1. CRESCCO Project IST-2001-33135 Work Package 2 Algorithms for Selfish Agents Università di Salerno giuper@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.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. 2.V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfish unsplittable traffic. Technical report of CRESCCO, 2003. 3.V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verification for one- parameter agents. Technical report of CRESCCO, 2003. 4.V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthful approximation mechanisms for scheduling related machines. In Proc. of STACS, 2004. 5.S. Kontogiannis, D. Fotakis and P. Spirakis. Selfish unsplittable flows. Technical report, Computer Technology Institute, 2003. 6.G. Melideo, P. Penna, G. Proietti, R. Wattenhofer, and P. Widmayer. Truthful mechanisms for generalized utilitarian problems. Technical report of CRESCCO, 2003. 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. SCHEDULING/ROUTING (WP1): [2,3,4,5]MECHANISM DESIGN THEORY: [3,6]EXPERIMENTS (WP5): [7]APPLICATIONS (workpackages):WIRELESS NETWORKS (WP1): [1,7,8]

7. 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

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

9. 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)

10. 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.

11. 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.

12. 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 )

13. Mechanism design Truthful 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)

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

15. 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

16. 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

17. 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]

18. 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 Existing approximation algorithms are not monotone!! We need new approximation algorithms M.I.T. (majana institute of technology)

19. 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

20. 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)

21. Selfish Scheduling Revised [3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verification for one-parameter agents. Technical report of CRESCCO, 2003. 1.Selfish Jobs: a user sends more traffic than the reported one (i.e., t i > r i ) 2.Selfish Machines: a machine declares to be faster than its real speed (i.e., s i < r i ) Can be verified!! (if the machine gets some job)

22. 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

23. 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

24. 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!

25. 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

26. 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.

27. 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

28. 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

29. 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

30. 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.

31. 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

32. 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

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

35. Recommendations and future plans 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 [1,7,8] [4] [2,3,5] [3,6] M.I.T. (majana institute of technology)

36. Thank You M.I.T. (majana institute of technology)