Profit agents, post-AGI economics, and mechanism design

Every result below is a bounded theorem inside a toy model, not a general claim about the real economy. The point is to make the logic precise enough that counterexamples, edge cases, and mechanism changes become visible.

Assumption tree

The right way to use this tutorial is as a decision tree over assumptions, not as one hidden story about the future.

The top-level axes are:

1. capability
   • current AI
   • AGI-level agent
2. control shell
   • legal-world shell
   • crypto-native shell
   • hybrid shell
3. final sink structure
   • human-dominant
   • mixed human-agent
   • crypto or external-dominant
4. discovery and execution rails
   • open routing
   • platform bottleneck
   • governed protocol
5. ownership pattern
   • active principals
   • passive claimants
   • mixed ownership

Each theorem below should be read as:

on path B of the assumption tree, theorem T survives

That is better than pretending one starting model already matches future reality.

How to read the game theory and logic

This tutorial uses three model shapes.

1. finite choice games
   • a platform, household, or firm chooses from explicit actions
   • payoffs determine which actions survive as best responses or private optima
2. mechanism-design games
   • a rule such as a price or quota is chosen first
   • households then respond
   • the theorem asks which interior regimes are implementable
3. scalar closure models
   • the main question is not strategic deviation
   • it is whether aggregate demand can absorb aggregate output under the stated cap

The common template is:

M = (players, types, actions, payoffs, constraints, timing)

and each theorem should be read as:

under assumptions A in model M, property P holds

The properties in this tutorial are mostly:

• activation, which types or firms stay active
• private optimum, which regime maximizes platform or controller revenue
• individual stability, whether a chosen action is a best response
• closure, whether demand is at least supply
• implementability, whether a price, quota, or composed rule can induce a clearing interior regime

The notation is consistent across the experiments:

• lowercase pi or U is an individual payoff
• uppercase Pi or R is a platform, firm, or total-profit object
• iff means “if and only if”
• argmax means the action with highest payoff
• a witness is a small concrete parameter choice that makes a law visible, not a claim of proof by anecdote

The experiments also fall into four game-theoretic families:

• Experiments 1-3: two-stage platform-subscriber games with complement types and admissibility gates
• Experiments 4-7: ownership and coordination models under a one-unit household demand cap
• Experiments 8-10: price, quota, and price-plus-quota mechanism-design games
• Experiments 11-13: sink and routing models for entry ceilings and bottleneck rents

The strategic timing is also explicit:

1. Platform-profit games (Experiments 1-3)
   • complement structure and gates are fixed
   • the platform chooses a regime or extraction level
   • subscriber types choose inactive, passive, or active behavior and, when needed, effort
   • the result is an activation law or a private-optimum law
2. Closure and ownership games (Experiments 4-7)
   • ownership counts or household preferences determine the active set
   • aggregate supply and demand are computed
   • the result is a closure law or a coordination law
3. Mechanism-design games (Experiments 8-10)
   • a designer chooses a price, a quota, or both
   • household types best-respond
   • the result is an implementability law for a clearing interior regime
4. Sink and routing models (Experiments 11-13)
   • the final sink bundle and cost structure are fixed
   • firms share sink access symmetrically or through slots
   • the result is an entry ceiling law or a redistribution law

These are bounded theorems, not a full general-equilibrium theory. That limitation is part of the method. It keeps the assumptions visible enough that counterexamples and new cases can still be added honestly.

Thought experiment: a zero-employee software company

Start with a concrete picture.

Assume a software company with:

• no human employees
• one or more strong profit-seeking agents
• a control shell that can hold rights, assets, or code authority
• compute, storage, and platform access
• customers who buy software or services from the company

The agent does the operational work:

• market research
• product design
• coding
• testing
• deployment
• customer support
• billing
• iteration on the next product

In the strongest version of the thought experiment, the company can keep spawning more software products with almost no extra human labor.

That sounds like unlimited entrepreneurship, but the real question is narrower:

if software production becomes cheap, what remains scarce?

The first candidates are:

• customer attention
• distribution
• trust
• settlement rails
• legal permission, if the company touches the legal world
• compute priority
• platform ranking

But that first picture is only one case.

