Flow-Based Network Creation Games

Echzell, Hagen; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna

doi:10.24963/ijcai.2020/20

Cited by 7 publications

(6 citation statements)

References 25 publications

(30 reference statements)

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“…The SNCG incorporates a robustness aspect since bridge-edges are expensive. This fits to a recent trend in the AI community for studying robust network formation [38,15,24,16,21].…”

Section: Model and Notationsupporting

confidence: 87%

Selfish Creation of Social Networks

Bilò¹,

Friedrich²,

Lenzner³

et al. 2020

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Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to nodes in a network strategically decide which links to form to optimize their centrality. Many versions have been introduced and analyzed, but none of them fits to modeling the evolution of social networks. In realworld social networks, connections are often established by recommendations from common acquaintances or by a chain of such recommendations. Thus establishing and maintaining a contact with a friend of a friend is easier than connecting to complete strangers. This explains the high clustering, i.e., the abundance of triangles, in real-world social networks.We propose and analyze a network creation model inspired by real-world social networks. Edges are formed in our model via bilateral consent of both endpoints and the cost for establishing and maintaining an edge is proportional to the distance of the endpoints before establishing the connection. We provide results for generic cost functions, which essentially only must be convex functions in the distance of the endpoints without the respective edge. For this broad class of cost functions, we provide many structural properties of equilibrium networks and prove (almost) tight bounds on the diameter, the Price of Anarchy and the Price of Stability. Moreover, as a proof-of-concept we show via experiments that the created equilibrium networks of our model indeed closely mimics real-world social networks. We observe degree distributions that seem to follow a power-law, high clustering, and low diameters. This can be seen as a promising first step towards game-theoretic network creation models that predict networks featuring all core real-world properties.

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“…The SNCG incorporates a robustness aspect since bridge-edges are expensive. This fits to a recent trend in the AI community for studying robust network formation [38,15,24,16,21].…”

Section: Model and Notationsupporting

confidence: 87%

Selfish Creation of Social Networks

Bilò¹,

Friedrich²,

Lenzner³

et al. 2020

Preprint

Self Cite

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“…Also variants with weighted traffic [1], a version on an incomplete host graph that specifies which edges can be formed [18], or a geometric version on host graphs with weighted edges [7,24]. Moreover, also NCG variants with non-uniform edge prices [34,16,13,7,8,11], locality [6,10,15], and robustness [35,12,21].…”

Section: Related Workmentioning

confidence: 99%

The Impact of Cooperation in Bilateral Network Creation

Friedrich¹,

Gawendowicz²,

Lenzner³

et al. 2022

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Many real-world networks, like the Internet, are not the result of central design but instead the outcome of the interaction of local agents who are selfishly optimizing for their individual utility. The famous Network Creation Game [23] enables us to understand such processes, their dynamics, and their outcomes in the form of equilibrium states. In this model, agents buy incident edges towards other agents for a price of α and simultaneously try to minimize their buying cost and their total hop distance. Since in many real-world networks, e.g., social networks, consent from both sides is required to maintain a connection, Corbo and Parkes [14] proposed a bilateral version of the Network Creation Game, in which mutual consent and payment are required in order to create edges. It is known that the bilateral version has a significantly higher Price of Anarchy, compared to the unilateral version. This is counter-intuitive, since cooperation should help to avoid socially bad states. We investigate this phenomenon by analyzing the Price of Anarchy of the bilateral version with respect to different solution concepts that allow for various degrees of cooperation among the agents. With this, we provide insights into what kind of cooperation is needed to ensure that socially good networks are created. We present a collection of asymptotically tight bounds on the Price of Anarchy that precisely map the impact of cooperation on the quality of tree networks and we find that weak forms of cooperation already yield a significantly improved Price of Anarchy. Moreover, for general networks we show that enhanced cooperation yields close to optimal networks for a wide range of edge prices.

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“…Besides NCG variants where agents minimize edge costs and distance costs, also models where the cost of an agent depends on her local clustering coefficient [14] or on the edge-connectivity of the created network [24] have been proposed.…”

Section: Related Workmentioning

confidence: 99%

Efficiency and Stability in Euclidean Network Design

Friedemann¹,

Friedrich²,

Gawendowicz³

et al. 2021

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Network Design problems typically ask for a minimum cost subnetwork from a given host network. This classical point-of-view assumes a central authority enforcing the optimum solution. But how should networks be designed to cope with selfish agents that own parts of the network? In this setting, minimum cost networks may be very unstable in that agents will deviate from a proposed solution if this decreases their individual cost. Hence, designed networks should be both efficient in terms of total cost and stable in terms of the agents' willingness to accept the network.We study this novel type of Network Design problem by investigating the creation of (𝛽, 𝛾)-networks, that are in 𝛽-approximate Nash equilibrium and have a total cost of at most 𝛾 times the optimal cost, for the recently proposed Euclidean Generalized Network Creation Game by Bilò et al. [11]. There, 𝑛 agents corresponding to points in Euclidean space create costly edges among themselves to optimize their centrality in the created network. Our main result is a simple O (𝑛 2 )-time algorithm that computes a (𝛽, 𝛽)-network with low 𝛽 for any given set of points. Moreover, on integer grid point sets or random point sets our algorithm achieves a low constant 𝛽. Besides these results for the Euclidean model, we discuss a generalization of our algorithm to instances with arbitrary, even non-metric, edge lengths. Moreover, in contrast to these algorithmic results, we show that no such positive results are possible when focusing on either optimal networks, i.e., (𝛽, 1)-networks, or perfectly stable networks, i.e., (1, 𝛾)-networks, as in both cases NP-hard problems arise, there exist instances with very unstable optimal networks, and there are instances for perfectly stable networks with high total cost. Along the way, we significantly improve several results from Bilò et al. and we asymptotically resolve their conjecture about the Price of Anarchy by providing a tight bound. CCS CONCEPTS• Theory of computation → Network formation; Quality of equilibria; Algorithmic game theory.

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Flow-Based Network Creation Games

Cited by 7 publications

References 25 publications

Selfish Creation of Social Networks

Selfish Creation of Social Networks

The Impact of Cooperation in Bilateral Network Creation

Efficiency and Stability in Euclidean Network Design

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