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.