# 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} }

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

#### 12 Citations

On the Constant Price of Anarchy Conjecture

- Mathematics, Computer Science
- ArXiv
- 2018

It is proved that the price of anarchy is constant for $\alpha > n(1+\epsilon)$ by showing that every equilibrium of diameter greater than some prefixed constant is a tree. Expand

On the Price of Anarchy for High-Price Links

- Computer Science, Mathematics
- WINE
- 2019

It is proved that for any small $\epsilon>0$, the price of anarchy is constant for $\alpha > n(1+\epsilons)$ by showing that any biconnected component of any non-trivial Nash equilibrium, if it exists, has at most a constant number of nodes. Expand

On the Tree Conjecture for the Network Creation Game

- Mathematics, Computer Science
- STACS
- 2018

A novel technique for analyzing stable networks for high edge-price $\alpha$ is introduced and it is shown that for $\alpha > 4n-13$ all equilibrium networks must be trees, which implies a constant price of anarchy for this range of $\alpha$. Expand

On the Tree Conjecture for the Network Creation Game

- Mathematics, Computer Science
- Theory of Computing Systems
- 2019

A novel technique for analyzing stable networks for high edge-price α is introduced and it is shown that for α > 4 n − 13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of α . Expand

New Insights into the Structure of Equilibria for the Network Creation Game

- Computer Science
- ArXiv
- 2020

It is proved that ne graphs satisfy very restrictive topological properties generalising some properties proved in the literature and providing new insights that might help settling the conjecture that the PoA is constant for the remaining range of α. Expand

On Tree Equilibria in Max-Distance Network Creation Games

- Computer Science
- ArXiv
- 2021

The main result shows that for α ≥ 23 all equilibrium graphs in the max-distance network creation game must be trees, while the best bound in previous work is α > 129, and improves the constant upper bound on the price of anarchy to 3 for tree equilibria. Expand

Efficiency and Stability in Euclidean Network Design

- Computer Science
- SPAA
- 2021

A simple O(n^2)-time algorithm that computes a (β,β)-network with low β for any given set of points, which achieves a low constant~β on integer grid point sets or random point sets and a generalization to instances with arbitrary, even non-metric, edge lengths. Expand

Network Creation Games with Traceroute-Based Strategies

- Computer Science
- Algorithms
- 2021

Network creation games have been extensively used as mathematical models to capture the key aspects of the decentralized process that leads to the formation of interconnected communication networks… Expand

Geometric Network Creation Games

- Computer Science
- SPAA
- 2019

Low-cost equilibria of the model proposed can be seen as the game-theoretic analogue of a variant of the classical Network Design Problem and correspond to decentralized and stable approximations of the optimum network design. Expand

Distance-Uniform Graphs with Large Diameter

- Mathematics, Computer Science
- SIAM J. Discret. Math.
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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

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