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- W3115219842 abstract "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 $alpha$. When studying this model we are mostly interested in emph{Nash equilibria} (NE) and the emph{Price of Anarchy} (PoA). It is conjectured that the PoA is constant for any $alpha$. Up until now, it has been proved constant PoA for the range $alpha = O(n^{1-delta_1})$ with $delta_1>0$ a positive constant and it has been proved constant PoA for the range $alpha >n(1+delta_2)$ with $delta_2>0$ a positive constant. 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 conjecture that the PoA is constant for the remaining range of $alpha$: (i) We show that emph{every} node has the majority of the other nodes of the NE graph at the emph{same} narrow range of distances. (ii) If instead of considering the average degree, we focus on the number of non-bridge links bought for any player, we can prove that there exists a constant $D$ such that the average degree is upper bounded by $max(R, frac{2n}{alpha}+6)$ for any NE graph of diameter larger than $D$, where $R$ is a positive constant." @default.
- W3115219842 created "2021-01-05" @default.
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- W3115219842 date "2020-12-28" @default.
- W3115219842 modified "2023-10-16" @default.
- W3115219842 title "New Insights into the Structure of Equilibria for the Network Creation Game." @default.
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