Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
Bounded budget connection (BBC) games or how to make friends and influence people, on a budget
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
The Price of Anarchy of a Network Creation Game with Exponential Payoff
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Social and Economic Networks
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
The max-distance network creation game on general host graphs
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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A network creation game simulates a decentralized and non-cooperative building of a communication network. Informally, there are n players sitting on the network nodes, which attempt to establish a reciprocal communication by activating, incurring a certain cost, any of their incident links. The goal of each player is to have all the other nodes as close as possible in the resulting network, while buying as few links as possible. According to this intuition, any model of the game must then appropriately address a balance between these two conflicting objectives. Motivated by the fact that a player might have a strong requirement about its centrality in the network, in this paper we introduce a new setting in which if a player maintains its (either maximum or average) distance to the other nodes within a given bound, then its cost is simply equal to the number of activated edges, otherwise its cost is unbounded. We study the problem of understanding the structure of pure Nash equilibria of the resulting games, that we call MaxBD and SumBD, respectively. For both games, we show that when distance bounds associated with players are non-uniform, then equilibria can be arbitrarily bad. On the other hand, for MaxBD, we show that when nodes have a uniform bound R on the maximum distance, then the Price of Anarchy (PoA) is lower and upper bounded by 2 and $O\left(n^{\frac{1}{\lfloor\log_3 R\rfloor+1}}\right)$ for R≥3 (i.e., the PoA is constant as soon as R is Ω(nε), for some ε0), while for the interesting case R=2, we are able to prove that the PoA is $\Omega(\sqrt{n})$ and $O(\sqrt{n \log n} )$. For the uniform SumBD we obtain similar (asymptotically) results, and moreover we show that the PoA becomes constant as soon as the bound on the average distance is $2^{\omega\big({\sqrt{\log n}}\big)}$.