Basic network creation games
Noga Alon,Erik D. Demaine,MohammadTaghi Hajiaghayi,Tom Leighton +3 more
- 13 Jun 2010
- pp 106-113
TL;DR: This model has no parameter α for the link creation cost, so the results automatically apply for all values of alpha without additional effort; furthermore, equilibrium can be checked in polynomial time in the model, unlike previous models.
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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
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Citations
Intrinsic Robustness of the Price of Anarchy
TL;DR: This work identifies a “canonical sufficient condition” for an upper bound on the price of anarchy of pure Nash equilibria, and proves that in congestion games, smoothness arguments are “complete” in a proof-theoretic sense: despite their automatic generality, they are guaranteed to produce optimal worst-case upper bounds on thePrice of anarchy.
On Nash Equilibria for a Network Creation Game
Susanne Albers,Stefan Eilts,Eyal Even-Dar,Yishay Mansour,Liam Roditty +4 more
- 01 Mar 2014
TL;DR: The tree conjecture is disproved, a constant upper bound on the price of anarchy of O(√α) is derived and characterizations of Nash equilibria are developed and extended to a weighted network creation game as well as to scenarios with cost sharing.
Improving Network Connectivity and Robustness Using Trusted Nodes With Application to Resilient Consensus
TL;DR: This paper extends two fundamental metrics of structural robustness with the notion of trusted nodes, network connectivity, and $r$-robustness, and shows that any desired connectivity and robustness can be achieved without adding extra links.
105
The Price of Anarchy in Network Creation Games Is (Mostly) Constant
TL;DR: 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.
On dynamics in basic network creation games
Pascal Lenzner
- 17 Oct 2011
TL;DR: A cubic upper bound on the number of steps needed for any improving response dynamic to converge to a stable tree and a linear-time algorithm for computing a best response on trees even if players are allowed to swap multiple edges at a time are given.
49
References
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Matteo Frigo,Charles E. Leiserson,Harald Prokop,Sridhar Ramachandran +3 more
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TL;DR: It is proved that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model can be simulated efficiently by LRU replacement.
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On a network creation game
Alex Fabrikant,Ankur Luthra,Elitza Maneva,Christos H. Papadimitriou,Scott Shenker +4 more
- 13 Jul 2003
TL;DR: 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.
Cache-oblivious algorithms
Charles E. Leiserson
- 28 May 2003
TL;DR: It is proved that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal across a multilevel cache hierarchy, and it is shown that the assumption of optimal replacement made by the ideal-cache model can be simulated efficiently by LRU replacement.
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Problems and results in extremal combinatorics-II
TL;DR: This paper contains a collection of problems and results in the area, including solutions or partial solutions to open problems suggested by various researchers, and is a sequel to a previous paper of the same flavor.
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