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CRESCCO ProjectIST-2001-33135
Work Package 2
Algorithms for Selfish AgentsAlgorithms for Selfish Agents
V. Auletta, P. Penna and G. PersianoV. Auletta, P. Penna and G. Persiano
Università di SalernoUniversità di [email protected]@unisa.it
Project funded by the Future and Emerging Technologies arm of Project funded by the Future and Emerging Technologies arm of the IST Programme – FET Proactive initiative “Global the IST Programme – FET Proactive initiative “Global Computing”Computing”
PROVIDERS
DIFFERENT SOCIO-ECONOMIC ENTITIES DIFFERENT GOALS
INTERNET
SELFISH ENTITIES THAT COOPERATE AUTONOMOUS SYSTEMS
UNIVERSITIES
INTERNET
PRIVATECOMPANIES
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 Goals1. 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 controlWhat is the price of anarchy?
Design a new “TCP protocol” robust wrt selfish users
Mathematical Tools
Theory of Computing
Microeconomics and Game Theory
Computational complexityDesign and Analysis of Algorithms
Nash equilibria
Mechanism design
Research Progress
Nash equilibria for routing problems:
Efficient mechanism design
Feasibility, optimality of the solution;
Existence, worst case, complexity
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
a b
Prisoner’s dilemma
Nash equilibria for routing problems
source destination
•m links with different speeds•Unsplittable traffic t1, t2 ,…, tn
•We look at the network congestion (max load)
•Selfish users choose the best path for their own traffic
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.
Nash equilibria for routing problems
…
1 1 1 Expected MAX LOAD: 1
1/nExpected MAX LOAD:
Θ(ln n/ln ln n)
…
1 2n
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]
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]
Mechanism design
•m links with different speeds s1, s2,…,sm
•Unsplittable traffic t1, t2 ,…, tn
•We look at the network congestion (makespan)
•Selfish users owns the links and privately know their speeds
source destination
Mechanism design
Task scheduling on related machines:
• m machines of with speeds s1 s2,…,sm
• n jobs of weight t1,t2,…,tn
• Each machine is owned by a selfish agent, and agents should reveal the speed of their own machine to the system
Mechanism design
•A machine i of speed si receiving load li incurs in a cost of li/si
•We pay the agents to provide an incentive in revealing the true speed
•Agents want to maximize their utility ui := paymenti – costi
Truthful Mechanisms
Truth-telling is always the best strategy:
for any agent i and for any false declaration bi
ui(si) ≥ ui(bi)
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
Mechanism Design
• Extensions of VCG to non-utilitarian problems– P. Penna, G. Proietti, R. Wattenhofer and P.
Widmayer. Truthful mechanisms for consistent problems. Submitted.
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]
Truthful Mechanisms
Existing approximation algorithms are not monotone!!
[Archer and Tardos 2001]
We need new approximation algorithms
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]
Research Progress
PTAS= OPT(t1,t2,…,th) + GREEDY(th+1,…,tn)
Not monotone
New monotone GREEDY algorithm
Future Plans1. 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
Thank You
CRESCCO ProjectIST-2001-33135
Work Package 2
Algorithms for Selfish AgentsAlgorithms for Selfish Agents
G. PersianoG. Persiano
Università di SalernoUniversità di [email protected]@unisa.it
Project funded by the Future and Emerging Technologies arm of Project funded by the Future and Emerging Technologies arm of the IST Programme – FET Proactive initiative “Global the IST Programme – FET Proactive initiative “Global Computing”Computing”
