When ignorance helps: Graphical multicast cost sharing games
Theoretical Computer Science
Approximate strong equilibrium in job scheduling games
Journal of Artificial Intelligence Research
Non-cooperative facility location and covering games
Theoretical Computer Science
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
On approximate nash equilibria in network design
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Nash equilibria with minimum potential in undirected broadcast games
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Theoretical Computer Science
Minimizing rosenthal potential in multicast games
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
Approximate strong equilibria in job scheduling games with two uniformly related machines
Discrete Applied Mathematics
Price of stability in polynomial congestion games
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Hi-index | 0.01 |
We study network design games where $n$ self-interested agents have to form a network by purchasing links from a given set of edges. We consider Shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge. It is well known that the price of anarchy of these games is as high as $n$. Another line of research has focused on evaluating the price of stability, i.e., the cost of the best Nash equilibrium relative to the social optimum. In this paper we investigate to which extent coordination among agents can improve the quality of solutions. We resort to the concept of strong Nash equilibria, which were introduced by Aumann and are resilient to deviations by coalitions of agents. We analyze the price of anarchy of strong Nash equilibria and develop lower and upper bounds for unweighted and weighted games in both directed and undirected graphs. These bounds are tight or nearly tight for many scenarios. It shows that, by using coordination, the price of anarchy drops from linear to logarithmic bounds. We complement these results by also proving the first superconstant lower bound on the price of stability of standard equilibria (without coordination) in undirected graphs. More specifically, we show a lower bound of $\Omega(\log W/\log\log W)$ for weighted games, where $W$ is the total weight of all the agents. This almost matches the known upper bound of $O(\log W)$. Our results imply that, for most settings, the worst-case performance ratios of strong coordinated equilibria are essentially always as good as the performance ratios of the best equilibria achievable without coordination. These settings include unweighted games in directed graphs as well as weighted games in both directed and undirected graphs.