This paper studies Substrate Games: strategic environments in which current play changes the future feasibility of actions by eroding or preserving a reconstructable capability base. The substrate is not current demand or current practice but the surviving stock of practitioners, trained maintainers, corpora, artifacts, institutional memory, and comparative reference from which a practice can be rebuilt. Collapse means this reconstructable base no longer survives and the substrate-dependent action is removed from the feasible set entirely, while ordinary declines in demand or use are treated as movement toward that boundary or as dormancy when a reconstructable base remains. The paper is the boundary theory of a one-parameter family of finite-cost lock-in models: when residual sub-threshold availability is strictly positive, recovery is steep, costly, and path-dependent but finite; the substrate case is the limiting pole at which availability is exactly zero, recovery adoption is identically zero after preference restoration, and the dependent action is structurally absent. Foundational architecture is organized around five layers with explicitly stated logical strength: a minimal observable-state theorem constructs the collapse-recovery state as the quotient of histories with identical future feasible-set responses; a no-free-scalarization result establishes why additional structure is necessary; the primary operational foundation derives both one-dimensional order and finite rank from observable restoration-contract choices using a benchmark difficulty quote, a common single-crossing condition, and a finite restoration grammar; the diagnostic route from binary feasibility probes is retained as an honest fallback; and a uniqueness theorem shows the representation is unique up to strictly increasing reparameterization of each substrate coordinate. Observational censoring is proved by showing that in the canonical sharp-threshold model the pre-collapse behavioral history is almost surely constant conditional on survival, giving it exactly zero mutual information with future collapse, while direct substrate measurement carries strictly positive information whenever the conditional collapse probability varies with the substrate level. Agent types are extended to a pair of current-use payoff and flow option value, and a dynamic game characterizes exactly when option value leaks into equilibrium behavior: agents must be pivotal for feasibility, the discounted option value must dominate the current sacrifice, and equilibrium beliefs must assign positive probability to threshold crossing. In the nonatomic or myopic limit individual pivotality vanishes and the old impossibility is recovered as a theorem about the feasibility externality. A model-class separation theorem and a crossed demand-availability experimental design with explicit finite-sample confidence inequalities together show that collapsed substrate models are structurally distinguishable from finite-cost fixed-feasible-set alternatives, while a moving-threshold extension shows that extinction depends on the margin between substrate stock and feasibility threshold rather than on the stock alone.The principal addition in this version is a formal theory of radical monopoly as a two-channel substrate phenomenon, providing the mathematical foundations for Illich’s concept and distinguishing it precisely from market monopoly, switching-cost lock-in, and capability extinction. The two-channel model introduces a public state consisting of a reconstructable capability stock and a smoothed aggregate adoption stock of the dominant means. The feasibility threshold is an endogenous function of the dominant-means adoption stock, yielding two channels through which adoption of the dominant means erodes the alternative: Channel 1 reduces maintenance practice and therefore lowers the capability stock, and Channel 2 raises the feasibility threshold by increasing the adoption stock. The sum of these two effects is the total margin derivative, whose sign is everywhere nonpositive and strictly negative when the threshold-adoption coupling is strictly positive. A well-posedness theorem establishes existence of stationary Markov perfect equilibria for the smoothed game and convergence of a subsequence to a sharp-limit equilibrium, and identifies three distinct attracting regimes under the affine threshold model: a viable regime in which the alternative remains feasible, a radical-monopoly regime in which the alternative is foreclosed but the reconstructable stock remains above the no-restructuring threshold so coordinated recovery is possible, and an extinction regime in which the reconstructable stock falls below the least-restructured threshold and collective recovery fails.The paper proves five theorems on radical monopoly. The existence and characterization theorem shows that when the maximal equilibrium practice mass is insufficient to sustain the capability stock above the endogenous threshold, every decentralized nonatomic Markov equilibrium path enters a radical-monopoly lock in which the margin is negative, individual exit is infeasible because no nonatomic agent can change aggregate stocks, and collective recovery is feasible in finite time by a coordinated de-adoption phase that lets the adoption stock decay and the threshold fall until it drops below the dormant capability stock. The dynamic voluntariness theorem shows that the path into the lock satisfies period-by-period best response, period Pareto efficiency relative to current feasible menus, and revealed-preference rationality on observed menus at every date, so the unfreedom is not a period welfare mistake but the structural consequence of a restructured feasible correspondence. The taxonomy theorem establishes a trichotomy among switching-cost lock-in where the alternative is feasible but privately costly, radical monopoly where the alternative is infeasible but collectively recoverable, and extinction where even coordinated recovery fails, and proves that finite payoff instruments such as price subsidies, price caps on the dominant means, or entry cannot dislodge a radical-monopoly lock because they cannot change the sign of the margin between a stock and an endogenous threshold. The strategic provider theorem shows that a dominant-means provider who can choose the Channel-2 coupling strength has private profit incentives to choose a foreclosure-inducing intensity whenever the gain from capturing the remaining adoption mass exceeds the restructuring cost, even though foreclosure is socially excessive relative to the substrate-welfare benchmark that counts use value, option value, and restructuring cost but not transfers. The remedies theorem characterizes feasibility-acting interventions: one-period feasibility restoration requires direct stock restoration plus threshold reduction summing to at least the absolute value of the current margin, threshold preservation regulations that cap the coupling coefficient prevent the dominant-means attractor from being a radical-monopoly lock, and a coordinated de-adoption phase whose duration is given by an explicit logarithmic formula restores feasibility and, once restored, a coordinated practice mass above the maintenance threshold drives the system to the viable attractor. The gap between the coordinated return kernel and the individual return kernel is identified as the formal structural-coercion component of radical monopoly, the object that gives the concept its precise content and distinguishes it from every configuration in which individual exit remains feasible.
K. Fathi (Sat,) studied this question.