Algorithms, Games, and the Internet
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Proceedings of the twenty-second annual symposium on Principles of distributed computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth 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
The price of anarchy in network creation games
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Network formation games with local coalitions
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the impact of combinatorial structure on congestion games
Journal of the ACM (JACM)
Minimizing Movement in Mobile Facility Location Problems
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
ACM Transactions on Algorithms (TALG)
The isolation game: A game of distances
Theoretical Computer Science
Nash Equilibria for Voronoi Games on Transitive Graphs
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Nash equilibria in Voronoi games on graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
The price of anarchy in cooperative network creation games
ACM SIGecom Exchanges
On the performances of Nash equilibria in isolation games
Journal of Combinatorial Optimization
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We introduce a new class of network creation games, called mobile network creation games, modelling the spontaneous creation of communication networks by the distributed and uncoordinated interaction of k selfish mobile devices. Each device is owned by a player able to select a node in an underlying positions graph so as to minimize a cost function taking into account two components: the distance from her home position, and the number of players she is not connected to, with the connectivity costs being prevailing, i.e., the Nash Equilibria are stable solution states in which communication is possible among all the players. We show that the game always admits a Pure Nash equilibrium, even if the convergence after a finite number of improving movements is guaranteed only when players perform their best possible moves. More precisely, if initial positions are arbitrary, that is not necessarily coinciding with the home ones, an order of kD best moves is necessary (and sufficient) to reach an equilibrium, where D is the diameter of the positions graph. As for the Nash equilibria performances, we first prove that the price of stability is 1 (i.e. an optimal solution is also a Nash equilibrium). Moreover, we show that the lack of centralized control of mobile devices is a major issue in terms of final performance guaranteed. Namely, the price of anarchy is Θ(kD). Nevertheless, we are able to prove that if players start at their home positions, in Θ(k min {k2,D}) best moves they reach an equilibrium approximating the optimal solution by a factor of Θ(k min {k,D}).