New Insights into the Structure of Equilibria for the Network Creation Game
Carme \`Alvarez, Arnau Messegu\'e

TL;DR
This paper investigates the structure of Nash equilibria in the network creation game, providing new topological properties that could help prove the conjecture that the Price of Anarchy remains constant across all link costs.
Contribution
It proves that Nash equilibrium graphs have highly restrictive topological properties, extending previous results and offering insights towards confirming the constant Price of Anarchy conjecture.
Findings
All nodes have most other nodes at similar distances in NE graphs.
In NE graphs with large diameter, average degree is bounded by a constant or a function of n and alpha.
Abstract
We study the sum classic network creation game introduced by Fabrikant et al. in which players conform a network buying links at individual price . 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 . Up until now, it has been proved constant \PoA for the range with a positive constant and it has been proved constant \PoA for the range with 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 : (i) We show that…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Applications · Opinion Dynamics and Social Influence · Digital Platforms and Economics