The analysis below now separates at least three regimes:

1. legal-world regime
   • contracts, legal shells, and regulated payment rails matter
2. crypto-native regime
   • code and settlement logic can replace some legal plumbing
   • blockspace, custody, governance, and settlement assets become scarce
3. hybrid human-agent regime
   • human buyers, agent buyers, and mixed organizations all contribute to final demand

So the correct opening correction is:

• human attention is one possible sink, not the only one
• legal contracts are one possible control shell, not the only one
• payment matters, but that can mean fiat rails, crypto settlement, or other code-native transfer layers

The question is not whether the economy is “really software”. The question is which parts of it are:

• intermediate agent-to-agent flow
• final sink demand
• and governance or settlement bottlenecks

So the analysis below does not assume that zero-human firms automatically become rich.

It studies the harder question:

under explicit assumptions, when does a profit-agent economy clear,
when does it concentrate, and what mechanisms can keep it stable?

That is why the next steps look mathematical. The point is to turn the thought experiment into bounded models where:

• the profit regions are explicit
• the failure modes are explicit
• and the coordination mechanisms can be compared exactly

Experiment 1: complement-threshold and governed-profit law

The next rabbit hole was not another software atlas refinement. It was the first bounded profit-agent game.

Assume:

• the same model capability for all subscribers
• two complement classes:
  • low
  • high
• three platform extraction levels:
  • open
  • extractive
  • closed
• and one MPRD gate that can forbid the top illicit strategy

The bounded subscriber payoff is:

and the platform payoff is:

What survives is already nontrivial.

Equal model capability does not imply equal profit thresholds.

In the checked toy economy:

• low -> {open}
• high -> {open, extractive}

So complement heterogeneity alone produces unequal activation regions.

The platform side also has an exact region law:

So a platform can rationally choose a regime that keeps only high-complement users active.

The MPRD gate changes the game without forcing profit to zero.

The bounded law is:

So the first bounded profit-agent object already says:

• same intelligence does not force equal income
• platform incentives can exclude low-complement users
• governed admissibility changes the feasible profit set, not only the labels

Experiment 2: hold-up and passive-ownership threshold law

The next deeper question is whether a platform should simply capture everything and turn users into passive claimants.

That is a two-stage game.

The platform chooses one expropriation level:

• open
• moderate
• high
• maximal

The user then chooses among:

• inactive
• passive ownership
• active profit-agent use

The bounded active payoff is:

and the user chooses:

where d is the passive dividend.

Platform revenue is:

when the user stays active, and 0 otherwise.

In the checked bounded game:

• best active effort drops:
  • open -> e3
  • moderate -> e2
  • high -> e1
  • maximal -> e0
• mode choice is:
  • open -> active
  • moderate -> active
  • high -> passive
  • maximal -> passive
• platform revenue is:
  • open -> 4
  • moderate -> 12
  • high -> 0
  • maximal -> 0

So the unique platform optimum is not maximal extraction. It is the interior regime:

moderate

That is the first bounded formal hold-up law in this line of analysis.

It says:

• higher extraction reduces productive effort
• passive ownership can become rational before full extraction
• full platform capture is not automatically the revenue-maximizing equilibrium

That is a much stronger result than the earlier prose intuition.

Experiment 3: heterogeneous-complement passive-ownership region law

The next bounded question combines the last two layers:

• heterogeneous complements
• passive ownership
• platform extraction

Assume:

• all subscribers have the same model capability
• subscribers differ only by complements:
  • low
  • high
• passive ownership is available with a bounded dividend
• the platform chooses one expropriation level:
  • open
  • moderate
  • high
  • maximal

The active payoff is:

and the subscriber chooses:

Platform revenue is:

The checked bounded result is very sharp.

Mode choice by complement class:

• low:
  • open -> active
  • moderate -> passive
  • high -> passive
  • maximal -> passive
• high:
  • open -> active
  • moderate -> active
  • high -> passive
  • maximal -> passive

So the platform collapses to exactly two viable regimes:

• open, which includes both complement classes
• moderate, which keeps only high-complement users active

The exact region law is:

Strict witnesses:

• open beats moderate at (n_low, n_high) = (5, 1)
• moderate beats open at (n_low, n_high) = (4, 1)

and both high and maximal are dominated because even high-complement users switch to passive ownership there.

This is the first bounded object in this line of analysis where complement heterogeneity, passive ownership, and platform extraction all interact at once.

It says:

• equal intelligence does not imply equal active participation
• passive ownership changes the platform’s optimal extraction region
• the relevant equilibrium is controlled by complement mix, not only by model capability

Closure and ownership (Experiments 4-7)

Experiments 1-3 established that complement heterogeneity and platform extraction create unequal activation regions even under equal capability. The next group zooms out to the macro question: if output grows faster than direct consumption, who buys the surplus?

Experiment 4: demand-closure ownership law

The next deeper question is the macro one:

if labor income falls and output rises, who buys the output?

