Braess's Paradox : a 1968 proof that adding capacity to a network can make every path through it worse. It shows up in roads, electricity grids, and game theory.
In 2002, Seoul demolished a highway running through the city center.
Traffic engineers braced for chaos. Instead, congestion got better. They’d accidentally been making things worse for years just by having that road exist.
Same thing happened in Stuttgart. And in a few US cities. And the weird part this isn’t a coincidence or bad city planning. There’s a theorem that explains exactly why, proved mathematically in 1968 by a German mathematician named Dietrich Braess.
The setuph2
Imagine a network with two paths from A to B. Some links slow down under load. Others have a fixed cost regardless of traffic.
When both types coexist, traffic self balances. Overload one path, it slows, requests shift to the other. It’s almost elegant.
Now add a zero-cost shortcut connecting the middle of one path to the middle of the other.
Every agent, every car, every request looks at the new option and independently concludes: this is cheaper, I’ll take it. And they’re right. Individually.
But when everyone makes that same call, the load sensitive links on both ends absorb everything. The “free” shortcut funneled all traffic through the two most congestion prone parts of the network.
You can play with this below :- add the shortcut and watch what happens to latency:
The game theory parth2
What makes this interesting isn’t the networking. It’s that nobody made a wrong decision.
Every routing choice was locally rational. The system landed in a state where no individual can improve their outcome by switching ; that’s a Nash Equilibrium. But collectively, everyone is worse off than if the shortcut had never existed.
Game theorists have a number for how bad this can get: the Price of Anarchy. It’s the ratio between what selfish routing actually delivers vs. what a coordinator could achieve. For simple networks like this, it tops out at 4/3 — about 33% worse. For more complex latency functions, it gets uglier.
This same structure shows up everywhere. The Prisoner’s Dilemma is the textbook version — two people making individually rational choices and landing in a collectively bad outcome. The Tragedy of the Commons is the same idea applied to shared resources. Arms races. Ad auctions. Traffic.
Braess’s Paradox is just one of the cleaner examples of how “every agent is rational” doesn’t imply “the system behaves rationally.”
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