CRESCCO Project IST-2001-33135

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## CRESCCO Project IST-2001-33135

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**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”**AUTONOMOUS**SYSTEMS PROVIDERS INTERNET INTERNET PRIVATE COMPANIES UNIVERSITIES DIFFERENT GOALS SELFISH ENTITIES THAT COOPERATE DIFFERENT SOCIO-ECONOMIC ENTITIES**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**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)**Mathematical Tools**• Theory of Computing • Computational complexity • Design and Analysis of Algorithms • Microeconomics and Game Theory • Nash equilibria • Mechanism design**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]**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)**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**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.**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.**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)**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)**Mechanism design**Question: Given A, is there P s.t. M=(A,P) is truthful? In general, NO! new algorithms**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.**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**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]**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**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**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**(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.**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.**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.**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**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.**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.**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.**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.**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.**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**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)**[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)