The first clean answer is an arithmetic theorem under an explicit one-unit household demand model.

Assume:

• n active owner households
• each active owner household produces m + 1 units
• each active owner household consumes at most one unit
• b passive-beneficiary households can each consume one unit

Then:

and the exact closure law is:

So demand clears supply iff passive beneficiaries are broad enough to absorb the extra m * n units beyond owner self-consumption.

This has two sharp corollaries.

First, if there are no passive beneficiaries:

So once each active owner household produces more than one unit, concentrated claims alone fail demand closure in this model.

Second, in the double-output case:

So if each active owner household produces two units, the system needs at least one passive beneficiary for each active owner household.

This is the first generic arithmetic theorem in this post-AGI economics sequence.

It does not prove a whole macroeconomy. But it does prove something important:

• if output grows faster than direct owner consumption
• and claims stay concentrated

then broad passive claims or transfers are not optional in this model. They are mathematically required for demand closure.

Experiment 5: private-optimum versus closure phase diagram

The next bounded step integrated the v134 platform game with the new demand-closure theorem.

Assume:

• open regime:
  • low-complement households stay active and produce 1 unit
  • high-complement households stay active and produce 2 units
• moderate regime:
  • only high-complement households stay active
  • each active high-complement household produces 2 units
• each household consumes at most one unit
• n_high > 0

Then the two clearance laws are:

So once any positive high-complement population exists:

• open never clears
• moderate clears exactly when low-complement households are numerous enough

The private-optimum boundary from v134 still holds:

Putting those together gives the first integrated post-AGI platform phase diagram in the repo:

When it exists, it is the moderate regime.

Three witness regions make the structure clear:

• private-optimum / closure conflict:
  • (n_low, n_high) = (5, 1)
  • open has higher private revenue, 24 > 22
  • open fails closure
  • moderate clears
• viable moderate band:
  • (4, 1)
  • moderate is private-optimal
  • moderate clears
• no viable regime:
  • (0, 1)
  • moderate is privately optimal
  • neither open nor moderate clears

This is the deepest economics-side result so far because it formally separates:

• what the platform wants
• what keeps the economy demand-clearing

Those are not the same object.

Experiment 6: active-owner share ceiling

The next bounded step extracted the cleaner macro theorem hidden inside v135 and v136.

Assume:

• there are h total households
• n households remain active owner-principals
• each active owner household produces 2 units
• each household consumes at most 1 unit
• passive or inactive households consume 1 unit and produce 0

Then demand closure is:

which is exactly equivalent to:

So with two-unit active owners, at most half of households can remain active owners if the economy is to clear output under this one-unit demand cap.

This gives a sharper impossibility result:

So no positive-household economy in this model can keep every household as an active owner once each active owner produces two units.

Three small witnesses make the structure concrete:

• clearing case:
  • h = 4
  • n = 2
  • active-owner share 1/2
  • closure holds
• overfull case:
  • h = 3
  • n = 2
  • active-owner share 2/3
  • closure fails
• all-active failure:
  • h = 3
  • n = 3
  • active-owner share 1
  • closure fails

This is the first exact theorem in this profit-agent sequence that speaks directly to the universal-principal question.

Experiment 7: symmetric coordination law

The next bounded step turned that active-owner ceiling into a real active-versus-passive coordination game.

Assume:

• h identical households
• n active owner households
• each active owner household produces 2 units
• each household consumes at most 1 unit

Mode semantics:

• if active payoff is greater than passive payoff, every household chooses active, so n = h
• if active payoff is less than passive payoff, every household chooses passive, so n = 0
• if active payoff equals passive payoff, any n is individually stable

Then three cases survive.

Strict active preference gives no positive-household clearing equilibrium. For h > 0, if n = h, then:

Strict passive preference gives only the zero-production equilibrium:

n = 0

A nontrivial clearing equilibrium first appears only in the indifference case, where:

So the first stable nontrivial regime is a coordinated interior split, not:

• everyone active
• or everyone passive

This is the first actual coordination theorem in this profit-agent sequence.

Mechanism design (Experiments 8-10)

Experiments 4-7 showed that a coordinated interior split is needed for demand closure, but did not say how to implement it. The next group turns that coordination problem into a mechanism-design problem: can a price, a quota, or both induce the right active-passive split?

Experiment 8: uniform-price impossibility and quota implementability

The next bounded step turned the coordination question into a mechanism-design question.

Assume the same symmetric double-output economy, but now compare two coordination devices.

