Download - CRESCCO Project IST-2001-33135
![Page 1: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/1.jpg)
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”
![Page 2: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/2.jpg)
PROVIDERS
DIFFERENT SOCIO-ECONOMIC ENTITIES DIFFERENT GOALS
INTERNET
SELFISH ENTITIES THAT COOPERATE AUTONOMOUS SYSTEMS
UNIVERSITIES
INTERNET
PRIVATECOMPANIES
![Page 3: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/3.jpg)
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
![Page 4: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/4.jpg)
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
![Page 5: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/5.jpg)
Mathematical Tools
Theory of Computing
Microeconomics and Game Theory
Computational complexityDesign and Analysis of Algorithms
Nash equilibria
Mechanism design
![Page 6: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/6.jpg)
Research Progress
Nash equilibria for routing problems:
Efficient mechanism design
Feasibility, optimality of the solution;
Existence, worst case, complexity
![Page 7: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/7.jpg)
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
![Page 8: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/8.jpg)
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
![Page 9: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/9.jpg)
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.
![Page 10: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/10.jpg)
Nash equilibria for routing problems
…
1 1 1 Expected MAX LOAD: 1
1/nExpected MAX LOAD:
Θ(ln n/ln ln n)
![Page 11: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/11.jpg)
…
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]
![Page 12: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/12.jpg)
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]
![Page 13: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/13.jpg)
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
![Page 14: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/14.jpg)
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
![Page 15: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/15.jpg)
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
![Page 16: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/16.jpg)
Truthful Mechanisms
Truth-telling is always the best strategy:
for any agent i and for any false declaration bi
ui(si) ≥ ui(bi)
![Page 17: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/17.jpg)
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
![Page 18: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/18.jpg)
Mechanism Design
• Extensions of VCG to non-utilitarian problems– P. Penna, G. Proietti, R. Wattenhofer and P.
Widmayer. Truthful mechanisms for consistent problems. Submitted.
![Page 19: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/19.jpg)
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]
![Page 20: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/20.jpg)
Truthful Mechanisms
Existing approximation algorithms are not monotone!!
[Archer and Tardos 2001]
We need new approximation algorithms
![Page 21: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/21.jpg)
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]
![Page 22: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/22.jpg)
Research Progress
PTAS= OPT(t1,t2,…,th) + GREEDY(th+1,…,tn)
Not monotone
New monotone GREEDY algorithm
![Page 23: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/23.jpg)
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
![Page 24: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/24.jpg)
Thank You
![Page 25: CRESCCO Project IST-2001-33135](https://reader035.vdocument.in/reader035/viewer/2022070404/56813afb550346895da38b2f/html5/thumbnails/25.jpg)
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”