In static network creation games, selfish agents build edges to minimize their distance to all other agents, and the price of anarchy — the ratio between the worst equilibrium and the optimum — is conjectured to be at most polylogarithmic. The static game is well-behaved: selfish networks aren't much worse than optimal ones.
Bilò, Lenzner, and Skretas show the temporal version is catastrophically different. In temporal network creation, edges must be labeled with time steps (they exist only at specific moments), and reachability requires paths that respect the temporal ordering. The price of anarchy can scale linearly with the number of vertices.
The linear scaling means temporal selfishness can waste almost the entire network budget. In a network of n agents, the equilibrium network can be n times worse than the optimum. The gap between static and temporal is not quantitative — a slightly larger constant — but qualitative. The polynomial/linear boundary is crossed.
The mechanism: temporal ordering creates asymmetric reachability. An edge from A to B at time 3 helps A reach B's future contacts but not B's past contacts. This asymmetry allows selfish agents to free-ride on temporal structure in ways that static networks prevent, because in static networks all edges are symmetric in their reachability contribution.
The same network creation game. The same selfish agents. Add time, and the price of selfishness jumps from suspected polylog to proven linear.