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.