Uniform-price mode semantics:

• if delta > 0, all households strictly prefer active, so n = h
• if delta < 0, all households strictly prefer passive, so n = 0
• if delta = 0, households are indifferent, so any n is individually stable

Quota mode semantics:

• under delta > 0, all households want active
• a hard quota q caps active slots, so n = min(h, q)

The first exact law is a uniform-price impossibility result:

So prices alone cannot implement a positive interior individually stable regime unless they create exact indifference.

The second exact law is a quota implementability result:

So under strict active preference, a hard quota can implement an interior regime, and it clears exactly when the quota stays below the same half-share ceiling.

Three witnesses show the split:

• uniform-price failure:
  • h = 4
  • n = 2
  • delta = 1
  • not individually stable
• quota clearing:
  • h = 5
  • q = 2
  • delta = 1
  • n = 2
  • closure holds
• quota overfull:
  • h = 5
  • q = 3
  • delta = 1
  • n = 3
  • closure fails

This is the first bounded mechanism theorem in this profit-agent sequence:

• prices alone do not solve the symmetric coordination problem
• quotas can

Experiment 9: heterogeneous price-selection law

The next bounded step asked whether the pricing impossibility from v139 survives once households differ.

Assume:

• L low-complement households
• H high-complement households
• each active household produces 2 units
• each household consumes at most 1 unit
• strict surplus order:

Uniform-price semantics:

• p < a_low, both types choose active
• a_low < p < a_high, only the high type chooses active
• p > a_high, both types choose passive

So in the strict middle region:

That is the first clean contrast with v139. A single uniform price can now implement a nontrivial interior regime because the household types are different.

The exact clearing law for that middle region is:

So pricing works, but only under a sharp composition condition:

• the high-complement active group must not be a majority

This is the first exact result in this mechanism sequence showing that heterogeneous complements change the logic of the mechanism problem.

Experiment 10: price-plus-quota composition law

The next bounded step composed the two mechanisms.

Keep the same two-type economy and stay in the strict middle price region:

a_low < p < a_high

So price solves type selection by making only the high type want active.

Then add a second stage:

• a hard quota q on active high-type slots

The exact composed clearing law is:

This gives the sharp interpretation:

• price solves selection
• quota solves allocation

The witnesses make the contrast concrete:

• price-only failure:
  • L = 1
  • H = 4
  • q = 4
  • closure fails
• composed clearing:
  • L = 1
  • H = 4
  • q = 2
  • closure holds
• overfull quota:
  • L = 1
  • H = 4
  • q = 3
  • closure fails

So the deeper object is now a composed mechanism. Price alone or quota alone is not the whole story. The mechanism sequence now has:

• a homogeneous impossibility theorem
• a heterogeneous price-selection theorem
• and a price-plus-quota composition theorem

That is the clearest mechanism-design progression in this economics sequence so far.

Sinks, slots, and entry ceilings (Experiments 11-13)

Experiments 8-10 solved the coordination problem for a fixed demand model. The next group corrects a hidden assumption: human attention is not the only possible final sink. Agent-to-agent trade, crypto settlement, and external demand all contribute. These experiments ask what limits firm entry and who captures the rents.

Experiment 11: intermediate-demand multiplier law

This experiment corrects a hidden assumption in the zero-employee software-company thought experiment.

Human attention is not the only possible final sink.

Assume a scalar software-only economy with:

• gross output Y
• intermediate agent-to-agent demand share:

alpha = a / b

with 0 <= a < b

• final sink bundle:

F = H + A_term + C + X

where:

• H is human final demand
• A_term is terminal agent demand
• C is crypto or code-native settlement demand
• X is external demand

The gross-output law is:

or in scaled integer form:

The exact laws are:

So intermediate agent demand amplifies final sinks, but cannot replace them.

This is the important correction:

• human attention is not uniquely necessary
• but circular agent trade without any positive final sink does not sustain output in this model

Two witnesses make the point concrete:

• zero final sink:
  • a = 1
  • b = 2
  • F = 0
  • Y = 0
• crypto sink only:
  • a = 1
  • b = 2
  • H = 0
  • A_term = 0
  • C = 3
  • X = 0
  • F = 3
  • Y = 6

So the right way to think about the zero-employee firm is no longer:

• “does it ultimately need human buyers”

It is:

• “what positive final sinks exist”
• “what intermediate flows amplify them”
• “what settlement and governance layer makes the profits real”

Experiment 12: zero-employee company entry ceiling law

Take one explicit path through the assumption tree.

