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Your Universe of Digital Possibilities
A diamond of roads carries four thousand selfish drivers at a 65-minute equilibrium. You get to build the shortcut everyone wants: a free, instant connector between the two halfway points. Every driver rationally switches to use it — and every commute in the city rises to 80 minutes.
At equilibrium every route anyone uses costs the same, and no unused route is cheaper — so no driver can gain by switching alone. On Braess’s diamond, 4 000 drivers split evenly at 20 + 45 = 65 minutes; open a free connector and the route through it (40 + 0 + 40 at full use) undercuts both old roads for each driver, until all 4 000 take it and every commute is 80. Both states are stable; the second is worse for everyone.
The ratio of the total travel time at the selfish equilibrium to the least total any routing could achieve. With latencies linear in the flow it never exceeds 4/3, on any network. On the diamond it is 1 while the connector is used by everyone or by no one, rises with demand, and touches 4/3 exactly at 4 500 drivers (90 against 67.5 minutes); at 4 000 it is 80/64.69 = 1.237. A toll of 22.5 minutes on the connector alone — the extra delay a connector driver imposes on everyone else, beyond what an old-road driver does — moves the equilibrium onto the optimum (Pigou’s fix).
Here the forecast is not a distribution: both equilibria are solved exactly at your demand before the first drag, and the needle must land on them — the edition’s band, solved instead of counted.
Individually rational choices can settle into a stable state that is worse for every single chooser, and adding capacity can be the trigger. Selfishness costs at most a third for linear latencies, and this diamond attains it. The Jam owns how traffic moves; The Hub owns how networks are shaped; and The Truel, next, plays the same lesson at the scale of three — the obvious move harms the mover.