Cuts and Options: A Theory of Strategic Autonomy in Production Networks¶

Stefane Fermigier (Abilian) · sf@abilian.com

Draft working paper v0.10, 2026-08-04. Complete draft; every proved statement is verified numerically, and the two Section 6 components are stated as open.

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Abstract¶

Modern production runs through deep vertical chains in which a producer needs all of its input classes and can, within each class, choose among substitutable suppliers. This paper develops the combinatorial theory of coercion and diversification on such structures. Its scope is the channels through which a controller can deny or condition another actor's operation (physical supply, technology and licensing, legal reach, distribution); the slower channels acting on the same structure, influence over rule-setters, capital, and the capture of suppliers, reshape the structure itself over time and are treated as dynamics, in the research programme of Section 6 and in companion work.

Two dual quantities organize the statics: the coercion number $\kappa$, the size of the smallest coalition of controllers able to cut every feasible realization of a buyer's production, and the option number $N$, the largest family of realizations sharing no controller. Coercion composes as a weakest link across independent input classes; $N \leq \kappa$ always; and the central result is a possibility theorem for certification failure: system-wide diversification can be strictly below every per-layer option count, with the gap opening exactly where the same controller appears at more than one layer. A per-layer independent-suppliers criterion, the form regulation actually takes, therefore certifies a quantity that can equal two at every layer while a single controller cuts everything. A forkable substrate acts as a standing, self-controlled option and caps exit costs. The graded Leontief operator of applied work coincides with the calculus in support and interpolates it monotonically in magnitude.

The primitives are classical, and the mathematics is kin to minimal cut sets in reliability theory and to network interdiction; the control overlay, the duality pair, and the certification theorem aimed at regulatory texts have, to our knowledge, no antecedent in the production-network economics literature. Applied to a measured 52-category graph of the European digital stack, the theory computes: every European demand node has $\kappa = 1$, with five distinct blocs each able to cut alone at full stack depth and the US bloc above the semiconductor floor for every buyer; on the legal channel both the US and China hold unilateral cut capability; and the public-sector buyer passes a per-layer two-suppliers test at every required class while its true option number is one. A supplier-resolution recomputation on pilot data splits both ways: a fully self-controlled productivity stack exists above the silicon floor, while the accelerator class offers seven suppliers under a single controller. The framework gives exact readings to the criteria in European cloud regulation and locates what they can and cannot certify.

Keywords: production networks, strategic autonomy, coercion, diversification, options, supply security, certification, digital sovereignty.

JEL: F52, L14, D85, L86, O25.

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Cite this paper¶

Fermigier, S. (2026). Cuts and Options: A Theory of Strategic Autonomy in Production Networks.
Draft working paper v0.10, Abilian Econ Lab.
https://econ.lab.abilian.com/papers/theory/