Network Selfish

Greedy Selfish Network Creation∗

(Full Version)

Pascal Lenzner†

arXiv:1210.7970v1 [cs.GT] 30 Oct 2012

Abstract 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 on the approximation ratio. 2 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 6 is in 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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Introduction

The area of Network Design is one of the classical and still very active fields in the realm of Theoretical Computer Science and Operations Research. But there is this curious fact: One of the most important networks which is increasingly...