1 / 22

Quantifying Trade-Offs in Networks and Auctions

Quantifying Trade-Offs in Networks and Auctions. Tim Roughgarden Stanford University. Algorithms and Game Theory. Recent Trend: design and analysis of algorithms that interact with self-interested agents Motivation: the Internet auctions (eBay, sponsored search, etc.)

carina
Download Presentation

Quantifying Trade-Offs in Networks and Auctions

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. Quantifying Trade-Offs in Networks and Auctions Tim Roughgarden Stanford University

  2. Algorithms and Game Theory Recent Trend: design and analysis of algorithms that interact with self-interested agents Motivation: the Internet • auctions (eBay, sponsored search, etc.) • competition among end users, ISPs, etc. Traditional approach: • agents classified as obedient or adversarial • examples: distributed algorithms, cryptography

  3. Trade-Offs and Pareto Curves Well known: trade-offs between competing objectives inevitable in algorithm/system design. Pareto curve: depicts what's feasible and what's not. Objective #2 (e.g. resource usage) Vilfredo Federico Damaso Pareto (1848-1923) feasible region Objective #1 (e.g. cost)

  4. Quantifying Trade-Offs Goal: quantitative analysis of Pareto frontier. Motivation: qualitative insights. • infer design principles • identify fundamental trade-offs between competing constraints/objectives • "litmus test" for algorithm/system design • identify solutions spanning the Pareto frontier

  5. Game-Theoretic Applications New Challenge: algorithm/system design under game-theoretic constraints. Difficulty #1:system (partially) controlled by independent, self-interested entities. • network examples: routing paths, rate of traffic injection, topology formation Difficulty #2:data (partially) controlled by independent, self-interested entities. • auctions: participants' values for goods

  6. Application #1: Routing The problem: given a network and a traffic matrix (pairwise traffic rates), select "optimal" routing paths for traffic.

  7. Application #1: Routing The problem: given a network and a traffic matrix (pairwise traffic rates), select "optimal" routing paths for traffic. Assumptions: fixed traffic matrix; • traffic = many small flows • goal: minimize average delay • link delay = fixed propagation delay + congestion-dependent queuing delay link capacity Delay [secs] Rate x

  8. Measuring Routing Quality Holy grail: centralized routing = globally compute optimal routes for all traffic. Distributed routing: scalable, but larger delay. Assume: at steady-state, only routes of minimum-delay are in use. • delay-minimizing end users ("selfish routing") • delay-minimizing routing policies Next: distributed routing vs. holy grail.

  9. d(x)  x100 s t d(x)  1 A Bad Example Example: large prop delay + large capacity vs. small prop delay + small capacity • one unit (comprising many flows) of traffic Delay [secs] Rate x

  10. d(x)  x100 1 s t d(x)  1 0 A Bad Example Example: large prop delay + large capacity vs. small prop delay + small capacity • one unit (comprising many flows) of traffic Delay [secs] "selfish" routing Rate x

  11. d(x)  x100 1 1-Є s t d(x)  1 0 Є A Bad Example Example: large prop delay + large capacity vs. small prop delay + small capacity • one unit (comprising many flows) of traffic Delay [secs] "selfish" routing "optimal" routing Rate x

  12. d(x)  x100 1 1-Є s t d(x)  1 0 Є A Bad Example Example: large prop delay + large capacity vs. small prop delay + small capacity • one unit (comprising many flows) of traffic Hope: distributed routing improves in overprovisioned network. Delay [secs] "selfish" routing "optimal" routing Rate x

  13. Routing: The Pareto Frontier Trade-off: performance of distributed routing vs. degree of overprovisioning. • "performance" = ratio between average delay of distributed, optimal routing • "Price of Anarchy" • "overprovisioning" = fraction of capacity unused at steady-state Goal: quantify Pareto curve to extract general design principles. Price of Anarchy feasible region Capacity

  14. Benefit of Overprovisioning Suppose: network is overprovisioned by β > 0 (β fraction of each edge unused). Then: Delay of selfish routing at most ½(1+1/√β) times that of optimal. • arbitrary network size/topology, traffic matrix Moral: Even modest (10%) over-provisioning sufficient for near-optimal routing.

  15. xd worst case s t 1 Main Theorem (Informal) Thm:[Roughgarden 02]2-node, 2-link networks always exhibit worst-possible performance. • quantitatively: can compute worst-case performance for given amount of overprovisioning • qualitatively: performance of distributed routing doesn't degrade with complexity of network, traffic complex network + traffic matrix

  16. Application #2: Search Auctions

  17. The Model • n advertisers, k slots • advertisers have willingness to pay per click • slot j has "click-through rate" j • top slots are better: j ³ j+1for all j • advertisers are ranked by bid • possibly with a "reserve price" • for simplicity, ignore issue of "ad relevance" • payments inspired by "second-price auction"

  18. What Is the Objective? Objective #1: revenue • [Myerson 81]: Suppose willingness to pay ("valuations") drawn i.i.d. from some distribution. • Choosing suitable reserve price (+ second-price-esque payments) maximizes expected revenue. Objective #2: "economic efficiency" • [Vickrey 61/Clarke 71/Groves 73]: suitable second-price-esque payments (no reserve price) works. • no assumptions on valuations

  19. Search Auctions: The Pareto Frontier Trade-off: economic efficiency vs. revenue. Goal: quantify revenue loss in efficient auction. Motivation: • efficient auction closer to those used in practice • does not require assumption and knowledge of distribution • good in non-monopoly settings EconomicEfficiency feasible region Revenue

  20. Competition Obviates Cleverness Theorem #1[Roughgarden/Sundararajan 07]: Expected revenue of the economically efficient auction with n+k bidders exceeds optimal expected revenue with n bidders. • for any fixed distribution (some technical conditions) Point: a little extra competition outweighs benefit of the optimal reserve price.

  21. Competition Obviates Cleverness Theorem #2[Roughgarden/Sundararajan 07]: Expected revenue of economically efficient auction is at least (1-k/n) times optimal expected revenue. • n advertisers in both auctions • for any fixed distribution (some technical conditions) Point: under modest competition, efficient auction has near-optimal revenue.

  22. What's Next? Networks: use Pareto frontier to inform algorithm/protocol design • different curves for different protocols • want "best" Pareto curve • see [Chen/Roughgarden/Valiant 07] Sponsored Search: need dynamic models • competition between search engines, etc. • short-term vs. long-term revenue trade-offs • role of budget constraints • vindictive bidding

More Related