Act 3 · The Machine · Station 08
The centralization frontier
The λ/α phase diagram at last: drag AI capability and watch the region where decentralization wins shrink.
Every parameter on this plane, you have already felt. λ is how much coordination across managers is worth — the reason a price, a single pointer, was ever worth watching in the first place. α is the man on the spot: how much a manager can still do alone, on local knowledge, if nobody coordinates them at all. Codifiability decides which world you're even in — whether local knowledge can reach headquarters at all. And K̄ is how much of it headquarters can actually act on once it arrives. Put all four on one plane, and here is Brynjolfsson & Hitzig's answer to Hayek.
With N = 6 managers and capacity K̄ = 3, centralization needs λ > 3.40 at α = 0.50.
Drag or click the plane to move the probe; with it focused, use the arrow keys (hold Shift to move faster).
What to try
- Raise K̄ and watch the brass "delegate" region shrink — this is the whole story of Station 7's four channels, replayed as geometry.
- Turn codifiability off and watch the plane go brass edge to edge — Hayek's whole-plane answer, undisturbed by how large λ or how small α gets.
- Find the flip point for your own café chain: pick an α for how much a store manager can improvise, and see how large coordination value λ has to get before headquarters should take over.
The condition the curve above is drawn from, stated for N interdependent managers and a headquarters that can only act on K̄ of them per decision cycle:
"If λ > (N/K̄)(1 + ((N + 1)/(N − 1))α), then centralized ownership yields higher surplus than decentralization. […] When K̄ = N the condition simplifies to λ > 1 + ((N + 1)/(N − 1))α (recovering λ > 1 + 3α when N = 2). As K̄ increases—for example via AI-enabled processing—the sufficient condition for centralization becomes easier to satisfy." Brynjolfsson & Hitzig, 2025, Proposition 3, §5.1