1. CRESCCO Project IST-2001-33135 Work Package 2 Algorithms for Selfish Agents V. Auletta, P. Penna and G. Persiano Università di Salerno pino.persiano@unisa.it Project funded by the Future and Emerging Technologies arm of the IST Programme – FET Proactive initiative “Global Computing”

2. PROVIDERS DIFFERENT SOCIO-ECONOMIC ENTITIES DIFFERENT GOALS INTERNET SELFISH ENTITIES THAT COOPERATE AUTONOMOUS SYSTEMS UNIVERSITIES INTERNET 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 protocol” robust wrt selfish users

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

6. Research Progress Nash equilibria for routing problems : Efficient mechanism design Feasibility, optimality of the solution ; Existence, worst case, complexity

7. Nash equilibria When no selfish agent has an incentive in changing his/her strategy: (3,3)(0,5) (5,0)(1,1) Player 1 Player 2 No other strategy improves the current payoff! a b ab Prisoner’s dilemma

8. Nash equilibria for routing problems sourcedestination m links with different speeds Unsplittable traffic t 1, t 2,…, t n We look at the network congestion (max load) Selfish users choose the best path for their own traffic

9. Nash equilibria for routing problems 1.D. Fotakis, S. Kontogiannis, E. Koutsoupias, M. Mavronicolas, and P.Spirakis. “The Structure and Complexity of Nash Equilibria for a Selfish Routing Game.” Proc. of the Int. Colloquium on Automata, Languages and Programming (ICALP), 2002. 2.E. Koutsoupias, M. Mavronicolas and P. Spirakis, “Approximate Equilibria and Ball Fusion.” Proc. of the 9th Int. Colloquium on Structural Information and Communication Complexity, June 2002. 3.A. Ferrante and M. Parente. “Existence of Nash Equilibria in Selfish Routing problems.” Technical Report, Università di Salerno, 2002.

10. Nash equilibria for routing problems … 111 Expected MAX LOAD: 1 1/n Expected MAX LOAD: Θ(ln n/ln ln n)

11. … 1 2 n SUPPORT Characterizing Nash equilibria: -- Existence for a given support set [3] … 1 2 m Computing Nash equilibria : -- For a given support, the best, the worst, any [1,3] Approximate Nash equilibria : -- users change strategy only if a sufficiently better one exists [2]

12. Achieved Results Characterizations of Nash equilibria: -- with a given support [3] Computing Nash equilibria: -- the best and the worst are NP-hard [1] -- any generalized fully mixed in P [1] -- is #P-complete [1], Computing the cost of a Nash equilibrium: -- but can be well approximated [1]

13. Mechanism design 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) Selfish users owns the links and privately know their speeds sourcedestination

14. Mechanism design Task scheduling on related machines: m machines of with speeds s 1 s 2,…,s m n jobs of weight t 1,t 2,…,t n Each machine is owned by a selfish agent, and agents should reveal the speed of their own machine to the system

15. Mechanism design A machine i of speed s i receiving load l i incurs in a cost of l i /s i We pay the agents to provide an incentive in revealing the true speed Agents want to maximize their utility u i := payment i – cost i

16. Truthful Mechanisms Truth-telling is always the best strategy: for any agent i and for any false declaration b i u i (s i ) ≥ u i (b i )

17. Mechanism design Classical problem from microeconomics –Vickrey Clarke Groves (VCG) mechanisms Unsuitable for our settings –VCG only applies to utilitarian problems minimize sum of costs instead we minimize max of costs –Requires solving optimally hard combinatorial problem

18. Mechanism Design Extensions of VCG to non-utilitarian problems –P. Penna, G. Proietti, R. Wattenhofer and P. Widmayer. Truthful mechanisms for consistent problems. Submitted.

19. Mechanism design Scheduling related machines Truthful mechanisms must allocate jobs monotonically: an agents 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 2001]

20. Truthful Mechanisms Existing approximation algorithms are not monotone!! [Archer and Tardos 2001] We need new approximation algorithms

21. Research Progress 1.V. Auletta, R. De Prisco, P. Persiano, and P. Penna. “Deterministic Truthful Approximation Mechanisms for Scheduling Related Machines”. Manuscript in preparation. Very close to a polynomial-time (2+ε)-approximation truthful mechanism. [3-approximation mechanism truthful in expectation only, Archer et al. 01]

22. Research Progress PTAS= OPT(t 1,t 2,…,t h ) + GREEDY(t h+1,…,t n ) Not monotone New monotone GREEDY algorithm

23. Future Plans 1. A deeper understanding of basic principles in the Internet 2. Methodology to develop good solutions 3. New concepts, new mathematical tools and new algorithmic techniques 4. Cross fertilization between TCS, micro- economics and game theory

24. Thank You

25. CRESCCO Project IST-2001-33135 Work Package 2 Algorithms for Selfish Agents G. Persiano Università di Salerno pino.persiano@unisa.it Project funded by the Future and Emerging Technologies arm of the IST Programme – FET Proactive initiative “Global Computing”