Basic Network Creation Games
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Demaine-Basic Network.pdf
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263.33 KB
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Adobe PDF
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c43b5e2635c08af63d5ba8811bcabed2
Author(s)
Alon, Noga
Demaine, Erik D.
Hajiaghayi, Mohammad Taghi
Leighton, Tom
Date Issued
June 2010
Journal
Proceedings of the 22nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '10 )
Publisher
Association for Computing Machinery (ACM)
Citation
Noga Alon, Erik D. Demaine, MohammadTaghi Hajiaghayi, and Tom Leighton. 2010. Basic network creation games. In Proceedings of the 22nd ACM symposium on Parallelism in algorithms and architectures (SPAA '10). ACM, New York, NY, USA, 106-113.
Version
Author's final manuscript
Abstract
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. The central question is what structure the resulting equilibrium graphs have, in particular, how well they globally minimize diameter. For the local-average-distance version, we prove an upper bound of 2O(√ lg n), a lower bound of 3, a tight bound of exactly 2 for trees, and give evidence of a general polylogarithmic upper bound. For the local-diameter version, we prove a lower bound of Ω(√ n), and a tight upper bound of 3 for trees. All of our upper bounds apply equally well to previously extensively studied network creation games, both in terms of the diameter metric described above and the previously studied price of anarchy (which are related by constant factors). In surprising contrast, our model has no parameter α for the link creation cost, so our results automatically apply for all values of alpha without additional effort; furthermore, equilibrium can be checked in polynomial time in our model, unlike previous models. Our perspective enables simpler and more general proofs that get at the heart of network creation games.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1145/1810479.1810502
