Dynamics in tree formation games

Arcaute, Esteban; Dyagilev, Kirill; Johari, Ramesh; Mannor, Shie

doi:10.1016/j.geb.2013.01.002

Cited by 8 publications

(15 citation statements)

References 19 publications

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“…Here we describe common properties of all pair-wise equilibria. We start by noting that, unlike the findings of several other studies Arcaute et al [2013Arcaute et al [ , 2009; Nisan N. [2007], in our model, at equilibrium, the type-B nodes are not necessarily organized in trees. This is shown in the next example.…”

Section: Equilibria's Propertiesmentioning

confidence: 55%

“…We take into consideration the agreement's bilateral nature, by noting that the establishment of a link requires the agreement of both nodes at its ends, while removing a link can be done unilaterally. This is known as a pairwise-stable equilibrium [Jackson and Wolinsky 1996;Arcaute et al 2013]. Fig.…”

Section: Introductionmentioning

confidence: 99%

“…Addressing social networks, [Vandenbossche and Demuynck 2012] describes a network formation game in which the link costs are heterogeneous and the benefit depends only on a player's nearest neighbors (i.e., no spillovers). In [Johari et al 2006], the authors discuss directed networks formation, where the information (or utility) flows in one direction along a link; the equilibria's existence properties of the model's extension to heterogeneous players was discussed in [Àlvarez and Fernàndez 2012].With very few exceptions, e.g., [Arcaute et al 2013], the vast majority of studies on the application of game theory to networks, and network formation games in particular, focus on static properties. However, it is not clear that the Internet, nor the economic relations between ASs, have reached an equilibrium.…”

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confidence: 99%

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Network formation games with heterogeneous players and the internet structure

Meirom

Mannor

Orda

2014

Proceedings of the Fifteenth ACM Conference on Economics and Computation

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We study the structure and evolution of the Internet's Autonomous System (AS) interconnection topology as a game with heterogeneous players. In this network formation game, the utility of a player depends on the network structure, e.g., the distances between nodes and the cost of links. We analyze static properties of the game, such as the prices of anarchy and stability and provide explicit results concerning the generated topologies. Furthermore, we discuss dynamic aspects, demonstrating linear convergence rate and showing that only a restricted subset of equilibria is feasible under realistic dynamics. We also consider the case where utility (or monetary) transfers are allowed between the players.

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Section: Equilibria's Propertiesmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Network formation games with heterogeneous players and the internet structure

Meirom

Mannor

Orda

2014

Proceedings of the Fifteenth ACM Conference on Economics and Computation

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“…Another important element of our framework is network design. Network design problem has been considered mostly in the context of network formation games among buyers who build or maintain the network, in both economics literature (e.g., see Jackson 2003, Epstein et al 2009, Arcaute et al 2013 and computer science literature (e.g., see Anshelevich et al 2003, Chen et al 2008, Marden and Wierman 2013. In these papers, the existence and quality of the equilibrium are studied from the perspective of independent buyers.…”

Section: Related Literaturementioning

confidence: 99%

Mechanism and Network Design with Private Negative Externalities

Belloni

Deng

Pekeč

2017

Operations Research

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A revenue-maximizing monopolist is selling a single indivisible good to buyers who face a loss if a rival buyer obtains it. The rivalry is modeled through a network, an arc between a pair of buyers indicates that a buyer considers another buyer its rival, and the magnitude of the loss is the private information of each buyer. First, given a network, we characterize the optimal mechanism. Second, we show that revenues depend on the network structure. Thus, in applications where it is possible, the monopolist might consider designing not only the mechanism but also the network (if not fully, at least partially). Third, we provide solutions to this joint network and mechanism design problem. Specifically, despite of the non-monotone impact of additional competition on the monopolist's revenues, we determine revenue-maximizing rivalry networks (which in turn induce optimal mechanisms), and show that they are independent of distributional assumptions on buyers' independent private loss values, provided virtual values are bounded from zero. We achieve these results under different restrictions on the network structure and formation. When rivalry is symmetric, matchings are optimal (with at most one path on three vertices). Thus, a market with a fragmented network structure yields higher revenues for the monopolist than a market with a fully connected network structure. However, asymmetric competitive relationships among buyers generate higher revenues than symmetric ones. The optimal asymmetric networks are characterized by (i) every buyer having at least one rival, and (ii) the existence of a buyer not considered a rival by anyone.

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“…The establishment of a link requires the bilateral agreement of the two parties at its ends, while removing a link can be done unilaterally. This is known as a pairwise-stable equilibrium [12], [18]. The resulting graph is referred to as a stabilizable graph.…”

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confidence: 99%

Strategic Formation of Heterogeneous Networks

Meirom

Mannor

Orda

2017

IEEE J. Select. Areas Commun.

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We establish a network formation game for the Internet's Autonomous System (AS) interconnection topology. The game includes different types of players, accounting for the heterogeneity of ASs in the Internet. In this network formation game, the utility of a player depends on the network structure, e.g., the distances between nodes and the cost of links. We also consider the case where utility (or monetary) transfers are allowed between the players. We incorporate reliability considerations in the player's utility function, and analyze static properties of the game as well as its dynamic evolution. We provide dynamic analysis of topological quantities, and explain the prevalence of some "network motifs" in the Internet graph. We assess our predictions with real-world data.

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Dynamics in tree formation games

Cited by 8 publications

References 19 publications

Network formation games with heterogeneous players and the internet structure

Network formation games with heterogeneous players and the internet structure

Mechanism and Network Design with Private Negative Externalities

Strategic Formation of Heterogeneous Networks

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