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

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

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) 2. Methodology to develop good solutions 3. New concepts, mathematical tools and algorithmic techniques Strict and centralized vs loose and local control What is the price of anarchy? Design a new “TCP/IP protocol” robust wrt selfish users 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 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. 3.V. Auletta, R. De Prisco, P. Penna, and G. Persiano. Monotone algorithms characterize mechanisms for selfish jobs. CRESCCO TR, 2004. 4.V. Auletta, A.V. Fishkin, and G. Persiano. On gaining a control over two links occupied by selfish agents. CRESCCO TR, 2004. 5.P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005. 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. SCHEDULING/ROUTING (WP1): [1,2,3,4]NEW GAME THEORY: [2,5,6,7]EXPERIMENTS (WP5): [7]APPLICATIONS (workpackages):WIRELESS NETWORKS (WP1): [5,6,7]

7. Routing/Scheduling Unsplittable traffic J 1, J 2,…,J n We look at the network congestion (makespan) sourcedestination Scheduling Selfish Machines: Selfish users own the links and privately know their speeds s1s1 smsm s2s2    0 0 0

8. Mechanism design Mechanism: M=(A,P) Computes a solution X=A(r 1,r 2,…, r i,…,r n ) Provides a payment P i (r 1,r 2,…, r i,…,r n ) Agents’ GOAL: maximize their own utility u i (r i ) := P i (r 1,r 2,…, r i,…,r n ) – cost i (X,t i ) cost i (X,t i ) t 1,t 2,…, t i,…,t n true input

9. Mechanism design Strategyproof mechanisms: no incentive to lie (report r i  t i ) u i (t i )  u i (r i ) (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. Translation techniques A’AM=(A’,P) AlgorithmMechanism M=(A,P)A hard loss of performance

13. Translation techniques A black-box, polytime A’A “easy” c-apx c’-apx offline: c’ = c(1+  ) online: c < c’  c  A’=AA Not needed [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. greedy (like) and speeds s i =2 k (selfish machines)

14. Loss of performance [2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005. Online vs Offline (m=2) offline online selfishunselfish (1+  ) 3/2  c   c’  c1.78 “<“ is possible hardest

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

16. Cost-Sharing Games U Q 1.Which customers to service? 2.At which price? S Service providerCustomers t i = willingness to pay

17. Cost-Sharing Games U Q S Service providerCustomers 1. Budget balanced: Cost(Q) =  P i 2. Users can form coalitions  Group strategyproof mechanisms

18. Cost-Sharing Games U Q S Service providerCustomers S 0.9 1 Multicast: S 0.9 1 wiredwireless

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

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

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

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

23. Answered Questions 1.When verification helps: Online YES, offline NO [2] 2.Online Setting: More difficult! [2] 3.Selfish Jobs vs Selfish Machines: Constant loss [3] 4.Wireless Networks: Budget-balance, Wireless vs Wired [6,7] 5.Mechanism Design Theory: Problem restrictions [6,7]

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

25. Thank You

26. M.I.T. (majana institute of technology)

27. Theory of ComputingGame Theory Combining Tools EfficientIncentive compatible  (strategyproof mechanism)(polytime apx algorithm) Which part do we change? “Good Protocol”: 1.Run fast, optimal resource allocation 2.Agents “follow” the protocol ?

28. New Game Theory: Helpful? Verification: 1. Offline Scheduling, NO 2. Online Scheduling, YES Cost-Sharing Methods 1. YES Other Issues: 1. Technology 2. Fairness M.I.T. (majana institute of technology)

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

30. Nash equilibria When no selfish agent has an incentive in unilaterally changing his/her strategy: (5,1)(0,0) (1,5) he she F T FT Football or Theater

31. Scheduling Selfish Jobs No selfish routing  Use a scheduler 1.Users cannot refuse the allocation 2.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.

32. Mechanisms for Wireless Networks Wireless Cost-Sharing: Source (e.g., popular sport event) [8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks. Technical report of CRESCCO, 2003. Also submitted for publication. 10E 3E 2E11E2E 10E GOAL: maximize benefits-costs 8E1E

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

34. Mechanism Design Theory [6] G. Melideo, P. Penna, G. Proietti, R. Wattenhofer, and P. Widmayer. Truthful mechanisms for generalized utilitarian problems. Technical report of CRESCCO, 2003 VCG mechanisms: 1.Objective function m(X) =  i  X COST i (X,t i ) 2.u i = P i - COST i (X,t i ) MRP problem: 1.Objective function m(X) =  e  X q i 2.u i = P i q i Utilitarian problems

35. Mechanism Design Theory Probability of link failure GOAL: find the Most Reliable Path [6] G. Melideo, P. Penna, G. Proietti, R. Wattenhofer, and P. Widmayer. Truthful mechanisms for generalized utilitarian problems. Technical report of CRESCCO, 2003 Payments: pay P e iff link e succeds  Utility: u e =q e ·P e Expected GAIN destination source 0.6 0.5 0.9 0.3 0.8 Not ADDITIVE

36. Mechanisms for Wireless Networks [8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks. Technical report of CRESCCO, 2003. Polynomial-time mechanisms: Lower boundUpper bound General graphs No R-APX, every R>1 Trees, “Metric-tree” graphs OPT, distributed mechanism Distributed APX mechanism for other casesSuggests 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.

