Coasean Disintegration: Cooperative Game Theory of the Firm under Autonomous Intelligence

In 1937 Ronald Coase asked a question that sounds almost naive: if markets allocate resources so well through prices, why do firms exist at all? Why do millions of people work inside hierarchies where a manager, not a price, tells them what to do?

His answer was transaction costs. Using the market is not free: you have to discover what the relevant prices are, and negotiate and conclude a separate contract for each exchange. A firm expands until the marginal cost of organising one more transaction inside equals the cost of carrying it out on the open market:

$$MC_{\text{internal}}(n) = MC_{\text{market}}$$

Coase also named what stops firms from growing forever: decreasing returns to the entrepreneurial function, rising organisational overhead as headcount grows, and a loss of agility relative to small, nimble firms. For nearly a century the balance favoured large hierarchies, because discovering, contracting, verifying and enforcing deals on the market was very expensive. Bureaucracy burned capital, but scale and proprietary distribution paid for it.

The paper argues that autonomous AI breaks that balance through two shocks at once. Market transaction costs collapse toward zero, and high-order cognitive work that used to sit in specialised departments (legal auditing, architecture, software, data science, financial modelling) becomes executable by one person with autonomous tools. The usual reading treats AI as an efficiency booster bolted onto existing companies. The paper’s claim is stronger: modelled as a cooperative game, the firm does not just become leaner, its mathematical Core ceases to exist.

The firm as a cooperative game

The paper recasts the firm as a cooperative game with transferable utility. There is a set of agents $N = \{1, \dots, n\}$ with $n \ge 2$, the human capital of the enterprise. Any group of them, $S \subseteq N$, is a coalition: a team, a department, a spinoff. The whole set $N$, the grand coalition, is the integrated corporation. Each coalition can generate some value, and the question cooperative game theory asks is whether there is a way to split the grand coalition’s value so that no group would rather leave.

Production is complementary: two disjoint groups working together produce at least as much as working apart. For tractability, each agent has a baseline talent endowment $f_i > 0$, and inside the grand coalition they enjoy an organisational synergy $\gamma \ge 1$, so gross output is $F(N) = \gamma \sum_i f_i$.

The cost side is where the model has teeth. In a group of size $|S|$ the number of possible pairwise communication channels is $|S|(|S|-1)/2$, which grows with the square of headcount. Drawing on Brooks’ Law and Williamson’s governance frictions, the paper assumes coordination, alignment, meetings, monitoring and rent-seeking grow super-linearly with size:

$$\tau(S) = c \, |S|^{\beta}, \qquad c > 0,\ \beta > 1$$

Here $c$ is the bureaucratic friction coefficient (approval tiers, compliance, politics) and $\beta$ is the elasticity of organisational diseconomy, typically around 2 because of the pairwise links. For a single person the friction is just $c$, which the paper treats as approximately zero: one person has nobody to coordinate with.

What a coalition can actually distribute is its gross value minus this friction, floored at zero:

$$\tilde{v}(S) = \max\{0,\ v(S) - c\,|S|^{\beta}\}$$

Before AI, the paper argues, an isolated worker produced almost nothing on their own, because physical capital, licences and distribution belonged to the firm. With every singleton worth roughly zero and the grand coalition worth a great deal despite heavy bureaucracy, the game is balanced and the Core is non-empty. The corporate manor was stable.

The AI shock: two propositions

AI enters as a cognitive capital multiplier $A \ge 1$ that grows exponentially over time, $A(t) = A_0 e^{\mu t}$ with $\mu > 0$. The central modelling choice is that this multiplier does not act the same way at every scale.

Proposition 1 (singleton leverage explosion). A solo builder directing autonomous pipelines has no interpersonal channels and therefore no agency loss. AI multiplies their talent directly:

$$\tilde{v}_A(\{i\}) = A \, f_i$$

The paper extends this to micro-coalitions much smaller than the firm.

Proposition 2 (corporate absorption drag). Inside a large firm, deploying AI runs through legal compliance, vendor risk review, committees, security guardrails and middle-management consensus. That discounts the multiplier by an absorption factor $\eta \in (0,1)$. And since $n$ humans still need to be governed, paid and politically reconciled, the coordination overhead is untouched:

$$\tilde{v}_A(N) = \eta \, A \, \gamma \sum_{i=1}^{n} f_i \; - \; c\, n^{\beta}$$

So AI raises the outside option of every individual at full strength, while raising the firm’s value only at a discount and leaving its internal friction where it was. Everything that follows comes from this asymmetry.

Theorem 1: the Core empties

A pay schedule, a vector $x$ of salaries, bonuses and equity, is an imputation if it spends exactly what the firm earns (budget balance) and gives everyone at least what they could earn alone (individual rationality). The Core is the set of imputations that no sub-group can profitably block by walking out together. If the Core is empty, then whatever compensation policy the firm proposes, some coalition does better by leaving.

