Basic Network Creation Games with Communication Interests

Cord-Landwehr, Andreas; Hüllmann, Martina; Kling, Peter; Setzer, Alexander

doi:10.1007/978-3-642-33996-7_7

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…Very recently, Cord-Landwehr et al [7] studied a variant of the MAX-SG, where agents have communication interests, and showed that this variant admits a best response cycle on a tree network as initial network. Hence the restricted-interest variant of the MAX-SG is not a FIPG -even on trees.…”

Section: Related Workmentioning

confidence: 99%

On dynamics in selfish network creation

Kawald

Lenzner

2013

Proceedings of the Twenty-Fifth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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We consider the dynamic behavior of several variants of the Network Creation Game, introduced by Fabrikant et al. [PODC'03]. Equilibrium networks in these models have desirable properties like low social cost and small diameter, which makes them attractive for the decentralized creation of overlay-networks. Unfortunately, due to the nonconstructiveness of the Nash equilibrium, no distributed algorithm for finding such networks is known. We treat these games as sequential-move games and analyze if (uncoordinated) selfish play eventually converges to an equilibrium. Thus, we shed light on one of the most natural algorithms for this problem: distributed local search, where in each step some agent performs a myopic selfish improving move.We show that fast convergence is guaranteed for all versions of Swap Games, introduced by Alon et al. [SPAA'10], if the initial network is a tree. Furthermore, we prove that this process can be sped up to an almost optimal number of moves by employing a very natural move policy. Unfortunately, these positive results are no longer true if the initial network has cycles and we show the surprising result that even one non-tree edge suffices to destroy the convergence guarantee. This answers an open problem from Ehsani et al. [SPAA'11] in the negative. Moreover, we show that on non-tree networks no move policy can enforce convergence. We extend our negative results to the well-studied original version, where agents are allowed to buy and delete edges as well. For this model we prove that there is no convergence guarantee -even if all agents play optimally. Even worse, if played on a non-complete host-graph, then there are instances where no sequence of improving moves leads to a stable network. Furthermore, we analyze whether cost-sharing has positive impact on the convergence behavior. For this we consider a version by Corbo and Parkes [PODC'05] where bilateral consent is needed for the creation of an edge and where edge-costs are shared among the involved agents. We show that employing such a cost-sharing rule yields even worse dynamic behavior.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. SPAA'13, Finally, we contrast our mostly negative theoretical results by a careful empirical study. Our simulations indicate two positive facts: (1) The non-convergent behavior seems to be confined to a small set of pathological instances and is unlikely to show up in practice.(2) In all our simulations we observed a remarkably fast convergence towards a stable network...

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Section: Related Workmentioning

confidence: 99%

On dynamics in selfish network creation

Kawald

Lenzner

2013

Proceedings of the Twenty-Fifth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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“…In [13] it was shown that greedy dynamics in a BNCG converge very quickly to a stable state if played on a tree. The authors of [5] analyzed BNCGs on trees with agents having communication interests. However, simplifying the model as in [3] is not without its problems.…”

Section: Related Workmentioning

confidence: 99%

Greedy Selfish Network Creation

Lenzner

2012

Lecture Notes in Computer Science

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We introduce and analyze greedy equilibria (GE) for the well-known model of selfish network creation by Fabrikant et al. [PODC'03]. GE are interesting for two reasons: (1) they model outcomes found by agents which prefer smooth adaptations over radical strategychanges, (2) GE are outcomes found by agents which do not have enough computational resources to play optimally. In the model of Fabrikant et al. agents correspond to Internet Service Providers which buy network links to improve their quality of network usage. It is known that computing a best response in this model is NP-hard. Hence, poly-time agents are likely not to play optimally. But how good are networks created by such agents? We answer this question for very simple agents. Quite surprisingly, naive greedy play suffices to create remarkably stable networks. Specifically, we show that in the Sum version, where agents attempt to minimize their average distance to all other agents, GE capture Nash equilibria (NE) on trees and that any GE is in 3-approximate NE on general networks. For the latter we also provide a lower bound of 3 2 on the approximation ratio. For the Max version, where agents attempt to minimize their maximum distance, we show that any GE-star is in 2-approximate NE and any GE-tree having larger diameter is in 6 5 -approximate NE. Both bounds are tight. We contrast these positive results by providing a linear lower bound on the approximation ratio for the Max version on general networks in GE. This result implies a locality gap of Ω(n) for the metric min-max facility location problem, where n is the number of clients.

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“…There are other variants of the network creation game, such as weighted network creation game proposed by Albers et al [12], bilateral network creation game studied by Demaine et al [2], Corbo and Parkes [16]. For more studies on these variants, as well as exact or approximation algorithms for the network creation game, we refer the readers to [2,12,16,17,18,19,20,21,22,23,24,25,26,27].…”

Section: Related Workmentioning

confidence: 99%

On Tree Equilibria in Max-Distance Network Creation Games

Wang

2021

Preprint

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We study the Nash equilibrium and the price of anarchy in the max-distance network creation game. The network creation game, first introduced and studied by Fabrikant et al.[1], is a classic model for real-world networks from a game-theoretic point of view. In a network creation game with n selfish vertex agents, each vertex can build undirected edges incident to a subset of the other vertices. The goal of every agent is to minimize its creation cost plus its usage cost, where the creation cost is the unit edge cost α times the number of edges it builds, and the usage cost is the sum of distances to all other agents in the resulting network. The max-distance network creation game, introduced and studied by Demaine et al. [2], is a key variant of the original game, where the usage cost takes into account the maximum distance instead. The main result of this paper 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 [3]. We also improve the constant upper bound on the price of anarchy to 3 for tree equilibria. 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.

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Basic Network Creation Games with Communication Interests

Cited by 10 publications

References 17 publications

On dynamics in selfish network creation

On dynamics in selfish network creation

Greedy Selfish Network Creation

On Tree Equilibria in Max-Distance Network Creation Games

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