Coase-information theory

From the Boundary of the Firm to the Boundary of the Agent

Boundaries move when an outside dependency creates more surprise, delay, error, or misalignment than it saves in cost. The examples below turn that tradeoff into a visual simulation.

Monolith vs microservices

Database dependency

Support triage

Coding agents

Security operations

Procurement automation

Boundary test

Keep a capability outside only while the interface is worth it.

A firm pulls work inside when shared state beats market coordination. It pushes work outside when a vendor, API, or agent can carry enough state more cheaply. If the interface fails, the boundary should move again.

Same engine, different settings: surprise, action loss, latency, governance, interpretation cost, and planning drag. The phase map below colors which boundary wins as interdependence and protocol quality vary; the dashed R* = κ diagonal is the capacity threshold where finer decomposition stops paying — a soft wall: past it, the split penalty decays roughly 4× per added bit of protocol capacity.

Coase–Information Theory

It's agents all the way down

The same boundary choice — coalesce or split — repeats at every scale: a firm is an agent in a market, and is itself made of agents.

HookA firm is an agent in a market — made of agents.

Inside the firmMonolith vs microservices — one agent or many.

BridgeAn agent is a service with a control loop.

In the marketIn-house capability or a vendor dependency.

PayoffChange the interface, move the boundary.

Every scaleThe same decision — agents, services, firms, markets.

Current problems

Semantic levers

Maps to abstract levers

Monte Carlo trials

Seed

Winning boundary

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Lowest objective at current settings.

Objective

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Surprise + loss + latency + cost + planning terms.

Agility

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Quality-adjusted speed proxy.

Action quality

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Correct action share.

Boundary field

Primitive agents coalesce, split, outsource, and route through brokers

ready

Everything in-houseModules / vendors / brokersEverything outsourced

Boundary pressure

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Blueprint posture

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Transition pressure

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Agents move as the model updates boundary costs.

Option table

How to read it

Surprise is prediction error under the boundary's internal representation.
Loss is squared action error against the latent state.
State/action fidelity is a Gaussian proxy from the simulated state/action correlation.
Objective is the modeled boundary criterion, including surprise, action loss, latency, cost, and planning drag.
Agility discounts quality-adjusted state/action fidelity by latency, cost, and volatility.
Setup / Runtime / Rigid show whether blueprint depth moved cost up front, left surprise for runtime, or created brittle plans.
Blueprint depth reduces runtime surprise when the world is stable, but adds up-front delay and rigidity when the world shifts.
Use-case levers translate database, support, coding, security, and procurement language into the same abstract model variables.
Phase map colors each interdependence × protocol-quality cell by the winning boundary; the dashed R* = κ diagonal is the capacity threshold from the paper, where decision-relevant cross-boundary information equals interface capacity.
Granularity: below the threshold, boundaries are information-clean and lower interface cost favors more, smaller units (m* = √(A/B)); above it, interdependence outruns capacity and coalescence wins.
Capacity deficit: the threshold is soft. The paper's exponential interface-deficit law (rev 1.2) prices the gap exactly in the Gaussian-quadratic team: the split penalty equals the partner's information value discounted by 2^−2κ — each added bit of interface capacity cuts it ~4×.

This is a comparative design language. It identifies which cost terms should move under a boundary change; calibration against production, support, security, or finance workflow traces is the next empirical step.

Current run metrics

Phase map

Which boundary wins, by interdependence and protocol quality

idle

Each cell re-runs the current scenario at that combination of protocol quality (κ) and task interdependence (R*), colored by the winning boundary form. The dashed diagonal is the capacity threshold R* = κ from the paper: below and right of it, boundaries are information-clean and finer decomposition (m* = √(A/B)) pays; above and left, interdependence outruns interface capacity and coalescence wins. The diagonal is a band, not a cliff: per the paper's interface-deficit law, the penalty for sitting above it decays exponentially in protocol capacity (~4× per bit), so near-threshold cells are decided by the other cost terms. The crosshair marks your current levers. Re-run after changing levers to refresh the map.