Affiliation:
1. Università degli Studi di Sassari, Italy
2. Università di Roma “Tor Vergata”, Italy
3. Università degli Studi dell'Aquila and Istituto di Analisi dei Sistemi ed Informatica -- CNR, Rome, Italy
Abstract
A
network creation game
simulates a decentralized and noncooperative construction of a communication network. Informally, there are
n
players sitting on the network nodes, which attempt to establish a reciprocal communication by activating, thereby incurring a certain cost, any of their incident links. The goal of each player is to have all the other nodes as close as possible in the resulting network, while buying as few links as possible. According to this intuition, any model of the game must then appropriately address a balance between these two conflicting objectives. Motivated by the fact that a player might have a strong requirement about her centrality in the network, we introduce a new setting in which a player who maintains her (maximum or average) distance to the other nodes within a given bound incurs a cost equal to the number of activated edges; otherwise her cost is unbounded. We study the problem of understanding the structure of pure Nash equilibria of the resulting games, which we call M
ax
BD and S
um
BD, respectively. For both games, we show that when distance bounds associated with players are nonuniform, then equilibria can be arbitrarily bad. On the other hand, for M
ax
BD, we show that when nodes have a uniform bound
D
≥ 3 on the maximum distance, then the
price of anarchy
(PoA) is lower and upper bounded by 2 and
O
(
n
1/⌊log
3
D
⌋+1
), respectively (i.e., PoA is constant as soon as
D
is Ω(
n
ϵ
), for any ϵ > 0), while for the interesting case
D
=2, we are able to prove that the PoA is Ω(√
n
) and
O
(√
n
log
n
). For the uniform S
um
BD, we obtain similar (asymptotically) results and moreover show that PoA becomes constant as soon as the bound on the average distance is 2
ω
(√log
n
)
.
Funder
Italian Ministry of Education, University, and Research
Research Grant PRIN 2010 “ARS TechnoMedia,”
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Marketing,Economics and Econometrics,Statistics and Probability,Computer Science (miscellaneous)
Reference15 articles.
1. Basic Network Creation Games
2. Noga Alon and Joel Spencer. 1992. The Probabilistic Method. John Wiley Hoboken NJ. Noga Alon and Joel Spencer. 1992. The Probabilistic Method. John Wiley Hoboken NJ.
3. The Price of Anarchy of a Network Creation Game with Exponential Payoff
4. The price of anarchy in network creation games
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献