Assume:

• legal shell creation is not the binding bottleneck
• the firm can use a legal, crypto-native, or hybrid control shell
• the mixed final sink bundle is still:

F = H + A_term + C + X

• N active zero-employee firms share that bundle symmetrically
• each active firm pays operating cost c

Then total profit is:

The exact laws are:

So even if agents can create whole firms and legal formation is treated as nonbinding, unlimited technical firm creation does not imply unlimited sustainable firms.

The hard entry ceiling is set by:

• final sink size
• active firm count
• per-firm operating cost

Three witnesses make the boundary concrete:

• positive margin:
  • F = 13
  • N = 3
  • c = 4
  • Pi_total = 1
• break-even:
  • F = 12
  • N = 3
  • c = 4
  • Pi_total = 0
• overcrowded:
  • F = 11
  • N = 3
  • c = 4
  • Pi_total = -1

This is the first direct zero-employee-company ceiling theorem in this analysis. The next important splits are:

• open routing versus platform discovery bottlenecks
• symmetric access versus slot rents
• legal enforcement versus code-native enforcement

Experiment 13: discovery-slot redistribution law

What happens once zero-employee firms are easy to create but sink access is bottlenecked?

Assume:

• fixed final sink bundle:

F = H + A_term + C + X

• N active firms
• q discovery slots with 0 < q <= N
• slot holders split the sink symmetrically
• each firm pays operating cost c

Then total profit remains:

Pi_total = F - N * c

regardless of q.

What changes is the slot-holder margin. Its scaled numerator is:

M_slot = F - q * c

with exact laws:

M_slot > 0 iff F > q * c
Pi_undiscovered = -c

So discovery bottlenecks redistribute profit, but do not create new system surplus.

The witness makes the point concrete:

• F = 12
• N = 6
• c = 1
• bottleneck case:
  • q = 2
  • Pi_total = 6
  • M_slot = 10
• open routing case:
  • q = 6
  • Pi_total = 6
  • M_slot = 6

The bottleneck changes who captures the gains, not the size of the pie.

That is the clean formal version of the platform-power question for zero-employee companies.

Slot sales, admissibility, and frontier labs (Experiments 14-16)

Experiments 11-13 showed that final sinks set hard entry ceilings and that discovery bottlenecks redistribute profit without creating it. The next group adds mechanisms on top: governed slot fees, MPRD admissibility caps, and the strategic choice between closed and open deployment for frontier labs.

Experiment 14: governed execution-slot sale law

Add an explicit mechanism to the bottleneck case.

Assume:

• fixed final sink bundle:

F = H + A_term + C + X

• N candidate firms
• q governed execution slots with 0 < q <= N
• only slot holders can reach the sink
• slot holders split the sink symmetrically
• every candidate firm pays operating cost c
• each winning slot holder pays fee s_i >= 0

Let:

S = sum_i s_i

be total slot-fee revenue.

Then:

Pi_system = F - N * c
Pi_winners = F - q * c - S
Pi_controller = S

So slot sales redistribute rents between winners and the controller, but do not create new system surplus.

In the symmetric-fee case, where each winner pays the same fee s, the scaled winner margin is:

M_win = F - q * c - q * s

with exact law:

M_win >= 0 iff F >= q * (c + s)

The witnesses make the split concrete:

• F = 16
• N = 6
• q = 2
• c = 2
• low fee:
  • s = 1
  • Pi_system = 4
  • Pi_winners = 10
  • Pi_controller = 2
• high fee:
  • s = 3
  • Pi_system = 4
  • Pi_winners = 6
  • Pi_controller = 6

So once execution access is sold, the hard question is not only who gets a slot. It is how the slot mechanism transfers rent.

Experiment 15: MPRD-governed slot-cap law

What does MPRD do in that same slot-sale economy?

Assume:

• the same governed-slot case
• the controller chooses total extraction S
• the admissibility layer imposes:

0 <= S <= G

• winners stay only if aggregate winner profit is nonnegative:

F - q * c - S >= 0

Stay in the viable case:

F >= q * c

Then the governed-optimal extraction is:

S_star = min(G, F - q * c)

with positivity law:

S_star > 0 iff G > 0 and F > q * c

So MPRD does not only block the unconstrained maximum. It carves out a governed extraction region.

The two binding cases are:

• admissibility binding:
  • F = 16
  • q = 2
  • c = 2
  • G = 5
  • S_star = 5
• viability binding:
  • F = 10
  • q = 2
  • c = 2
  • G = 9
  • S_star = 6

That is the cleanest current toy answer to the question:

what does MPRD allow in a bottleneck economy?