37. 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. Lower bound Upper bound General graphs No R-APX, every R>1 Metric, Well-spread remain NP-hard 1.5-APX O(1)-APX

38. Mechanisms for Wireless Networks Ad Hoc Nets: i power i (j) j Private knowledge of i [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. GOAL: Strong connectivity, minimal total power k

39. Mechanisms for Wireless Networks Ad Hoc Nets: i repow i (j) >> power i (j) j Reported power repow i (j)k [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.

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

41. Scheduling Selfish Jobs [2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfish unsplittable traffic. Technical report of CRESCCO, 2003. Speed ratio r=smax/smin Lower boundUpper bound identical speeds No exact with dominant strategies Exact (non polytime) (polytime) Bayesian-Nash Different speeds, one job per agent, Bayesian-Nash M.I.T. (majana institute of technology) Bayesian-Nash

42. Scheduling Selfish Jobs [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 k vs mLower boundUpper bound Identical speeds, k jobs per agent, Bayesian-Nash

43. 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 Machine speeds Our resultPrevious results [ArcTar01] Any 4+  3+  Divisible 2 +  3+  Randomized, no dominant strategies Deterministic, dominant strategies

44. 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 Machine speeds Our resultPrevious results [ArcTar01] Any 4+  3+  Divisible 2 +  3+  Real cases (e.g., Sonet/SDH standards)

45. Applications of restricted one-parameter agents: Selfish Jobs 1. (1+  )-APX mechanism ( breaks lower bounds in [2]) Selfish Machines: 1.first (1+  )-APX mechanism 2.breaks a lower bound in [ArcTar01] for a weighted variant of scheduling Approximation and selfish 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. Also submitted for publication Verification helps!

46. Approximation and selfish 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.  No need for new algorithms! (TCS gets its revenge) We introduce restricted one-parameter agents

47. Approximation and selfish 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. We introduce restricted one-parameter agents Theorem [3]: Polynomial-time c-approximation algorithm A  M = (A , P) truthful polynomial-time (c+  )- approximation

48. Mechanism design Mechanism: M=(A,P) Computes a solution X=A(r 1,r 2,…, r i,…,r n ) Provides a payment P i (r 1,r 2,…, r i,…,r n ) cost i (X,t i ) Agents’ GOAL: maximize their own utility u i (r 1,r 2,…, r i,…,r n ) := P i (r 1,r 2,…, r i,…,r n ) – cost i (X,t i )

49. Mechanism design Strategyproof mechanisms: no incentive to lie 1. Bayesian-Nash u i (t 1,t 2,…, t i,…,t n )  u i (t 1,t 2,…, r i,…,t n ) (truth-telling is Nash equilibrium) 2.With dominant strategies u i (r 1,r 2,…, t i,…,r n )  u i (r 1,r 2,…, r i,…,r n ) (truth-telling is always the best strategy)

50. Mechanisms for Wireless Networks Wireless Cost-Sharing: Source (e.g., popular sport event) [8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks. Technical report of CRESCCO, 2003. 10E 3E 2E11E2E 10E GOAL: maximize benefits-costs

51. Nash equilibria for selfish routing … 111 Expected MAX LOAD: 1 1/m Expected MAX LOAD: Θ(ln m/ln ln m) Price of anarchy Worst-case equilibria Coordination ratio M.I.T. (majana institute of technology)

52. Routing/Scheduling m links with different speeds s 1, s 2,…,s m Unsplittable traffic t 1, t 2,…, t n We look at the network congestion (makespan) sourcedestination Selfish Routing: users choose the best path for their own traffic Scheduling Selfish Jobs: Selfish users own the traffic and privately know their weights Scheduling Selfish Machines: Selfish users own the links and privately know their speeds

53. Routing/Scheduling m links with different speeds s 1, s 2,…,s m Unsplittable traffic t 1, t 2,…, t n We look at the network congestion (makespan) sourcedestination Scheduling Selfish Jobs: Selfish users own the traffic and privately know their weights Scheduling Selfish Machines: Selfish users own the links and privately know their speeds