Braess's Paradox: The Road That Slows Everyone

Adding a FREE road increases everyone's commute. Total cars: 100
Road Network (S → T)
Congestion road (time = n×t₀)
Constant road (45 min)
Free road V→W (0 min)
New Road Toggle
Free road: ABSENT
Traffic Split (without new road)
All via S→V (top) All via S→W (bottom)
50 cars top / 50 cars bottom
Travel Times (minutes)
Route S→V→T —
Route S→W→T —
Avg Commute —
Parameters
t₀ = 1 min/car (congestion cost)
T = 45 min (constant road time)
Without new road Nash: 50+45 = 95 min
With new road Nash: 100+0+100 = 200 min
Social optimum: 50+45 = 95 min