Proceedings of the twenty-second annual symposium on Principles of distributed computing
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
Social and Economic Networks
Proceedings of the twenty-second 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
Basic network creation games with communication interests
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Bounded-Distance network creation games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Greedy selfish network creation
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
The max-distance network creation game on general host graphs
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
On dynamics in selfish network creation
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
On the structure of equilibria in basic network formation
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
On Nash Equilibria for a Network Creation Game
ACM Transactions on Economics and Computation
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We study the price of anarchy and the structure of equilibria in network creation games. A network creation game (first defined and studied by Fabrikant et al. [4]) is played by n players {1, 2, . . . , n}, each identified with a vertex of a graph (network), where the strategy of player i, i = 1, . . . , n, is to build some edges adjacent to i. The cost of building an edge is α 0, a fixed parameter of the game. The goal of every player is to minimize its creation cost plus its usage cost. The creation cost of player i is α times the number of built edges. In the SUMGAME (the original variant of Fabrikant et al. [4]) the usage cost of player i is the sum of distances from i to every node of the resulting graph. In the MAXGAME (variant defined and studied by Demaine et al. [3]) the usage cost is the eccentricity of i in the resulting graph of the game. In this paper we improve previously known bounds on the price of anarchy of the game (of both variants) for various ranges of α, and give new insights into the structure of equilibria for various values of α. The two main results of the paper show that for α 273 ċ n all equilibria in SUMGAME are trees and thus the price of anarchy is constant, and that for α 129 all equilibria in MAXGAME are trees and the price of anarchy is constant. For SUMGAME this (almost) answers one of the basic open problems in the field - is price of anarchy of the network creation game constant for all values of α? - in an affirmative way, up to a tiny range of α.