Network Creation Games: Think Global – Act Local

Cord-Landwehr, Andreas; Lenzner, Pascal

doi:10.1007/978-3-662-48054-0_21

Cited by 17 publications

(10 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Concerning local coalitions, a notion of equilibrium close in spirit to our LSE has been studied in the context of network design games in [19]. Moreover, locality aspects have been also considered when restricting the strategy space in single-player deviations (see for example [4,10]).…”

Section: Introductionmentioning

confidence: 99%

Coalition Resilient Outcomes in Max k-Cut Games

Carosi

Fioravanti

Gualà

et al. 2019

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We investigate strong Nash equilibria in the max k-cut game, where we are given an undirected edge-weighted graph together with a set {1, . . . , k} of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player v consists of the k colors. When players select a color they induce a k-coloring or simply a coloring. Given a coloring, the utility (or payoff ) of a player u is the sum of the weights of the edges {u, v} incident to u, such that the color chosen by u is different from the one chosen by v. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish agents and extend or are related to several fundamental classes of games. Very little is known about the existence of strong equilibria in max k-cut games. In this paper we make some steps forward in the comprehension of it. We first show that improving deviations performed by minimal coalitions can cycle, and thus answering negatively the open problem proposed in [13]. Next, we turn our attention to unweighted graphs. We first show that any optimal coloring is a 5-SE in this case. Then, we introduce x-local strong equilibria, namely colorings that are resilient to deviations by coalitions such that the maximum distance between every pair of nodes in the coalition is at most x. We prove that 1-local strong equilibria always exist. Finally, we show the existence of strong Nash equilibria in several interesting specific scenarios.

show abstract

Section: Introductionmentioning

confidence: 99%

Coalition Resilient Outcomes in Max k-Cut Games

Carosi

Fioravanti

Gualà

et al. 2019

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Quite recently, a constant PoA was proven by Chauhan et al [15] for a version with non-uniform edge prices. In contrast, non-constant lower bounds on the PoA have been proven for local versions of the network creation game by Bilò et al [10,12] and Cord-Landwehr & Lenzner [18].…”

Section: Related Workmentioning

confidence: 99%

On the Tree Conjecture for the Network Creation Game

Bilò

Lenzner

2019

Theory Comput Syst

Self Cite

View full text Add to dashboard Cite

Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. [PODC'03] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of α per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all α and that for α ≥ n all equilibrium networks are trees.We introduce a novel technique for analyzing stable networks for high edge-price α and employ it to improve on the best known bounds for both conjectures. In particular we show that for α > 4n − 13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of α. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.

show abstract

“…It was shown that the PoA may deteriorate heavily if agents only know their local neighborhood or only a shortest path tree of the network [8,9]. In contrast, a global view with a restriction to only local edge-purchases yields only a moderate increase of the PoA [11].…”

Section: Related Workmentioning

confidence: 99%

Selfish Network Creation with Non-uniform Edge Cost

Chauhan

Lenzner

Melnichenko

et al. 2017

Algorithmic Game Theory

Self Cite

View full text Add to dashboard Cite

Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC'03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games.We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has constant Price of Anarchy.

show abstract

Network Creation Games: Think Global – Act Local

Cited by 17 publications

References 32 publications

Coalition Resilient Outcomes in Max k-Cut Games

Coalition Resilient Outcomes in Max k-Cut Games

On the Tree Conjecture for the Network Creation Game

Selfish Network Creation with Non-uniform Edge Cost

Contact Info

Product

Resources

About