The tool for testing this is the Bondareva–Shapley theorem (Bondareva 1963; Shapley 1967): a game has a non-empty Core if and only if, for every balanced collection of coalitions with weights $\lambda_S$, the weighted sum of coalition values does not exceed the value of the grand coalition. The paper needs only the simplest balanced collection, all the singletons, each with weight 1. That gives a necessary condition for the firm to be stable: the sum of everyone’s standalone value must not exceed what the firm can pay out.

Theorem 1 (Coasean disintegration and Core emptiness). Assume symmetric talent, $f_i = f_0 > 0$.

1. If $\eta\gamma \le 1$, meaning institutional inertia weakly dominates organisational synergy, the Core is empty for every $A \ge 1$.
2. If $\eta\gamma > 1$, there is a finite critical threshold

$$A^{*} \equiv \frac{c\, n^{\beta}}{n f_0 (\eta\gamma - 1)}$$

such that for every $A > A^*$ the Core of the firm is empty.

The proof sketch is short. The singletons are together worth $n A f_0$; the firm is worth $\eta A \gamma n f_0 - c n^{\beta}$. Stability requires the first to be at most the second, which rearranges to

$$c\, n^{\beta} \le A \cdot n f_0 (\eta\gamma - 1)$$

If $\eta\gamma \le 1$ the right-hand side is never positive while the left-hand side is, so the condition always fails. If $\eta\gamma > 1$ the condition holds exactly when $A \le A^*$. Once $A$ passes $A^*$, any pay schedule that gives each person at least their outside option must pay out more in total than the firm has, contradicting budget balance. No stable imputation exists.

The formula is worth reading closely. The threshold rises with bureaucratic friction $c$ and headcount through $n^{\beta - 1}$, and falls as the firm’s net synergy advantage $\eta\gamma - 1$ grows. Read at face value: a firm survives the AI shock only if, after the absorption discount, its synergy still beats what its people could do alone by enough to pay for its coordination costs.

Corollary: the optimal firm is one person

Coase defined the optimal firm size as the headcount that maximises net surplus per person. In this model, average net surplus is

$$\frac{\eta A \gamma n f_0 - c\, n^{\beta}}{n} = \eta A \gamma f_0 - c\, n^{\beta - 1}$$

Its derivative in $n$ is $-c(\beta - 1)n^{\beta - 2}$, strictly negative whenever $c > 0$ and $\beta > 1$. So Corollary 1.1 states that the unconstrained optimal size collapses to the singleton boundary, $n^*(A) = 1$ for all $A \ge 1$. Super-linear communication overhead makes every additional head a net loss per capita.

Theorem 2: why firms unravel through layoffs, not pay rises

If people are worth more outside, why don’t firms just pay them more? The paper’s answer runs through the gap between what a person contributes and what a hierarchy is willing to pay.

The Shapley value $\phi_i$ is a person’s average marginal contribution across every order in which the coalition could have formed:

$$\phi_i(\tilde{v}_A) = \sum_{S \subseteq N \setminus \{i\}} \frac{|S|!\,(n - |S| - 1)!}{n!} \Big[\tilde{v}_A(S \cup \{i\}) - \tilde{v}_A(S)\Big]$$

For a high-capacity producer, adding them to any coalition raises its output by something of order $A$, so the paper takes $\phi_i \propto A f_i$: their theoretical equilibrium wage grows linearly with technology.

Real hierarchies do not pay Shapley values. Personnel economics (Frank 1984; Lazear and Shaw 2007; Baker, Jensen and Murphy 1988) documents systematic wage compression, used to limit internal friction, preserve status equity and satisfy union or regulatory constraints. The paper models it as

$$w_i = \bar{w} + \theta(\phi_i - \bar{w}), \qquad 0 < \theta \ll 1$$

where $\bar{w}$ is the median corporate wage and $\theta$ the compression elasticity. The defection gap is the difference between a person’s autonomous outside option and their corporate wage:

$$\Delta_i(A) \equiv A f_i - \Big[\bar{w} + \theta(\phi_i - \bar{w})\Big], \qquad \frac{\partial \Delta_i}{\partial A} \approx (1 - \theta) f_i > 0$$

Because $\theta$ is small, technological progress widens the gap steadily for high-talent agents. Theorem 2 (the adverse-selection unraveling spiral) describes what happens past $A^*$:

1. The top producers, those with a positive defection gap, leave to work as autonomous producers.
2. Their departure lowers gross firm output to what the remaining coalition can produce.
3. Bureaucracy cannot shrink instantly (real estate, compliance, middle management), so administrative cost per remaining head rises.
4. To avoid insolvency the firm turns to broad layoffs and salary freezes, lowering wages for the second tier.
5. That pushes the defection gap positive for the median producers too, and the firm unravels faster.

The paper presents this cascade as a sequence of steps rather than a full equilibrium derivation, and its Shapley scaling is an approximation, not a closed-form result.

