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Network Formation by Reciprocity Versus Sparsity Tradeoffs | IEEE Journals & Magazine | IEEE Xplore

Network Formation by Reciprocity Versus Sparsity Tradeoffs


Abstract:

We introduce a cost-benefit model for network formation, where exchanges among nodes are based on reciprocity. Peers receive from the network an amount of resources comme...Show More

Abstract:

We introduce a cost-benefit model for network formation, where exchanges among nodes are based on reciprocity. Peers receive from the network an amount of resources commensurate with their contribution. When creating links is costly, peers tend to limit the number of their connections, and sparsity of the exchange network may be desirable. In a fully connected graph, finding the sparsest exchanges that achieve a desired level of reciprocity is in general NP-hard. To capture near optimal allocations, we consider variants of the Eisenberg-Gale program, and an equivalent formulation given by Shmyrev, with sparsity penalties. We propose two decentralized algorithms for reciprocation, whereby peers approximately compute the sparsest allocations, by submitting bids for each other's resources. The algorithms extend the proportional-response dynamics, and promote sparsity through nonlinear pricing either at the bidding or the allocation stage. Numerical results illustrate the network formation process by peers who achieve almost-perfect reciprocity, with a small number of active connections. The proposed self-organization model leverages the reciprocity vs sparsity tradeoff to generate cyclic motifs in exchange networks.
Published in: IEEE Transactions on Network Science and Engineering ( Volume: 7, Issue: 3, 01 July-Sept. 2020)
Page(s): 1752 - 1763
Date of Publication: 08 November 2019

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