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On the Tree Conjecture for the Network Creation Game [article]

Davide Bilò, Pascal Lenzner
2018 arXiv   pre-print
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al.  ...  The most famous conjectures state that the price of anarchy is constant for all α and that for α≥ n all equilibrium networks are trees.  ...  On nash equilibria for a network creation game. ACM TEAC, 2(1):2, 2014.  ... 
arXiv:1710.01782v2 fatcat:mdjlal5bszawlebhxgzxag7kte

On the Tree Conjecture for the Network Creation Game

Davide Bilò, Pascal Lenzner
2019 Theory of Computing Systems  
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al.  ...  The most famous conjectures state that the price of anarchy is constant for all α and that for α ≥ n all equilibrium networks are trees.  ...  S TA C S 2 0 1 8 14:12 On the Tree Conjecture for the Network Creation Game Improved Price of Anarchy for Stable Tree Networks In this section we show a better bound on the PoA of stable tree networks  ... 
doi:10.1007/s00224-019-09945-9 fatcat:fbsdnlq6q5ghfo57exix5dsdla

On Tree Equilibria in Max-Distance Network Creation Games [article]

Qian Wang
2022 arXiv   pre-print
Our work brings new insights into the structure of Nash equilibria and takes one step forward in settling the so-called tree conjecture in the max-distance network creation game.  ...  We also improve the constant upper bound on the price of anarchy to 3 for tree equilibria.  ...  For the max-distance network creation game, there is no work formally stating an adapted tree conjecture.  ... 
arXiv:2106.15961v3 fatcat:5dy32nci4vgtxivrsesub437ga

On Strong Equilibria and Improvement Dynamics in Network Creation Games [chapter]

Tomasz Janus, Bart de Keijzer
2017 Lecture Notes in Computer Science  
We study strong equilibria in network creation games.  ...  For α > 2, Andelman et al. [4] prove that a star graph in which every leaf buys one edge to the center node is a strong equilibrium, and conjecture that in fact any star is a strong equilibrium.  ...  Apt for many useful suggestions concerning the results and organization of this paper. We thank Mateusz Skomra for many helpful discussions and feedback.  ... 
doi:10.1007/978-3-319-71924-5_12 fatcat:pmovsnb4lndjnanq54p33fonr4

Basic network creation games

Noga Alon, Erik D. Demaine, MohammadTaghi Hajiaghayi, Tom Leighton
2010 Proceedings of the 22nd ACM symposium on Parallelism in algorithms and architectures - SPAA '10  
Our perspective enables simpler and more general proofs that get at the heart of network creation games.  ...  We study 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.  ...  Indeed, we show that results for our basic network creation game carry over directly to other network creation games for all values of the parameter α.  ... 
doi:10.1145/1810479.1810502 dblp:conf/spaa/AlonDHL10 fatcat:dqjbvah4efcqldrs37gfddmod4

Basic Network Creation Games

Noga Alon, Erik D. Demaine, Mohammad T. Hajiaghayi, Tom Leighton
2013 SIAM Journal on Discrete Mathematics  
Our perspective enables simpler and more general proofs that get at the heart of network creation games.  ...  We study 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.  ...  Indeed, we show that results for our basic network creation game carry over directly to other network creation games for all values of the parameter α.  ... 
doi:10.1137/090771478 fatcat:q3p63wqjgve3noj6tr7vvchoce

Tree Nash Equilibria in the Network Creation Game [chapter]

Akaki Mamageishvili, Matúš Mihalák, Dominik Müller
2013 Lecture Notes in Computer Science  
In the network creation game with n vertices, every vertex (a player) buys a set of adjacent edges, each at a fixed amount α > 0.  ...  It has been conjectured that for α ≥ n, every Nash equilibrium is a tree, and has been confirmed for every α ≥ 273 · n. We improve upon this bound and show that this is true for every α ≥ 65 · n.  ...  This work has been partially supported by the Swiss National Science Foundation (SNF) under the grant number 200021 143323/1.  ... 
doi:10.1007/978-3-319-03536-9_10 fatcat:vuvyrihb6bgbpcdjjxsuwouu6a

Tree Nash Equilibria in the Network Creation Game [article]

Akaki Mamageishvili, Matus Mihalak, Dominik Muller
2013 arXiv   pre-print
In the network creation game with n vertices, every vertex (a player) buys a set of adjacent edges, each at a fixed amount α > 0.  ...  It has been conjectured that for α >= n, every Nash equilibrium is a tree, and has been confirmed for every α >= 273n. We improve upon this bound and show that this is true for every α >= 65n.  ...  This work has been partially supported by the Swiss National Science Foundation (SNF) under the grant number 200021 143323/1.  ... 
arXiv:1310.8245v1 fatcat:j55iyktawrbrlnx6neikxeoaqa

