Article

Network Creation Games with Disconnected Equilibria

Authors:

Bobo NickAuthors Info & Claims

WINE '08: Proceedings of the 4th International Workshop on Internet and Network Economics

Pages 394 - 401

https://doi.org/10.1007/978-3-540-92185-1_45

Published: 17 December 2008 Publication History

Abstract

In this paper we extend a popular non-cooperative networkcreation game (NCG) [11] to allow for disconnected equilibriumnetworks. There are n players, each is a vertex in a graph, and astrategy is a subset of players to build edges to. For each edge aplayer must pay a cost ±, and the individual cost for aplayer represents a trade-off between edge costs and shortest pathlengths to all other players. We extend the model to a penalizedgame (PCG), for which we reduce the penalty for a pair ofdisconnected players to a finite value ². We prove that thePCG is not a potential game, but pure Nash equilibria always exist,and pure strong equilibria exist in many cases. We provide tightconditions under which disconnected (strong) Nash equilibria canevolve. Components of these equilibria must be (strong) Nashequilibria of a smaller NCG. But in contrast to the NCG, for thevast majority of parameter values no tree is a stable component.Finally, we show that the price of anarchy is ˜(n), severalorders of magnitude larger than in the NCG. Perhaps surprisingly,the price of anarchy for strong equilibria increases only to atmost 4.

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Cited By

Janus Tde Keijzer B(2017)On Strong Equilibria and Improvement Dynamics in Network Creation GamesWeb and Internet Economics10.1007/978-3-319-71924-5_12(161-176)Online publication date: 17-Dec-2017
https://dl.acm.org/doi/10.1007/978-3-319-71924-5_12
Àlvarez CBlesa MDuch AMessegué ASerna M(2016)Celebrity gamesTheoretical Computer Science10.1016/j.tcs.2016.08.005648:C(56-71)Online publication date: 4-Oct-2016
https://dl.acm.org/doi/10.1016/j.tcs.2016.08.005
Àlvarez CSerna MFernàndez A(2016)Network Formation for Asymmetric Players and Bilateral ContractingTheory of Computing Systems10.1007/s00224-015-9640-659:3(397-415)Online publication date: 1-Oct-2016
https://dl.acm.org/doi/10.1007/s00224-015-9640-6
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Network Creation Games with Disconnected Equilibria

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cover image Guide Proceedings

WINE '08: Proceedings of the 4th International Workshop on Internet and Network Economics

December 2008

731 pages

ISBN:9783540921844

Editors:
Christos Papadimitriou
Computer Science Division, University of California at Berkeley, Berkeley, USA
,
Shuzhong Zhang
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong,

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 17 December 2008

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Cited By

Janus Tde Keijzer B(2017)On Strong Equilibria and Improvement Dynamics in Network Creation GamesWeb and Internet Economics10.1007/978-3-319-71924-5_12(161-176)Online publication date: 17-Dec-2017
https://dl.acm.org/doi/10.1007/978-3-319-71924-5_12
Àlvarez CBlesa MDuch AMessegué ASerna M(2016)Celebrity gamesTheoretical Computer Science10.1016/j.tcs.2016.08.005648:C(56-71)Online publication date: 4-Oct-2016
https://dl.acm.org/doi/10.1016/j.tcs.2016.08.005
Àlvarez CSerna MFernàndez A(2016)Network Formation for Asymmetric Players and Bilateral ContractingTheory of Computing Systems10.1007/s00224-015-9640-659:3(397-415)Online publication date: 1-Oct-2016
https://dl.acm.org/doi/10.1007/s00224-015-9640-6
Ehsani SFadaee SFazli MMehrabian ASadeghabad SSafari MSaghafian M(2015)A Bounded Budget Network Creation GameACM Transactions on Algorithms10.1145/270161511:4(1-25)Online publication date: 13-Apr-2015
https://dl.acm.org/doi/10.1145/2701615
Kawald BLenzner PBlelloch GVöcking B(2013)On dynamics in selfish network creationProceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures10.1145/2486159.2486185(83-92)Online publication date: 23-Jul-2013
https://dl.acm.org/doi/10.1145/2486159.2486185
Anshelevich EHoefer M(2012)Contribution Games in NetworksAlgorithmica10.5555/3226239.322636063:1-2(51-90)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.5555/3226239.3226360

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