We study a learning dynamic model of routing (congestion) games to explore how an increase in the total demand influences system performance. We focus on non-atomic routing games with two parallel edges of linear cost, where all agents evolve using Multiplicative Weights Updates with a fixed learning rate. Previous game-theoretic equilibrium analysis suggests that system performance is close to optimal in the large population limit, as seen by the Price of Anarchy reduction. In this work, however, we reveal a rather undesirable consequence of non-equilibrium phenomena driven by population increase. As the total demand rises, we prove that the learning dynamics unavoidably become non-equilibrating, typically chaotic. The Price of Anarchy predictions of near-optimal performance no longer apply. To the contrary, the time-average social cost may converge to its worst possible value in the large population limit.
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