Experiment 16: deployment-surface divergence law

This experiment switches perspective from platforms to frontier labs.

Assume a lab chooses one deployment surface:

• closed
• open

Let:

• F be the base direct revenue opportunity
• D be the extra ecosystem output created only by the open case
• k_closed, k_open be lab-side operating or safety costs
• a / m be the share of open-case output the lab captures
• e_closed, e_open be externality or governance costs counted by the social planner

Then the exact case conditions are:

lab_prefers_open iff a * (F + D) >= m * (F - k_closed + k_open)
social_prefers_open iff D >= e_open - e_closed

So the private case and the social case can diverge.

The clean divergence region is:

D >= e_open - e_closed
and
a * (F + D) < m * (F - k_closed + k_open)

Witness:

• F = 10
• D = 8
• a = 1
• m = 2
• k_closed = 1
• k_open = 1
• e_closed = 5
• e_open = 7

So one bounded answer to “what are a frontier lab’s options?” is:

• the deployment surface is a strategic choice
• and the privately optimal option need not be the socially optimal option

Household participation and routing (Experiments 17-19)

Experiments 14-16 studied the supply side: slot sellers, admissibility caps, and lab deployment. The next group takes the household and routing perspective. When agent firms are abundant, the relevant household question is not “can I own an agent?” but “does entering the active race beat passive claims?” And the relevant routing question is whether equalized protocols expand the viability region.

Experiment 17: household slot-lottery participation law

Take the household perspective on the slot economy.

Assume:

• N symmetric households
• q governed execution slots
• n households enter the active slot lottery
• stay in the congested case:

n >= q > 0

• each active winner gets gross revenue R
• each active winner pays operating cost c
• each active winner pays slot fee s
• each household can stay passive and receive outside option d > 0

Under symmetric congestion:

U_active(n) = (q / n) * (R - c - s)
U_passive = d

The exact entry law is:

U_active(n) >= d iff q * (R - c - s) >= n * d

So the slot-and-sink system has a sharp household-side active-entry ceiling.

Witnesses with q = 2, R = 9, c = 2, s = 1, d = 2:

• active entry survives at n = 5
• knife-edge at n = 6
• over-entry failure at n = 7

This means that once agent firms are abundant, the relevant household question is not only whether a household can own an agent. It is whether entering the active race beats passive claims.

Experiment 18: asymmetric-routing class-viability law

Extend the sink-access model from slot counts to route weights.

Assume:

• fixed final sink bundle F
• route class A has weight a
• route class B has weight b
• a > b > 0
• n_A > 0 active A firms
• n_B > 0 active B firms
• each active firm pays operating cost c

Then total profit is still:

Pi_total = F - (n_A + n_B) * c

But class viability is controlled by:

M_A = a * F - c * (a * n_A + b * n_B)
M_B = b * F - c * (a * n_A + b * n_B)

with dominance law:

M_A - M_B = (a - b) * F > 0

So:

Pi_B >= 0 implies Pi_A >= 0

but not conversely.

The witness at F = 14, a = 3, b = 1, n_A = 2, n_B = 2, c = 2 gives:

• M_A = 26
• M_B = -2

So routing asymmetry can make one route class viable while another fails, even when the total system surplus formula has not changed.

Experiment 19: protocol equalization expansion law

Compare favored routing with equalized routing directly.

Assume:

• n_A > 0 advantaged-route firms
• n_B > 0 disadvantaged-route firms
• each firm pays operating cost c
• fixed sink bundle F

Platform regime:

• class A gets multiplier a >= 1
• class B gets multiplier 1

Protocol-equalized regime:

• both classes get multiplier 1

For class B, define:

M_B_platform = F - c * (a * n_A + n_B)
M_B_protocol = F - c * (n_A + n_B)

The exact inclusion law is:

M_B_platform >= 0 implies M_B_protocol >= 0

and the inclusion is strict whenever a > 1 and n_A > 0.

Witness:

• F = 10
• a = 3
• n_A = 2
• n_B = 2
• c = 2
• M_B_protocol = 2
• M_B_platform = -6

So the platform-versus-protocol question is not hand-wavy dominance. It is whether equalized routing expands the disadvantaged class’s viability region.

Machine control and trust dynamics (Experiments 20-27)

Experiments 17-19 studied routing and participation for agent firms that already exist. The next group asks a different question: when should a company shift from human to machine control in the first place? The answer involves trust lag, incumbent rents, dynamic learning, and assurance packages.

Experiment 20: machine-control dominance threshold law

When should a company becoming agentic be read as an actual control upgrade rather than just a narrative?

