • Multi-billion dollar market • Totally revolutionized advertising, especially by small companies.

15. New algorithmic and game-theoretic questions • Monika Henzinger, 2004: Find an on-line algorithm that maximizes Google’s revenue.

16. The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine

17. The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine queries (online)

18. The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine Select one Ad Advertiser pays his bid queries (online)

19. The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine Select one Ad Advertiser pays his bid queries (online) Maximize total revenue Online competitive analysis - compare with best offline allocation

20. The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine Select one Ad Advertiser pays his bid queries (online) Maximize total revenue Example – Assign to highest bidder: only ½ the offline revenue

21. Algorithm Greedy Bidder 1 Bidder 2 Example: Bidder1 Bidder 2 Book Queries: 100 Books then 100 CDs CD B1 = B2 = $100 LOST Revenue 100$

22. Optimal Allocation Bidder 1 Bidder 2 Example: Bidder1 Bidder 2 Book Queries: 100 Books then 100 CDs CD B1 = B2 = $100 Revenue 199$

23. Generalizes online bipartite matching • Each daily budget is $1, and each bid is $0/1.

24. Online bipartite matching queries advertisers

25. Online bipartite matching queries advertisers

26. Online bipartite matching queries advertisers

27. Online bipartite matching queries advertisers

28. Online bipartite matching queries advertisers

29. Online bipartite matching queries advertisers

30. Online bipartite matching queries advertisers

31. Online bipartite matching • Karp, Vazirani & Vazirani, 1990: 1-1/e factor randomized algorithm.

32. Online bipartite matching • Karp, Vazirani & Vazirani, 1990: 1-1/e factor randomized algorithm. Optimal!

33. Online bipartite matching • Karp, Vazirani & Vazirani, 1990: 1-1/e factor randomized algorithm. Optimal! • Kalyanasundaram & Pruhs, 1996: 1-1/e factor algorithm for b-matching: Daily budgets $b, bids $0/1, b>>1

34. Adwords Problem • Mehta, Saberi, Vazirani & Vazirani, 2005: 1-1/e algorithm, assuming budgets>>bids.

35. Adwords Problem • Mehta, Saberi, Vazirani & Vazirani, 2005: 1-1/e algorithm, assuming budgets>>bids. Optimal!

36. New Algorithmic Technique • Idea: Use both bid and fraction of left-over budget

37. New Algorithmic Technique • Idea: Use both bid and fraction of left-over budget • Correct tradeoff given by tradeoff-revealing family of LP’s

38. Historically, the study of markets • has been of central importance, especially in the West

39. A Capitalistic Economy depends crucially on pricing mechanisms, with very little intervention, to ensure: • Stability • Efficiency • Fairness

40. Do markets even have inherentlystable operating points?

41. General Equilibrium TheoryOccupied center stage in MathematicalEconomics for over a century Do markets even have inherentlystable operating points?

42. Leon Walras, 1874 • Pioneered general equilibrium theory

43. Supply-demand curves

44. Irving Fisher, 1891 • Fundamental market model

45. wine bread cheese Fisher’s Model, 1891 $ $$$$$$$$$ ¢ $$$$ milk • People want to maximize happiness – assume linear utilities. Find prices s.t. market clears

46. Fisher’s Model • n buyers, with specified money, m(i) for buyer i • k goods (unit amount of each good) • Linear utilities: is utility derived by i on obtaining one unit of j • Total utility of i,

47. Fisher’s Model • n buyers, with specified money, m(i) • k goods (each unit amount, w.l.o.g.) • Linear utilities: is utility derived by i on obtaining one unit of j • Total utility of i, • Find prices s.t. market clears, i.e., all goods sold, all money spent.

49. Arrow-Debreu Theorem, 1954 • Celebrated theorem in Mathematical Economics • Established existence of market equilibrium under very general conditions using a deep theorem from topology - Kakutani fixed point theorem.

50. Kenneth Arrow • Nobel Prize, 1972