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algorithms

did you know a new road can make everyone's journey slower?

a shortcut for each driver can become a bottleneck for everyone.

the idea at a glance

65 → 80 min

before → after the shortcut

a worked toy network with 4,000 drivers and congestion-dependent travel times.

  1. two balanced routes
  2. one new shortcut
  3. everyone takes longer

the idea

sometimes adding a road makes every driver's journey slower, even without adding more cars. the new shortcut changes everyone's route choices, concentrating traffic in the wrong places. this is Braess's paradox.

how it works

suppose 4,000 drivers choose between two routes. each has one 45-minute road and one road taking x/100 minutes, where x is its traffic. an even split gives everyone 45 + 20 = 65 minutes.

go deeper

how can an extra option hurt?

sometimes adding a road makes every driver's journey slower, even without adding more cars. the new shortcut changes everyone's route choices, concentrating traffic in the wrong places. this is Braess's paradox.

drivers usually choose the quickest route available to them. but their choice changes how quick that route is for other drivers. individually sensible decisions need not produce the best shared outcome.

build a tiny imaginary road network

suppose 4,000 drivers choose between two routes. each has one 45-minute road and one road taking x/100 minutes, where x is its traffic. an even split gives everyone 45 + 20 = 65 minutes.

now connect the two variable-time roads with a zero-minute shortcut. all 4,000 drivers can end up using both, taking 40 + 40 = 80 minutes. changing alone to an old route would take 85, so nobody has an incentive to leave.

why does the worse outcome stick?

80 minutes is an equilibrium in this toy network: a driver cannot improve their trip by switching alone. the original balanced outcome was better collectively.

before: 45 + 2,000/100 = 65 min; after: 4,000/100 + 4,000/100 = 80 min

does this mean roads are always bad?
  • no. the result depends on the network, congestion, and route choices. many extra connections help; some create this particular trap.
  • route guidance, tolls, or access rules can change incentives. network design has to account for how people respond.
sources & further reading

concepts: Braess's paradox · game theory · networks

2 minute read