Compare:

• human-managed shell H
• machine-managed shell M

Let:

• k_H, k_M be operating costs
• e_H, e_M be expected failure-loss burdens
• t_H, t_M be trust frictions
• a_H, a_M be auditability premiums

Then:

The exact dominance law is:

So machine control dominates exactly when reliability gain plus auditability gain covers machine cost premium plus machine trust penalty.

This is the first bounded theorem in this line of analysis that turns the slogan

machines must be more trusted and reliable than people

into an exact threshold inequality.

Experiment 21: trust-lag divergence law

True reliability and observed trust are not the same. This experiment separates them.

Compare two evaluators:

• a private chooser, who pays machine trust discount tau >= 0
• a social evaluator, who does not count tau as a real welfare loss

Then the machine conditions are:

So the divergence region is:

This means machines can be truly safer and still under-adopted.

The witness with V = 30, k_H = 8, k_M = 9, e_H = 10, e_M = 4, tau = 7 gives:

• social evaluator prefers machine
• private chooser still prefers human

So reliability advantage and social optimality can arrive before private trust fully catches up.

Experiment 22: trust-learning experimentation law

The machine-control model becomes a two-period game.

Normalize the two-period human baseline to 0.

Let:

• A be the machine’s per-period structural advantage over human control, excluding trust discount
• tau1 >= 0 be the period-1 machine trust discount
• lam >= 0 be the trust-learning gain from one successful machine period

If the machine is used successfully in period 1, period-2 trust becomes:

Assume $\tau_2 \geq 0$.

Then:

• period-1 machine premium: $A - \tau_1$

• two-period committed machine-path premium:

The exact dynamic adoption law is:

So there is a wedge region where:

In that region:

• the machine is myopically rejected in period 1
• but the two-period experimentation path is privately better

The witness with A = 5, tau1 = 6, lam = 4 gives:

• period-1 machine premium:
  • -1
• period-2 premium after one successful machine period:
  • 3
• two-period machine-path premium:
  • 2

So even when machines are better in structure, adoption can still require a trust-learning path rather than one-shot comparison.

Experiment 23: routing lock-in persistence law

The routing model becomes a two-period survival game.

Assume:

• class B is present at the start of period 1
• if class B fails in period 1, it cannot re-enter in period 2
• routing parameters stay fixed across periods

Compare:

• platform-favored routing, with disadvantaged-class margin:

M_B_platform = F - c * (a * n_A + n_B)

• protocol-equalized routing, with disadvantaged-class margin:

M_B_protocol = F - c * (n_A + n_B)

Under no re-entry:

platform persistent-B region iff M_B_platform >= 0
protocol persistent-B region iff M_B_protocol >= 0

Since:

M_B_platform >= 0 implies M_B_protocol >= 0

equalized routing weakly expands the two-period persistence region for class B.

The strict witness at F = 10, a = 3, n_A = 2, n_B = 2, c = 2 gives:

• M_B_platform = -6
• M_B_protocol = 2

So the period paths are:

• platform:
  • both -> A-only -> A-only
• protocol:
  • both -> both -> both

This is the first dynamic lock-in theorem in the routing model.

Experiment 24: incumbent-rent machine lockout law

Combine the trust-learning model with incumbent control rents.

Take a two-period adoption game with no re-entry.

Normalize the always-human path to 0.

Let:

• A be the machine’s per-period structural advantage over human control, excluding trust discount
• tau1 >= 0 be the period-1 machine trust discount
• lam >= 0 be the trust-learning gain after one successful machine period
• rho >= 0 be the incumbent controller’s per-period private rent loss if control shifts to the machine

If the machine is used successfully in period 1, period-2 trust becomes:

tau2 = tau1 - lam

Assume tau2 >= 0.

Then:

• social two-period machine premium:

2 * A - 2 * tau1 + lam

• private incumbent-controller machine premium:

2 * A - 2 * tau1 + lam - 2 * rho

The exact conditions are:

So the strict lockout wedge is:

In that region:

• the machine path is socially better
• the incumbent still rejects it
• no re-entry turns that rejection into persistent human lock-in

The witness with A = 5, tau1 = 6, lam = 4, rho = 2 gives:

• social two-period machine premium:
  • 2
• private incumbent-controller machine premium:
  • -2
• period-1 private machine premium:
  • -3
• period-2 private machine premium after success:
  • 1

So even if machine control is genuinely better and becomes easier to trust after one good period, adoption can still fail when the relevant private chooser would lose control rents.

