Proceedings of the twenty-second annual symposium on Principles of distributed 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
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The price of anarchy in network creation games
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
The price of anarchy in network creation games is (mostly) constant
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On a bounded budget network creation game
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
On dynamics in basic network creation games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Asymmetric swap-equilibrium: a unifying equilibrium concept for network creation games
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by [2], in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural characterization of equilibrium graphs. We show how to use this characterization in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest k-vicinity (defined as the the set of vertices within distance k from a vertex), for any k≥1 and in terms of the number of edges, thus settling positively a conjecture of [2] in the cases of graphs of large k-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough. Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an induced star. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.