Game Theory & Distributed Systems...Game Theory & Distributed Systems Akaki Mamageishvili Paolo...
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Game Theory & Distributed Systems Akaki Mamageishvili Paolo Penna Institute of Theoretical Computer Science, ETH Z ¨ urich 1 Game Theory Altruism Selfish (Rational Behavior) ⇒ 2 Why should we care? open anarchic The Internet self-organized ? Play on a Network: ? Build a Network: Share Resources: 3 Tools - + + - 1 2 0 0 Nash Equilibria Potential 4 Selfish ⇒ Inefficient? worst Nash Opt best Nash Opt Nash Price of Anarchy = Price of Stability = 5 Dynamics Nash • Noise (mistakes) • Synchronization • Time 6 Network Creation Games Player cost = sum of shortest distances + (#edges) · a 0 2003 2006 2010 2013 2008 2006 2003 2 n 1/2 n 1-e 65n 273n 12nlogn n 2 PoA=O(1)? a Conjecture: PoA = O(1) 7 Network Design Games Share the costs ··· 1 n PoA = n 2 1 POPoA = 4/3 2 POPoA = 2 PoA too pessimistic ⇒ Potential Opt PoA (PoS and dynamics) 8 Selfish Load balancing POPoA at least 7/6 k (5k-1)/2 k 2k-1 k+1 2k-2 2k-1 k k k k k+1 2k-1 2k-1 k+1 Min Potential Social OPT Current Collaborations and References Mat ´ us Mihal ´ ak, Maastricht University Laurent Viennot, Univ. Paris Diderot Auletta – Ferraioli – Pasquale – Penna – Persiano: Logit Dynamics with Concurrent Updates for Local Interaction Potential Games. Algorithmica 2015. Auletta – Ferraioli – Pasquale – Penna – Persiano: Convergence to Equilibrium of Logit Dynamics for Strategic Games. Algorithmica 2015. Ferraioli – Penna: Imperfect Best-Response Mechanisms, Theory of Computing Systems 2015. Mamageishvili – Mihal ´ ak – M ¨ uller: Tree Nash Equilibria in the Network Creation Game. Internet Mathematics 2015. Mamageishvili – Mihal ´ ak – Montemezzani: An H(n/2) Upper Bound on the Price of Stability of Undirected Network Design Games. MFCS 2014. Mamageishvili – Mihal ´ ak: Multicast Network Design Game on a Ring. COCOA 2015. Mamageishvili – Penna: A Lower Bound on Potential Optimal Price of Anarchy in Load Balancing. In preparation. Penna: The price of anarchy and stability in general noisy best-response dynamics. Submitted. Penna – Viennot: Lazy and asynchronous best-response dynamics on networks. In preparation.
Transcript of Game Theory & Distributed Systems...Game Theory & Distributed Systems Akaki Mamageishvili Paolo...
Game Theory & Distributed Systems
Akaki Mamageishvili Paolo PennaInstitute of Theoretical Computer Science, ETH Zurich
1 Game Theory
Altruism Selfish(Rational Behavior)
⇒
2 Why should we care?
open
anarchic
The Internet
self-organized
? Play on a Network:
?
Build a Network:
Share Resources:
3 Tools
−
+
+−
1
20
0
Nash Equilibria Potential
4 Selfish⇒ Inefficient?worst Nash
Opt
best NashOpt
Nash
Price of Anarchy =
Price of Stability =
5 Dynamics
Nash
• Noise (mistakes)
• Synchronization
• Time
6 Network Creation Games
Player cost = sum of shortest distances +(#edges) · a
0
2003200620102013200820062003
2 n1/2 n1-e 65n 273n 12nlogn n2PoA=O(1)?
a
Conjecture: PoA = O(1)
7 Network Design Games
Share the costs· · · 1
n
PoA = n
2
1
POPoA = 4/3
2
POPoA = 2
PoA too pessimistic⇒ Potential Opt PoA (PoS and dynamics)
8 Selfish Load balancing
POPoA at least 7/6
k
(5k-1)/2
k
2k-1
k+1
2k-2
2k-1
k
k
k
k
k+1
2k-1
2k-1
k+1
Min Potential Social OPT
Current Collaborations and References
Matus Mihalak, Maastricht University
Laurent Viennot, Univ. Paris Diderot
Auletta – Ferraioli – Pasquale – Penna – Persiano: Logit Dynamics with Concurrent Updates for Local Interaction Potential Games.Algorithmica 2015.Auletta – Ferraioli – Pasquale – Penna – Persiano: Convergence to Equilibrium of Logit Dynamics for Strategic Games. Algorithmica 2015.Ferraioli – Penna: Imperfect Best-Response Mechanisms, Theory of Computing Systems 2015.Mamageishvili – Mihalak – Muller: Tree Nash Equilibria in the Network Creation Game. Internet Mathematics 2015.Mamageishvili – Mihalak – Montemezzani: An H(n/2) Upper Bound on the Price of Stability of Undirected Network Design Games. MFCS2014.Mamageishvili – Mihalak: Multicast Network Design Game on a Ring. COCOA 2015.Mamageishvili – Penna: A Lower Bound on Potential Optimal Price of Anarchy in Load Balancing. In preparation.Penna: The price of anarchy and stability in general noisy best-response dynamics. Submitted.Penna – Viennot: Lazy and asynchronous best-response dynamics on networks. In preparation.