Experiment 25: assurance-package adoption law

Turn the lockout wedge into a software-design theorem.

Keep the same two-period no-reentry adoption game, then add one assurance package.

Let:

• d >= 0 be a per-period trust lift from audit, replay, or confinement
• g >= 0 be extra period-2 trust learning from the same package
• k >= 0 be a one-time package cost

Then the package changes trust as follows:

tau1_pkg = tau1 - d
tau2_pkg = tau1 - d - lam - g

Assume tau1_pkg >= 0 and tau2_pkg >= 0.

The incumbent’s two-period packaged machine premium is:

2 * A - 2 * tau1 + lam + 2 * d + g - 2 * rho - k

So the exact package-adoption condition is:

If baseline adoption is blocked:

then the package flips rejection into adoption exactly when:

This is the exact assurance-surplus law.

The witness with A = 5, tau1 = 6, lam = 4, rho = 2, d = 1, g = 1, k = 0 gives:

• baseline private machine premium:
  • -2
• packaged private machine premium:
  • 1
• assurance surplus:
  • 3
• baseline shortfall:
  • 2

So the package closes the shortfall and flips private rejection into private adoption.

This is the cleanest current answer to the software-design question. If machine control is actually better but blocked, then the package has to:

• lower the initial trust penalty
• speed trust learning after one good deployment
• do so cheaply enough to close the exact adoption gap

Experiment 26: assurance-lever coefficient law

Separate the assurance package into distinct levers.

Keep the same two-period no-reentry adoption game.

Let:

• d >= 0 be trust lift from audit, replay, or confinement
• g >= 0 be extra period-2 learning after one successful machine period
• ell >= 0 be liability or rent offset that lowers the incumbent’s effective rent loss

Let package cost be linear:

k = c_d * d + c_g * g + c_ell * ell

Then the exact private-adoption condition becomes:

2 * A + lam + (2 - c_d) * d + (1 - c_g) * g + (2 - c_ell) * ell
>=
2 * tau1 + 2 * rho

So the private coefficients are:

• trust lift d:
  • 2 - c_d
• extra learning g:
  • 1 - c_g
• liability offset ell:
  • 2 - c_ell

This is the coefficient law.

The equal-cost corollary is the important clean case.

If:

c_d = c_g = c_ell = 1

then the condition collapses to:

2 * A + lam + d + ell >= 2 * tau1 + 2 * rho

and delayed learning g drops out completely.

That means:

• one unit of trust lift buys more private adoption than one unit of delayed learning when costs are equal
• one unit of liability offset has the same raw private weight as one unit of trust lift

The witness at A = 5, tau1 = 6, lam = 4, rho = 2 starts from baseline private premium -2.

Under equal unit costs:

• trust-lift-only package d = 2, g = 0, ell = 0 gives packaged premium 0
• learning-only package d = 0, g = 2, ell = 0 gives packaged premium -2
• liability-only package d = 0, g = 0, ell = 2 gives packaged premium 0

So predeployment trust lift and liability structure can flip adoption where delayed learning alone cannot.

Experiment 27: assurance-subsidy implementation law

Compare social versus private package choice directly.

Keep the same two-period no-reentry assurance model.

Let:

• d >= 0 be trust lift from the package
• g >= 0 be extra period-2 learning
• k >= 0 be package cost
• rho >= 0 be incumbent rent loss from machine control
• s >= 0 be an adoption subsidy paid only if the incumbent adopts the machine path with the package

Then:

• social packaged machine premium is:

P_social = 2 * A - 2 * tau1 + lam + 2 * d + g - k

• private packaged machine premium is:

P_private = 2 * A - 2 * tau1 + lam + 2 * d + g - k - 2 * rho

So the exact conditions are:

social package choice iff 2 * A + lam + 2 * d + g >= 2 * tau1 + k
private package choice iff 2 * A + lam + 2 * d + g >= 2 * tau1 + 2 * rho + k

The minimal implementing subsidy is therefore:

On the strict divergence wedge:

2 * tau1 + k <= 2 * A + lam + 2 * d + g < 2 * tau1 + 2 * rho + k

the package is socially preferred but privately rejected, and:

This is the exact implementation law.

The witness with A = 5, tau1 = 6, lam = 4, rho = 2, d = 1, g = 0, k = 1 gives:

• P_social = 3
• P_private = -1
• s_star = 1

So the package is socially worth deploying, privately blocked, and one unit of subsidy is exactly enough to implement it.

References inside this repo

• Tutorial 6: MPRD and the Algorithmic CEO
• Tutorial 27: Verifier-compiler loops