  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.

Optimization and Control;Computer Science and Game Theory