New Insights into the Structure of Equilibria for the Network Creation Game (original) (raw)
We study the sum classic network creation game introduced by Fabrikant et al. in which n players conform a network buying links at individual price α. When studying this model we are mostly interested in Nash equilibria (ne) and the Price of Anarchy (PoA). It is conjectured that the PoA is constant for any α. Up until now, it has been proved constant PoA for the range α = O(n1−δ1) with δ1 > 0 a positive constant, upper bounding by a constant the diameter of any ne graph jointly with the fact that the diameter of any ne graph plus one unit is an upper bound for the PoA of the same graph. Also, it has been proved constant PoA for the range α > n(1 + δ2) with δ2 > 0 a positive constant, studying extensively the average degree of any biconnected component from equilibria. Our contribution consists in proving that ne graphs satisfy very restrictive topological properties generalising some properties proved in the literature and providing new insights that might help settling the...
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