Adding a shortcut can make everyone slower: individual rationality leads to collective inefficiency in network routing
In 1968, Dietrich Braess showed that adding a road to a traffic network can paradoxically increase everyone's travel time. When drivers selfishly choose the fastest route for themselves (Nash equilibrium), they may collectively achieve a worse outcome than if they cooperated. The paradox arises because each driver's choice changes the congestion experienced by others — an externality not accounted for in individual decisions.
The classic network has 4 nodes: Start (A), End (D), and intermediate nodes (B, C). Two routes always exist: A→B→D and A→C→D. Edge costs are either fixed (constant time regardless of traffic) or variable (time = base/T_ref × traffic). The shortcut edge B→C, when added, creates a new route A→B→C→D that uses both variable-cost edges. This route seems attractive to individual drivers but increases congestion on both variable edges, degrading total system performance. At Nash equilibrium, no driver can reduce their travel time by unilaterally switching routes.
Braess's paradox has been observed in real cities: closing 42nd Street in NYC improved traffic; Seoul demolished an elevated highway and restored a river, improving flow. Beyond traffic, the paradox appears in network routing (internet traffic), power grids, sports team strategies, and mechanical spring systems. The "Price of Anarchy" metric quantifies how much worse selfish behavior is compared to social optimum, guiding infrastructure investment and toll policy design.
Start with the Classic Braess preset. Observe the travel time without the shortcut (A→B→D and A→C→D). Then toggle the shortcut ON and press Run to apply the current settings and animate the resulting flow. Adjust driver count and edge costs to see when the paradox emerges and when it doesn't. The Price of Anarchy compares average selfish travel time against the average social optimum. Compare "Mild Paradox" (small effect) vs "Severe Paradox" (large effect) vs "No Paradox" (shortcut is unused or harmless) presets to understand the conditions.