// load balancing · game theory · selfish routing
Braess's Paradox — Why a Faster Link Can Slow Everyone Down
A zero-cost shortcut between two server pools causes every request to pile onto the same congested path
Nash Latency (actual)
1.50ms
Social Optimum
1.50ms
best if coordinated
Price of Anarchy
1.00×
no overhead
Active Paths
2
balanced split
Load Balancer Topology
Nash = Social Optimum
load-sensitive (latency ∝ traffic)
fixed latency (network hop)
zero-cost internal link (paradox)
active request flow
Load (N): 2.0
What's happening right now
🌐 BGP & Internet Routing Networking
BGP lets every Autonomous System pick the cheapest route for itself — no global coordinator. When a new peering link opens between two networks, every AS independently reroutes through it. The result can be a global latency regression for paths that never used the link. Network engineers sometimes deliberately withdraw "free" peering links to restore balance — removing capacity to improve performance. Classic Braess.
⚡ Electrical Power Grids Physics
Current doesn't get routed — it follows Kirchhoff's laws, splitting across paths according to resistance. This is mathematically identical to selfish routing: each electron takes the path of least resistance independently. Adding a new transmission line between two nodes can shift load distribution and overload existing lines. The European interconnected grid has observed this directly — new capacity causing unexpected congestion elsewhere.
🤖 Jevons Paradox & LLMs AI
OpenAI cuts token prices 80%. Anthropic does the same. Everyone expects cloud bills to drop.

They go up. Because now it's cheap enough to stuff entire codebases into context, chain five agents together, re-run evals on every commit. The cheaper the resource, the more liberally you use it — so total consumption rises. Jevons Paradox: efficiency gains don't reduce usage, they expand what you think is worth doing. Same story as Braess — the "free" path changes behavior in ways that erase the original benefit.
Baseline state: two server pools, balanced traffic, selfish routing matches the social optimum. Add the zero-cost internal link to trigger the paradox →
Braess (1968) · Roughgarden & Tardos (2002)