Local Two-Stage Myopic Dynamics for Network Formation Games

Arcaute, Esteban; Johari, Ramesh; Mannor, Shie

doi:10.1007/978-3-540-92185-1_33

Cited by 12 publications

(8 citation statements)

References 17 publications

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“…This bilateral process leads to the creation of a new link between both players. Since Nash equilibrium does not allow us to represent the link formation as a bilateral process, we adopt the notion of pairwise Nash stability used in [6].…”

Section: Pairwise Nash Equilibriummentioning

confidence: 99%

“…Each player can contract bilaterally with others to form bidirectional links or break unilaterally contracts to eliminate the corresponding links. Our model is an extension of the traffic routing model considered in [5,6,7] in which we do not require the traffic to be uniform and all-to-all. Player i specifies the amount of traffic tij ≥ 0 that wants to send to player j.…”

Section: Introductionmentioning

confidence: 99%

“…In the models studied by Arcaute el al. in [5,6,7] each node derives utility from connectivity and incurs a cost. The cost is comprised of three different terms: the cost of routing traffic, the maintenance cost of its links, and the disconnection cost.…”

mentioning

confidence: 99%

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Network Formation for Asymmetric Players and Bilateral Contracting

2015

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We study a network formation game where players wish to send traffic to other players. Players can be seen as nodes of an undirected graph whose edges are defined by contracts between the corresponding players. Each player can contract bilaterally with others to form bidirectional links or break unilaterally contracts to eliminate the corresponding links. Our model is an extension of the traffic routing model considered in [5,6,7] in which we do not require the traffic to be uniform and all-to-all. Player i specifies the amount of traffic tij ≥ 0 that wants to send to player j. Our notion of stability is the network pairwise Nash stability, when no node wishes to deviate unilaterally and no pair of nodes can obtain benefit from deviating bilaterally. We show a characterization of the topologies that are pairwise Nash stable for a given traffic matrix. We prove that the best response problem is NP-hard and devise a myopic dynamics so that the deviation of the active node can be computed in polynomial time. We show the convergence of the dynamics to pairwise Nash configurations, when the contracting functions are anti-symmetric and affine, and that the expected convergence time is polynomial in the number of nodes when the node activation process is uniform.

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Section: Pairwise Nash Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Network Formation for Asymmetric Players and Bilateral Contracting

2015

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“…The aforementioned models of network formation have the limitation that each individual (or node) needs to know global information about the structure of the network in order to compute its pay-off. A few recent models (Arcaute et al, 2008;Buskens and Van De Rijt, 2008;Kleinberg et al, 2008) in the literature make an attempt to overcome the above limitation.…”

Section: Literature Reviewmentioning

confidence: 99%

“…2. Arcaute et al (2008) study the myopic dynamics in network formation games. A key aspect of the dynamics studied in this model is the local information and the authors show that these dynamics converge to efficient or near efficient outcomes.…”

Section: Literature Reviewmentioning

confidence: 99%

Strategic Network Formation with Localized Pay-offs

Vallam¹,

Subramanian²,

Narayanam³

et al. 2014

Studies in Microeconomics

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In this investigation, we analyze a network formation game in a strategic setting where pay-offs of individuals depend only on their immediate neighbourhood. These localized pay-offs incorporate the social capital emanating from bridging positions that nodes hold in the network. Using this simple and novel model of network formation, our study explores the structure of networks that form, satisfying pairwise stability or efficiency or both. We derive sufficient conditions for the pairwise stability of several interesting network structures. We characterize topologies of efficient networks by drawing upon classical results from extremal graph theory and discover that the Turan graph (or the complete equi-bipartite network) emerges as the unique efficient network under many configurations of parameters. We examine the trade-offs between topologies of pairwise stable networks and efficient networks using the notion of price of stability. Interestingly, we find that price of stability is equal to 1 for almost all configurations of parameters in the proposed model; and for the rest of the configurations, we obtain a lower bound of 0.5. This leads to another key insight of this article: under mild conditions, efficient networks will form when strategic individuals choose to add or delete links based on only localized pay-offs. We study the dynamics of the proposed model by designing a simple myopic best response updating rule and implementing it on a customized network formation testbed.

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