1. Expense constrained bidder optimization in repeated auctions Ramki Gummadi Stanford University (Based on joint work with P. Key and A. Proutiere)

2. Overview Introduction/Motivation Budgeted Second Price Auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

3. Three Aspects of Sponsored Search 1.Sequential setting. 2. Micro-transactions per auction. 3. The long tail of advertisers is expense constrained.

4. Motivation: Expense Constraints Payments are explicit, but valuations are abstract. Significantly alters bidding behavior. Critical for advertisers in the long tail.

5. Modeling Expense Constraints Balance time T0 B

6. Modeling Expense Constraints Stochastic fluctuations could cause spend rate different from target. Balance time T0 B

7. Modeling Expense Constraints “…the nature of what this budget limit means for the bidders themselves is somewhat of a mystery. There seems to be some risk control element to it, some purely administrative element to it, some bounded- rationality element to it, and more…” -- “Theory research at google”, SIGACT News, 2008.

8. Modeling Expense Constraints Balance time 0 B

9. Responsibility for expense constraints Auctioneer Bidder Bids fixed -- Auction entry throttled. Bids adjusted dynamically. Online bipartite matching between queries and bidders. Online knapsack type problems. Expense constraints = fixed budget. Possible to model more general expense constraints.

10. Bid optimization

11. Modeling aspects Expense constraints include a running balance constraint together with a fixed income per time slot. Random i.i.d. environment models aggregate statistics. -- observable and non-observable components. Bids are lower because any money saved can instead be used to buy a cheaper auction in the future. Objective function is infinite horizon expected utility, but with a discount factor that models limited patience.

12. Preview

13. Preview: Optimal Shading factors

14. Overview Introduction Budgeted Second Price auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

15. Model: Budgeted Second Price

17. The Value Function

18. But boundary conditions can not be inferred from the DP argument. Current auction Loss Win

19. Future opportunity cost Characterization of value function

20. Value Iteration:

22. Limiting case: micro-value auctions

23. Overview Introduction Budgeted Second Price Auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

24. General Online Budgeting Model Decision Maker Unobservable

25. Ex1: Second Price Auction

26. Ex2: GSP Auction Click events for L slots

27. Overview Introduction Budgeted Second Price Auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

28. Notation:

29. Theorem

31. Application to Second Price Auctions

32. Second Price Auction Example Opponents bid p Value functions

33. Optimal bid i.e., Static SP with shaded valuation:

34. Optimal Scaling factor

35. Optimal Bid: GSP Static GSP with “virtual valuation”:

36. Proof Overview Next 2 slides

38. time B(t) B Play U*

39. Overview Introduction MDP for budgeted SP auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

40. Stationarity in large markets

41. Conclusion A two parameter model for expense constraints in online budgeting problems. Optimal bid can be mapped to static auction with a shaded virtual valuation. Paper has more contents: MFE analysis and a finite horizon model.