Braess's Paradox

What is Braess's Paradox?

Braess's Paradox is the counter-intuitive observation that removing capacity from a network, can paradoxically increase the network's overall performance. Discovered by mathematician Dietrich Braess in 1968, this principle reveals a fundamental conflict between individual incentives and the collective good.

It applies to any decentralized network where users make individual routing decisions—from road traffic and data packets to electrical grids. The paradox arises when a new, seemingly superior path diverts flow in a way that creates new system-wide bottlenecks, leading to a worse outcome for every single user.

Classic Example: Traffic Flow 🚗

The canonical example involves traffic. Each driver, acting selfishly, chooses the route they believe is fastest. The system eventually settles into a Nash Equilibrium, a stable state where no single driver can improve their travel time by unilaterally changing their route. The paradox shows how adding a "shortcut" can lead to a new, but worse, Nash Equilibrium.

Modern Example: Power Grids ⚡️

In power systems, electricity flow follows the laws of physics (specifically, the path of least impedance), not driver choice. An Optimal Power Flow (OPF) calculation finds the most economic dispatch of generators to meet load while respecting grid constraints. The paradox can occur when adding a new transmission line creates loop flows and congestion. This may force the system operator to perform a costly redispatch—turning down cheap generators and turning up expensive ones—to avoid overloading lines, paradoxically increasing the total cost of electricity.