The macro picture: intensive versus extensive margins

The paper uses the model to step into a live debate in AI macroeconomics. Acemoglu (2024, NBER WP 32487) uses Hulten’s theorem to bound AI-driven total factor productivity gains at no more than 0.66% over ten years, arguing that only about 4.6% of tasks can be profitably automated. The paper’s objection is that this is an intensive-margin calculation: it sums cost savings on automated tasks inside a fixed organisational envelope, as if AI only reduced costs inside existing corporate boundaries.

Aghion, Antonin and Bunel (2024) instead stress the extensive margin, where general-purpose technologies work through the idea production function (Romer 1990). On the paper’s reading, when AI empties the firm’s Core, human capital is not destroyed but ejected into the market, where displaced knowledge workers start micro-enterprises and multiply the number of experiments. It points to two pieces of supporting data: US Census Bureau high-propensity business applications rising from an annual baseline of 1.2M (2010–2019) to plateaus of about 1.8M a year after 2022; and revenue per employee of roughly USD 1.5M to USD 2.0M at Alphabet and Meta, against over USD 7.5M ARR per employee at AI-native micro-firms such as Midjourney (about 40 employees, USD 300M+ ARR), which the paper describes as running with near-zero internal friction ($\beta \to 1$). These figures are cited as consistent with the mechanism; the paper does not estimate the model on them.

What it implies, and what it costs

The paper does not present disintegration as a free lunch. A corporate wage, it argues, was a variance-reduction subsidy: the firm smoothed cash flow and paid a predictable mean in exchange for keeping the right-tail upside $\phi_i - w_i$. Leaving the firm means taking on the full heavy-tailed distribution of the market. It cites BLS survival data (20% of new ventures fail in year one, 50% by year five, 70% by year ten); Hamilton (2000), who found the median entrepreneur earns 35% less over ten years than a comparable wage worker; and Hall and Woodward (2010) on returns whose mean is driven by a thin right tail. And with Herbert Simon’s line that “a wealth of information creates a poverty of attention”, it argues that when production costs approach zero, production stops being a moat and rent moves to distribution access, proprietary data pipelines and verified reputation.

The conclusion is that the current wave of corporate downsizing is not a temporary aberration but a structural phase transition: as AI leverage passes $A^*$, the Coasean firm dissolves into autonomous, high-leverage producers who bear the market’s variance and capture its uncapped upside.

The result rests on modelling assumptions worth keeping in view:

• Symmetric talent. Theorem 1 assumes $f_i = f_0$ for everyone; heterogeneity enters only informally in Theorem 2.
• Asymmetric multiplier. AI multiplies solo output at full strength but firm output only after the discount $\eta < 1$, and leaves the firm’s coordination friction unchanged. These are the propositions the theorem depends on.
• Frictionless singletons. Solo friction is $c \cdot 1^{\beta} = c$, which the model treats as approximately zero.
• Singleton test only. The proof uses only the singleton balanced collection. Violating it is enough to empty the Core, but the paper does not characterise which smaller coalitions, if any, would remain stable.
• Stylised dynamics. Shapley scaling with $A$ is approximate, and the spiral is laid out step by step rather than derived as a dynamic equilibrium. The macro figures are illustrative, not an empirical test.

Selected references

• Coase, R. H. (1937). “The Nature of the Firm.” Economica, New Series, 4(16), 386–405.
• Bondareva, O. N. (1963). “Some Applications of Linear Programming Methods to the Theory of Cooperative Games.” Problemy Kibernetiki, 10, 119–139.
• Shapley, L. S. (1967). “On Balanced Sets and Cores.” Naval Research Logistics Quarterly, 14(4), 453–460.
• Frank, R. H. (1984). “Are Workers Paid Their Marginal Products?” American Economic Review, 74(4), 549–571.
• Acemoglu, D. (2024). “The Simple Macroeconomics of AI.” NBER Working Paper No. 32487.
• Aghion, P., Antonin, C., and Bunel, L. (2024). “AI and Growth: Where Do We Stand?” Federal Reserve Bank of San Francisco Working Paper Series.
• Hamilton, B. H. (2000). “Does Entrepreneurship Pay?” Journal of Political Economy, 108(3), 604–631.
• Simon, H. A. (1971). “Designing Organizations for an Information-Rich World.” In M. Greenberger (Ed.), Computers, Communications, and the Public Interest, 37–72.

The full list is in the paper.

Cite

@article{ozyavuz2026coasean,
  title={Coasean Disintegration: Cooperative Game Theory of the Firm under Autonomous Intelligence},
  author={Ozyavuz, Ogulcan},
  journal={Working Paper, DICE Venture Builder},
  year={2026},
  url={https://github.com/ogulcan-ozyavuz/cooperative-game-theory-of-the-firm}
}

Version 1.0.0, released 27 September 2026. The full paper, with every proof, is in the GitHub repository.