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Selfish Agents in Autonomous Systems: Towards Efficient Internet Routing

Explore algorithmic solutions for selfish entities in internet routing. Investigate Nash equilibria, mechanism design, and coordination ratios.

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Selfish Agents in Autonomous Systems: Towards Efficient Internet Routing

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  1. CRESCCO ProjectIST-2001-33135 Work Package 2 Algorithms for Selfish Agents Università di Salerno giuper@dia.unisa.it M.I.T. (majana institute of technology) Project funded by the Future and Emerging Technologies arm of the IST Programme – FET Proactive initiative “Global Computing”

  2. AUTONOMOUS SYSTEMS PROVIDERS INTERNET INTERNET PRIVATE COMPANIES UNIVERSITIES DIFFERENT GOALS SELFISH ENTITIES THAT COOPERATE DIFFERENT SOCIO-ECONOMIC ENTITIES

  3. The Internet Open, self organized, no central authority, anarchic: 1. A router may forward packets to optimize its own traffic 2. A client may “ignore” the server ackws and not follow the TCP packet transmission rate 3. An Autonomous System may report false link status to redirect traffic to another AS

  4. Main Goals 1. A deeper understanding of basic principles of a complex system (Internet) Strict and centralized vs loose and local control What is the price of anarchy? 2. Methodology to develop good solutions Design a new “TCP/IP protocol” robust wrt selfish users 3. New concepts, mathematical tools and algorithmic techniques M.I.T. (majana institute of technology)

  5. Mathematical Tools • Theory of Computing • Computational complexity • Design and Analysis of Algorithms • Microeconomics and Game Theory • Nash equilibria • Mechanism design

  6. Research Progress • C. Ambuehl, A. Clementi, P. Penna, G. Rossi, and R. Silvestri. Energy Consumptionin Radio Networks: Selfish Agents and Rewarding Mechanisms. In Proc. of SIROCCO, 2003. Also accepted in Theoretical Computer Science. • V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfishunsplittable traffic. Technical report of CRESCCO, 2003. • V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verificationfor one-parameter agents. Technical report of CRESCCO, 2003. • V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthfulapproximationmechanisms for scheduling related machines. In Proc. of STACS, 2004. • S. Kontogiannis, D. Fotakis and P. Spirakis. Selfish unsplittable flows.Technical report, Computer Technology Institute, 2003. • G. Melideo, P. Penna, G. Proietti, R. Wattenhofer, and P. Widmayer. Truthful mechanisms for generalizedutilitarian problems.Technical report of CRESCCO, 2003. • P. Penna and C. Ventre. Energy-efficient broadcasting in ad-hoc networks: combiningMSTs with shortest-path trees. Technical report of CRESCCO, 2003. • P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wirelessnetworks. Technical report of CRESCCO, 2003. APPLICATIONS (workpackages): SCHEDULING/ROUTING (WP1): [2,3,4,5] MECHANISM DESIGN THEORY: [3,6] EXPERIMENTS (WP5): [7] WIRELESS NETWORKS (WP1): [1,7,8]

  7. Routing/Scheduling SchedulingSelfish Jobs: Selfish users own the traffic and privately know their weights Selfish Routing: users choose the best path for their own traffic SchedulingSelfish Machines: Selfish users own the links and privately know their speeds source destination • m links with different speeds s1, s2,…,sm • Unsplittable traffic t1, t2 ,…, tn • We look at the network congestion (makespan)

  8. Expected MAX LOAD: Θ(ln m/ln ln m) 1 1 1 1/m Expected MAX LOAD: 1 Nash equilibria for selfish routing … M.I.T. (majana institute of technology) Price of anarchy Worst-case equilibria Coordination ratio

  9. Nash equilibria for selfish routing Layered graphs Identical links … destination source 1 2 l Theorem [5]: Every l-layered network has coordination ratio at most O(logm/log logm) Corollary: 1-layered graphs are the worst instances. Theorem [5]: Some l-layered networks do not have pure Nash equilibria. [5] S. Kontogiannis, D. Fotakis and P. Spirakis. Selfish unsplittable flows.Technical report, Computer Technology Institute, 2003.

  10. Scheduling Selfish Jobs • No selfish routing Use a scheduler • Users cannot refuse the allocation • May lie about their traffic weights • Provide correct incentives (mechanism design) [2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfishunsplittabletraffic. Technical report of CRESCCO, 2003.

  11. Computes a solution X=A(r1,r2,…, ri,…,rn) Provides a payment Pi(r1,r2,…, ri,…,rn) costi(X,ti) Mechanism design Mechanism:M=(A,P) Agents’ GOAL: maximize their ownutility ui(r1,r2,…, ri,…,rn) := Pi(r1,r2,…, ri,…,rn) – costi(X,ti)

  12. Mechanism design Truthful mechanisms: no incentive to lie • Bayesian-Nash ui(t1,t2,…, ti,…,tn) ui(t1,t2,…, ri,…,tn) (truth-telling is Nash equilibrium) • With dominant strategies ui(r1,r2,…, ti,…,rn) ui(r1,r2,…, ri,…,rn) (truth-telling is always the best strategy)

  13. Mechanism design Question: Given A, is there P s.t. M=(A,P) is truthful? In general, NO!  new algorithms

  14. Bayesian-Nash Scheduling Selfish Jobs Different speeds, one job per agent, Bayesian-Nash M.I.T. (majana institute of technology) [2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfishunsplittabletraffic. Technical report of CRESCCO, 2003.

