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The Braess Paradox

Build a new road and traffic gets worse. When does adding capacity hurt?

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Characterization

In 1968, the German mathematician Dietrich Braess proved a result that defied engineering intuition: adding a new road to a traffic network can increase the total travel time for all drivers. The paradox arises because each driver independently chooses the fastest route, and the new road can create a Nash equilibrium in which everyone is worse off. The phenomenon is not merely theoretical. When 42nd Street in New York City was closed for Earth Day in 1990, traffic in midtown improved. When the Cheonggyecheon Expressway in Seoul was demolished in 2003 and replaced with a park and stream, traffic flow in the surrounding area did not worsen — it improved. When a new bypass was added in Stuttgart, journey times increased. Braess's paradox occurs in any network where individual optimisation conflicts with system-level performance — not only roads but also power grids, communication networks, mechanical spring systems, and even basketball team dynamics. Tim Roughgarden's work has connected the paradox to the Price of Anarchy, showing that the paradox is a specific instance of the general phenomenon in which selfish behaviour degrades social welfare. The general conditions under which adding capacity helps versus hurts remain an active area of research. The Academy hosts the Braess Paradox in the World School because it is the simplest demonstration of a deep truth: in interconnected systems, more can be less, and helping can hurt — and knowing when requires mathematics we are still developing.

Lineage

Dietrich Braess, "Über ein Paradoxon aus der Verkehrsplanung," Unternehmensforschung 12, 1968; English translation in Transportation Science 39(4), 2005. The 42nd Street observation during Earth Day 1990 documented by Michael Gastner. The Cheonggyecheon expressway removal in Seoul, 2003. Tim Roughgarden, "On the Severity of Braess's Paradox," FOCS, 2003. Joel Cohen and Paul Horowitz, "Paradoxical Behaviour of Mechanical and Electrical Networks," Nature 352(6337), 1991. Brian Skinner, "The Price of Anarchy in Basketball," Journal of Quantitative Analysis in Sports 6(1), 2010.

Quests

Three quests — one for each archetype. Choose the one that fits your way of taking up the discipline.

  • Construct a network — on paper, in code, or with a physical model — that exhibits the Braess Paradox. Define the nodes, edges, latency functions, and traffic demand. Show that when a specific link is removed, the equilibrium travel time decreases for all users. Compute the Price of Anarchy for both the original and reduced networks. If possible, identify the general conditions under which your network triggers the paradox and test whether adding a different link would avoid it.

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  • Find and document a real-world instance of the Braess Paradox — a case in which removing capacity improved system performance, or adding capacity made it worse. This may come from transportation (the 42nd Street closure, the Stuttgart road removal, the Seoul Cheonggyecheon restoration), electrical engineering, internet routing, or another domain. Describe the system, the intervention, and the counterintuitive outcome. If a published account exists, cite it; if you observe it firsthand, document your observation.

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  • Explain the Braess Paradox to a reader who has never encountered it. Begin with Braess's 1968 paper, give a concrete numerical example, describe at least one real-world instance, and connect the paradox to Roughgarden's work on the Price of Anarchy and to the broader principle that in interdependent systems, more options can produce worse outcomes. Cite Braess, Roughgarden, and at least one empirical study.

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