A Game Theoretic Perspective on Network Topologies

Details A Game Theoretic Perspective on Network Topologies A Game Theoretic Perspective on Network Topologies

2011-06-13

arxiv.org/abs/1106.2440v2

Mathematics

Optimization and Control

25 pages, this revised version has been resubmitted to Computational and Mathematical Organization Theory after being reviewed

Scientific paper

As an alternative view to the graph formation models in the statistical physics community, we introduce graph formation models using \textit{network formation} through selfish competition as an approach to modeling graphs with particular topologies. We further investigate a specific application of our results to collaborative oligopolies. We extend the results of Goyal and Joshi (S. Goyal and S. Joshi. Networks of collaboration in oligopoly. Games and Economic behavior, 43(1):57-85, 2003), who first considered the problem of collaboration networks of oligopolies and showed that under certain linear assumptions network collaboration produced a stable complete graph through selfish competition. We show with nonlinear cost functions and player payoff alteration that stable collaboration graphs with an arbitrary degree sequence can result.

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