  15. Scheduling Selfish Jobs Identical speeds, k jobs per agent, Bayesian-Nash [2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfishunsplittabletraffic. Technical report of CRESCCO, 2003. Also submitted for publication

  16. Scheduling Selfish Machines • Truthful mechanisms must allocate jobs monotonically: an agent declaring higher speed does not get less load; • A monotone algorithm can be turned into a truthful mechanism with the same performances. • [Archer and Tardos, STOC 2001]

  17. Scheduling Selfish Machines Existing approximation algorithms are not monotone!! We need new approximation algorithms M.I.T. (majana institute of technology) [1] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthfulapproximationmechanisms for scheduling related machines. In Proc. of STACS, 2004

  18. Randomized, nodominant strategies Deterministic, dominant strategies Scheduling Selfish Machines [1] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthfulapproximationmechanisms for scheduling related machines. In Proc. of STACS, 2004

  19. Real cases (e.g., Sonet/SDH standards) Scheduling Selfish Machines [1] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthfulapproximationmechanisms for scheduling related machines. In Proc. of STACS, 2004

  20. (if the machine gets some job) Selfish Scheduling Revised • Selfish Jobs: a user sends more traffic than the reported one (i.e., ti >ri) • Selfish Machines: a machine declares to be faster than its real speed (i.e., si < ri) Can be verified!! [3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verificationfor one-parameter agents. Technical report of CRESCCO, 2003.

  21. Approximation and selfish agents We introduce restricted one-parameter agents Theorem [3]: Polynomial-time c-approximation algorithm A  M = (A , P) truthful polynomial-time (c+)-approximation [3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verificationfor one-parameter agents. Technical report of CRESCCO, 2003.

  22. Approximation and selfish agents  Noneed for new algorithms! (TCS gets its revenge) We introduce restricted one-parameter agents [3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verificationfor one-parameter agents. Technical report of CRESCCO, 2003.

  23. Verification helps! Approximation and selfish agents • Applications of restricted one-parameter agents: • Selfish Jobs • (1+)-APX mechanism (breaks lower bounds in [2]) • Selfish Machines: • first (1+)-APX mechanism • breaks a lower bound in [ArcTar01] for a weighted variant of scheduling [3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verificationfor one-parameter agents. Technical report of CRESCCO, 2003. Also submitted for publication

  24. Private knowledge of i Mechanisms for Wireless Networks • Ad Hoc Nets: poweri(j) k j i GOAL: Strong connectivity, minimal totalpower [1] C. Ambuehl, A. Clementi, P. Penna, G. Rossi, and R. Silvestri. Energy Consumptionin Radio Networks: Selfish Agents and Rewarding Mechanisms. In Proc. of SIROCCO, 2003. Also accepted in Theoretical Computer Science.

  25. Mechanisms for Wireless Networks Polynomial-time VCG-based mechanisms: [1] C. Ambuehl, A. Clementi, P. Penna, G. Rossi, and R. Silvestri. Energy Consumptionin Radio Networks: Selfish Agents and Rewarding Mechanisms. In Proc. of SIROCCO, 2003. Also accepted in Theoretical Computer Science.

  26. Mechanisms for Wireless Networks • Wireless Cost-Sharing: 3E 10E 10E 2E 2E 11E Source (e.g., popular sport event) GOAL: maximize benefits-costs [8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wirelessnetworks. Technical report of CRESCCO, 2003.

  27. Mechanisms for Wireless Networks • Wireless Cost-Sharing: 3E 10E 10E 2E 2E 11E 1E 8E Source (e.g., popular sport event) GOAL: maximize benefits-costs [8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wirelessnetworks. Technical report of CRESCCO, 2003. Also submitted for publication.

  28. Mechanisms for Wireless Networks Polynomial-time mechanisms: Distributed APX mechanism for other cases Suggests a better new broadcast algorithm [7] P. Penna and C. Ventre. Energy-efficient broadcasting in ad-hoc networks: combiningMSTs with shortest-path trees. Technical report of CRESCCO, 2003. [8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wirelessnetworks. Technical report of CRESCCO, 2003.

  29. Consistent problems Mechanism Design Theory Problems Most Reliable Path Arbitrage Task Scheduling Knapsack Utilitarian problems VCG [1961] M.I.T. (majana institute of technology) [6] G. Melideo, P. Penna, G. Proietti, R. Wattenhofer, and P. Widmayer. Truthful mechanisms forgeneralizedutilitarian problems.Technical report of CRESCCO, 2003

  30. New algorithms [1-4,7,8] New models/tools [6,3] Sometimes helpful!! Important Issues • Computational issues • Efficiency • Technological issues • Different assumptions • Existing game theory • Not always suitable , extract infos M.I.T. (majana institute of technology)

  31. [1,7,8] [4] [2,3,5] [3,6] Recommendations and future plans • Consider Algorithms and Game Theory jointly • Technological Issues • Wireless vs Wired • Assumptions (e.g., link speeds) • How much technology can help (e.g. verification, known users traffic vs known router speeds) • New concepts, new mathematical tools and new algorithmic techniques •  • Cross fertilization between TCS, micro-economics and game theory M.I.T. (majana institute of technology)

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