Braess’s Paradox, explained.
Braess's Paradox shows that adding a route can make everyone's journey slower when travelers independently choose routes that benefit themselves.
Why it happens
A shortcut changes incentives throughout the network. Each driver can find it personally attractive while the resulting combined traffic congests shared roads. The individually stable routing pattern need not minimize total travel time.
Individual route choices can make a new connection harmful at equilibrium.
Read the result
Toggle the shortcut while keeping demand fixed, then compare equilibrium journey times. Try other demand levels: the paradox depends on congestion and route costs rather than appearing in every network.
A worked example
A shortcut that slows the commute
In the classic teaching network, 4,000 drivers split between two routes and take 65 minutes.
A free connecting road makes a different route attractive. If everyone follows it, the two congestion-sensitive segments each take 40 minutes.
The new equilibrium takes 80 minutes. A new option changed collective behavior enough to outweigh its apparent benefit.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
In the classic four-node toy network, two outer links each cost flow/100 minutes, two fixed links each cost 45 minutes, and the shortcut costs zero. Route flows are solved by enumerating symmetric equilibrium choices. The chart compares equilibrium travel time with and without the shortcut over demand.
Where this idea is useful
A practical use
Road planners can test whether a new link changes route incentives rather than only adding capacity.
A common misconception
“More roads always reduce travel time.”
Additional capacity can help, but an added connection can also change incentives. Network design and routing behavior must be assessed together.
What this explanation leaves out
- The model assumes identical travelers and deterministic travel-time functions; real road networks require calibration.
Does closing a road always help?
No. This example demonstrates a possibility under particular congestion costs. A real closure requires an assessment of the actual network and demand.
Could an individually attractive shortcut overload the resources everyone shares?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.