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CRESCCO Project IST-2001-33135

CRESCCO Project IST-2001-33135. Work Package 2 Critical Resources and Selfish Agents Paolo Penna Università di Salerno penna@dia.unisa.it. M.I.T. (majana institute of technology).

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CRESCCO Project IST-2001-33135

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  1. CRESCCO ProjectIST-2001-33135 Work Package 2 Critical Resources and Selfish Agents Paolo Penna Università di Salerno penna@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 • P. Ambrosio and V. Auletta. Deterministic Monotone Algorithms for Scheduling on Related Machines. In Proc. of WAOA, 2004. • V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005. • V. Auletta, R. De Prisco, P. Penna, and G. Persiano. Monotone algorithms characterize mechanisms for selfish jobs. CRESCCO TR, 2004. • V. Auletta, A.V. Fishkin, and G. Persiano. On gaining a control over two links occupied by selfish agents. CRESCCO TR, 2004. • P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005. • P. Penna and C. Ventre. When is cost-sharing possible? CRESCCO TR, 2004. • P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004. APPLICATIONS (workpackages): SCHEDULING/ROUTING (WP1): [1,2,3,4] NEW GAME THEORY: [2,5,6,7] EXPERIMENTS (WP5): [7] WIRELESS NETWORKS (WP1): [5,6,7]

  7. 0  0  0 Routing/Scheduling SchedulingSelfish Machines: Selfish users own the links and privately know their speeds s1 s2 source destination sm • Unsplittable traffic J1, J2 ,…,Jn • We look at the network congestion (makespan)

  8. Computes a solution X=A(r1,r2,…, ri ,…,rn) Provides a payment Pi(r1,r2,…, ri ,…,rn) t1,t2,…, ti ,…,tn costi(X,ti) true input Mechanism design Mechanism:M=(A,P) Agents’ GOAL: maximize their own utility ui(ri) := Pi(r1,r2,…, ri ,…,rn) – costi(X,ti)

  9. Mechanism design Strategyproof mechanisms: no incentive to lie (report ri  ti) ui(ti) ui(ri) (truth-telling is the best strategy)

  10. Mechanism design Question: Given A, is there P s.t. M=(A,P) is strategyproof? In general, NO!

  11. Scheduling Selfish Machines • Monotone algorithms: an agent declaring a higher speed does not get less work/load. • A monotone M=(A,P) strategyproof • [Archer and Tardos, STOC 2001]

  12. Algorithm Mechanism A M=(A,P) hard A A’ M=(A’,P) loss of performance Translation techniques

  13. Not needed A A’=A “easy” A A’ c-apx c’-apx A black-box, polytime Translation techniques (selfish machines) greedy (like) and speeds si=2k offline: c’ = c(1+) online: c < c’ c• [1] P. Ambrosio and V. Auletta. Deterministic Monotone Algorithms for Scheduling on Related Machines. In Proc. of WAOA, 2004. [2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005.

  14. “<“ is possible hardest online offline (1+) (1+) unselfish selfish Loss of performance Online vs Offline (m=2) 3/2 c   c’ c•1.78 [2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005.

  15. future selfish selfish selfish selfish loss 1+ future  loss < 1.83 Verification [Auletta et al, ICALP’04]  < loss <  selfish “Unknown” input Input: jobs speeds  < loss <   < loss <  [2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005. [3] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. Monotone algorithms characterize mechanisms for selfish jobs. CRESCCO TR, 2004.

  16. Service provider Customers S Q Cost-Sharing Games U ti = willingness to pay • Which customers to service? • At which price?

  17. Service provider Customers S Q Cost-Sharing Games U • Budget balanced: Cost(Q) =  Pi • Users can form coalitions •  • Group strategyproof mechanisms

  18. Service provider Customers S Q S 1 1 0.9 0.9 wired wireless Cost-Sharing Games U Multicast: S 0.9 0.9

  19. A=OPT (1+)-APX NP-hard [7] A M=(A,P) [7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004. Cost-Sharing Games [Moulin-Shenker’97] A M=(A,P) A  any OPT (wired:polytime)  (wireless: NP-hard)

  20. A=OPT (1+)-APX NP-hard [7] A M=(A,P) [7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004. Cost-Sharing Games A M=(A,P) Free-riders (fairness) [5] P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005.

  21. A=OPT (1+)-APX NP-hard [7] A M=(A,P) [6] [6] P. Penna and C. Ventre. When is cost-sharing possible? CRESCCO TR, 2004. [7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004. Cost-Sharing Games A M=(A,P) characterization [5] P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005.

  22. [5,6,7] [1,4] [2,3] [2,5,6,7] This year: Recommendations and future plans (from 2nd year review talk) • 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)

  23. Answered Questions • When verification helps: • Online YES, offline NO [2] • Online Setting: • More difficult! [2] • Selfish Jobs vs Selfish Machines: • Constant loss [3] • Wireless Networks: • Budget-balance, Wireless vs Wired [6,7] • Mechanism Design Theory: • Problem restrictions [6,7]

  24. 3rd New Algorithms [1-4,7,8] [1-4] New Game Theory [6,3] [2,3,5-6] Provably Better Important Issues (2nd year review talk) • Computational issues • Efficiency • Technological issues • Different assumptions • Existing game theory • Not always suitable , extract infos 2nd year work: ICALP (2), IFIP-TCS, SPAA, STACS, SIROCCO, Theor. Comp. Sci. Technology Helps Theory

  25. Thank You

  26. “Good Protocol”: • Run fast, optimal resource allocation • Agents “follow” the protocol Combining Tools ? Theory of Computing Game Theory Efficient  Incentive compatible (polytime apx algorithm) (strategyproof mechanism) Which part do we change?

  27. New Game Theory: Helpful? • Verification: • Offline Scheduling, NO • Online Scheduling, YES • Cost-Sharing Methods • YES • Other Issues: • Technology • Fairness M.I.T. (majana institute of technology)

  28. new game theory easier A A’ M=(A’,P) no loss, provably better New Game Theory hard A A’ M=(A’,P) loss

  29. 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 selfish unsplittable traffic. Technical report of CRESCCO, 2003.

  30. 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 wireless networks. Technical report of CRESCCO, 2003. Also submitted for publication.

  31. 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 for generalized utilitarian problems. Technical report of CRESCCO, 2003

  32. 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: combining MSTs with shortest-path trees. Technical report of CRESCCO, 2003. [8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks. Technical report of CRESCCO, 2003.

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

  34. 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 Consumption in Radio Networks: Selfish Agents and Rewarding Mechanisms. In Proc. of SIROCCO, 2003. Also accepted in Theoretical Computer Science.

  35. 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.

  36. 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 selfish unsplittable traffic. Technical report of CRESCCO, 2003.

  37. 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 selfish unsplittable traffic. Technical report of CRESCCO, 2003. Also submitted for publication

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

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

  40. 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 verification for one-parameter agents. Technical report of CRESCCO, 2003. Also submitted for publication

  41. 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 verification for one-parameter agents. Technical report of CRESCCO, 2003.

  42. 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 verification for one-parameter agents. Technical report of CRESCCO, 2003.

  43. 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 own utility ui(r1,r2,…, ri ,…,rn) := Pi(r1,r2,…, ri ,…,rn) – costi(X,ti)

  44. Mechanism design Strategyproof 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)

  45. 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 wireless networks. Technical report of CRESCCO, 2003.

  46. 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

  47. 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)

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

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