Thank you for visiting this site. This article covers “Braess’s Paradox.”
Traffic is congested because there aren’t enough roads. Build more roads and the problem is solved — this commonsense reasoning can, in practice, make congestion significantly worse. Discovered in 1968 by German mathematician Dietrich Braess, this paradox has profound implications for urban planning and network design.
Understanding It with a Simple Example
Suppose 4,000 cars need to travel from A to B. There are two routes.
Route 1: A → waypoint X → B. The A→X leg is a congested road where travel time equals (number of cars / 100) minutes. X→B is a fixed 45 minutes.
Route 2: A → waypoint Y → B. A→Y is a fixed 45 minutes. The Y→B leg is a congested road where travel time equals (number of cars / 100) minutes.
At equilibrium, 2,000 cars take each route and every driver’s journey takes 20 + 45 = 65 minutes.
Now suppose a bypass road connecting X and Y directly is built (travel time essentially 0).
Every driver now chooses A → X (congested but only 40 min with all 4,000) → Y (0 min) → B (congested but only 40 min with all 4,000). Why? Because A→X at 20 min beats A→Y at 45 min, and Y→B at 20 min beats X→B at 45 min.
With everyone on this route, the total journey time becomes 40 + 0 + 40 = 80 minutes.
“All we did was add a convenient road, yet everyone’s travel time increased from 65 minutes to 80 minutes.” That is Braess’s Paradox.
The key point is that using the bypass is each driver’s free choice. Nobody is forced. Yet the result of every individual making a rational decision is that everyone suffers.
Why Does This Happen?
The cause is that each driver choosing “the shortest route for themselves” leads to a state that is suboptimal for everyone.
Without the new road, traffic spread across two routes and reached equilibrium. But with the new road, the individually optimal route converges to one path, intensifying congestion.
This is what game theory calls a “mismatch between Nash equilibrium and Pareto optimum.” The outcome where every driver chooses their individually optimal route (Nash equilibrium) is not the best outcome for everyone collectively (Pareto optimum). It is structurally identical to the Prisoner’s Dilemma.
Crucially, not using the bypass is individually irrational. If everyone else uses it and you alone don’t, only you lose out. Even knowing that everyone would be better off if nobody used the bypass, individual rational decision-making prevents that outcome.
Real-World Cases
Braess’s Paradox is not just theoretical — it has been confirmed in reality.
In New York, closing 42nd Street in 1990 reportedly improved surrounding traffic contrary to expectations. In Seoul, South Korea, demolishing the elevated expressway that ran over Cheonggyecheon (carrying 160,000 vehicles daily) in 2003 and restoring the stream likewise improved traffic conditions in the area. In Stuttgart, Germany, opening a new road worsened congestion, and closing it later improved the situation.
From these cases, the paradoxical approach of “reducing roads to ease congestion” has become known in urban planning as “traffic evaporation.” When road capacity is reduced, some drivers switch to public transport or shift their departure times, and the total volume of traffic decreases.
It Applies to All Networks
Braess’s Paradox applies not just to roads but to any network.
In communications networks, adding a new link can reduce overall throughput. In power grids, adding a new transmission line can lower overall efficiency.
Adding resources to a network does not necessarily lead to improvement — this lesson is critically important for anyone involved in system design.
The same dynamic appears in sports. Adding a brilliant shooter to a basketball team can sometimes lower the team’s overall performance, because other players flood that shooter with passes and the team’s movement becomes one-dimensional. In a broad sense, this too shares the structure of Braess’s Paradox.
Summary
This article covered “Braess’s Paradox.”
This paradox completely overturns the naive intuition that more roads means less congestion, teaching us that in complex systems, simple addition does not always work.
To return to the full list of paradoxes, follow the link below.
Thank you for reading. We hope to see you in the next article.
