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
Algorithmic Game Theory
The Price of Anarchy of a Network Creation Game with Exponential Payoff
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
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
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
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
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We initiate the study of game dynamics in the Sum Basic Network Creation Game, which was recently introduced by Alon et al.[SPAA'10]. In this game players are associated to vertices in a graph and are allowed to "swap" edges, that is to remove an incident edge and insert a new incident edge. By performing such moves, every player tries to minimize her connection cost, which is the sum of distances to all other vertices. When played on a tree, we prove that this game admits an ordinal potential function, which implies guaranteed convergence to a pure Nash Equilibrium. We show a cubic upper bound on the number of steps needed for any improving response dynamic to converge to a stable tree and propose and analyse a best response dynamic, where the players having the highest cost are allowed to move. For this dynamic we show an almost tight linear upper bound for the convergence speed. Furthermore, we contrast these positive results by showing that, when played on general graphs, this game allows best response cycles. This implies that there cannot exist an ordinal potential function and that fundamentally different techniques are required for analysing this case. For computing a best response we show a similar contrast: On the one hand we give a linear-time algorithm for computing a best response on trees even if players are allowed to swap multiple edges at a time. On the other hand we prove that this task is NP-hard even on simple general graphs, if more than one edge can be swapped at a time. The latter addresses a proposal by Alon et al..