Abstract: In a network creation game, several players try to build an efficient network together. Each player, however, is greedy and selfish, and only cares to minimize their own costs. Tragically, some outcomes of this game may result in an equilibrium in which players are much worse off than if a single network creator just told them what to do. How much worse off? Alon, Demaine, Hajiaghayi, and Leighton answer the question for one version of the game, proving that any equilibrium graph has diameter at most 2^O(sqrt(log n)). Moreover, taking a sufficiently power of an equilibrium graph produces a distance-uniform graph. This is a very strong graph property that seems certain to produce a much better diameter bound. Alas, this is not to be. We show that distance-uniform graphs with diameter 2^O(sqrt(log n)) exist, and that this bound is tight. This is joint work with Po-Shen Loh and Arnau Messegué.