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Explore a network formation game where players strategically wire outgoing links to maximize their PageRank centrality in this 45-minute research seminar. Delve into the game's potential structure, local best response characteristics, and equilibrium conditions. Examine the homogeneous case with equal out-links, focusing on potential-maximizing equilibria and complete classifications for specific scenarios. Discover how this formation mechanism leads to undirected, disconnected, or loosely connected networks. Gain insights from the collaborative research of Giacomo Como, Costanza Catalano, Maria Castaldo, and Fabio Fagnani presented at the ISS Informal Systems Seminar hosted by GERAD Research Center.