Corpus ID: 30363654

# Network Creation Games: Structure vs Anarchy

@article{lvarez2017NetworkCG,
title={Network Creation Games: Structure vs Anarchy},
author={C. {\A}lvarez and A. Messegu{\'e}},
journal={ArXiv},
year={2017},
volume={abs/1706.09132}
}`
• Published 2017
• Computer Science, Mathematics
• ArXiv
We study Nash equilibria and the price of anarchy in the classical model of Network Creation Games introduced by Fabrikant et al. In this model every agent (node) buys links at a prefixed price $\alpha>0$ in order to get connected to the network formed by all the $n$ agents. In this setting, the reformulated tree conjecture states that for $\alpha > n$, every Nash equilibrium network is a tree. Since it was shown that the price of anarchy for trees is constant, if the tree conjecture were true… Expand

#### Tables and Topics from this paper

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#### References

SHOWING 1-10 OF 10 REFERENCES
The price of anarchy in network creation games
• Mathematics, Computer Science
• PODC '07
• 2007
A variant of both network creation games, in which each player desires to minimize α times the cost of its created links plus the maximum distance to the other players, is introduced, and the first aconstant upper bound for general α is proved, namely 2<sup><i>O</i></sup>(√lg <i>n</i>). Expand
On nash equilibria for a network creation game
• Mathematics
• SODA 2006
• 2006
We study a network creation game recently proposed by Fabrikant, Luthra, Maneva, Papadimitriou and Shenker. In this game, each player (vertex) can create links (edges) to other players at a cost of αExpand
Tree Nash Equilibria in the Network Creation Game
• Mathematics, Computer Science
• WAW
• 2013
It is shown that if there is a cycle in a Nash equilibrium, then {\alpha} = 41n, then every such Nash equilibrium is a tree, and that this is true for every {\alpha] >= 65n. Expand
The Price of Anarchy in Network Creation Games Is (Mostly) Constant
• Mathematics, Computer Science
• Theory of Computing Systems
• 2013
The two main results of the paper show that for α>273⋅n all equilibria in SumGame are trees and thus the price of anarchy is constant, and that forα>129 all equibria in MaxGame are Trees and the price is constant. Expand
Basic Network Creation Games
• Computer Science, Mathematics
• SIAM J. Discret. Math.
• 2013
This work studies a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes by swapping one incident edge at a time, and proves an upper bound of 2, a lower bound of 3, and a tight bound of exactly 2 for trees. Expand
On a network creation game
• Computer Science
• PODC '03
• 2003
The Nash equilibria of this game are studied, and results suggesting that the "price of anarchy" in this context (the relative cost of the lack of coordination) may be modest are proved. Expand
Distance-Uniform Graphs with Large Diameter
• Mathematics, Computer Science
• SIAM J. Discret. Math.
• 2019
There exist $\epsilon$-distance-uniform graphs with critical distance 2-Omega, disproving a conjecture of Alon et al. that $d$ can be at most logarithmic in $n$. Expand
Correction: Basic Network Creation Games
• Mathematics, Computer Science
• SIAM J. Discret. Math.
• 2014
There is a diameter-3 graph in which replacing any edge of the graph with another graph for any vertex does not decrease the total sum of distances from v to all other nodes (a property called sum equilibrium). Expand
rection : Basic network creation games
• SIAM J . Discrete Math .
• 2014
On the price of anarchy of a network creation game
• Class final project. December,
• 2003