On Strong Equilibria and Improvement Dynamics in Network Creation Games [article]

Tomasz Janus, Bart de Keijzer
2018 arXiv   pre-print
We study strong equilibria in network creation games.  ...  For α > 2, Andelman et al. (2009) prove that a star graph in which every leaf buys one edge to the center node is a strong equilibrium, and conjecture that in fact any star is a strong equilibrium.  ...  Apt for useful suggestions concerning the organization of this paper and some of its topics. Moreover, we thank Mateusz Skomra for various helpful discussions and feedback.  ... 
arXiv:1711.03466v2 fatcat:qdcyy3mktfhmrf6vxbngmrii5i

On a network creation game

Alex Fabrikant, Ankur Luthra, Elitza Maneva, Christos H. Papadimitriou, Scott Shenker
2003 Proceedings of the twenty-second annual symposium on Principles of distributed computing - PODC '03  
We introduce a novel game that models the creation of Internet-like networks by selfish node-agents without central design or coordination.  ...  Nodes pay for the links that they establish, and benefit from short paths to all destinations.  ...  a network creation game in which node costs reflect Vickrey payments --a proposal from [3] .  ... 
doi:10.1145/872035.872088 dblp:conf/podc/FabrikantLMPS03 fatcat:pgraamxlljc4njskjrg5cln3gy

Tree Nash Equilibria in the Network Creation Game

Akaki Mamageishvili, Matúš Mihalák, Dominik Müller
2015 Internet Mathematics  
It has been conjectured that for α ≥ n, every Nash equilibrium of this game is a tree and has been confirmed for every α ≥ 273 • n.  ...  In the network creation game with n vertices, every vertex (player) creates an (adjacent) edge and decides to which other vertices the created edge should go.  ...  CONCLUSIONS In this article, we have described steps toward resolving the conjecture "Every Nash equilibrium of a Network Creation Game with α ≥ n is a tree."  ... 
doi:10.1080/15427951.2015.1016248 fatcat:hkp7uehcbvamdaba34sysinhpa

An Improved Bound for the Tree Conjecture in Network Creation Games [article]

Jack Dippel, Adrian Vetta
2021 arXiv   pre-print
A long-standing conjecture states that if α≥ n then every Nash equilibrium in the game is a spanning tree. We prove the conjecture holds for any α>3n-3.  ...  We study Nash equilibria in the network creation game of Fabrikant et al.[10].  ...  They then conjectured that, for α greater than some constant, every Nash equilibrium is a spanning tree. This was the original tree conjecture for network creation games.  ... 
arXiv:2106.05175v1 fatcat:4wlf66yy5rczbjfrc74adokomi

On the Price of Anarchy for High-Price Links [article]

Carme Àlvarez, Arnau Messegué
2019 arXiv   pre-print
We study Nash equilibria and the price of anarchy in the classic model of Network Creation Games introduced by Fabrikant, Luthra, Maneva, Papadimitriou and Shenker in 2003.  ...  One of the main conjectures for this model states that the price of anarchy, i.e. the relative cost of the lack of coordination, is constant for all α.  ...  In this work we provide a new understanding of the structure of the equilibrium networks for the classical network creation game [12] .  ... 
arXiv:1909.09799v1 fatcat:tyr4ttezarbi3pnb4jlesh6bau

The price of selfish behavior in bilateral network formation

Jacomo Corbo, David Parkes
2005 Proceedings of the twenty-fourth annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '05  
The proof of Proposition 5 that all Nash graphs of the unilateral connection game (UCG) are pairwise stable in the BCG (for the same link cost) was incorrect, and the result is restated here for trees.  ...  We develop an upper and lower bound on the price of anarchy of the bilateral game.  ...  We also thank Geoff Exoo for helping to generalize the lower bound on the price of anarchy result.  ... 
doi:10.1145/1073814.1073833 dblp:conf/podc/CorboP05 fatcat:ewhrlngx5jg6vcabyfoipfrjyu

The price of anarchy in cooperative network creation games

Erik D. Demaine, Mohammadtaghi Hajiaghayi, Hamid Mahini, Morteza Zadimoghaddam
2009 ACM SIGecom Exchanges  
In this paper, we pursue two important facets of the network creation game.  ...  This bound is the first result of this type for any version of the network creation game; most previous general upper bounds are polynomial in n.  ...  [15] conjectured that equilibrium graphs in the unilateral model were all trees, but this conjecture was disproved by Albers et al. [2] .  ... 
doi:10.1145/1980522.1980524 fatcat:atcvdwrudjg3jbofrfhyxk6zoa
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