Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Non-cooperative multicast and facility location games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Algorithmic Game Theory
Graphical congestion games with linear latencies
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Selfish routing with oblivious users
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Multicast transmissions in non-cooperative networks with a limited number of selfish moves
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
The Impact of Social Ignorance on Weighted Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Local and global price of anarchy of graphical games
Theoretical Computer Science
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In non-cooperative games played on highly decentralized networks the assumption that each player knows the strategy adopted by any other player may be too optimistic or even unfeasible. In such situations, the set of players of which each player knows the chosen strategy can be modeled by means of a social knowledge graph in which nodes represent players and there is an edge from ito jif iknows j. Following the framework introduced in [3], we study the impact of social knowledge graphs on the fundamental multicast cost sharing game in which all the players wants to receive the same communication from a given source. Such a game in the classical complete information case is known to be highly inefficient, since its price of anarchy can be as high as the total number of players ρ. We first show that, under our incomplete information setting, pure Nash equilibria always exist only if the social knowledge graph is directed acyclic (DAG). We then prove that the price of stability of any DAG is at least $\frac 1 2\log\rho$ and provide a DAG lowering the classical price of anarchy to a value between $\frac 1 2\log\rho$ and log2ρ. If specific instances of the game are concerned, that is if the social knowledge graph can be selected as a function of the instance, we show that the price of stability is at least $\frac{4\rho}{\rho+3}$, and that the same bound holds also for the price of anarchy of any social knowledge graph (not only DAGs). Moreover, we provide a nearly matching upper bound by proving that, for any fixed instance, there always exists a DAG yielding a price of anarchy less than 4. Our results open a new window on how the performances of non-cooperative systems may benefit from the lack of total knowledge among players and can be considered, in some sense, as another evidence of the famous Braess' paradox.