Substrate Games and Capability Extinction: Endogenous Feasibility, Radical Monopoly, Mechanism Design, and Recovery

This paper develops a general theory of Substrate Games: strategic environments in which the feasible strategy set is endogenous because it depends on a substrate state that is itself affected by play. The framework separates agents’ preferences over currently available actions from the persistence of the conditions that make those actions available. The paper introduces substrate-indexed feasible-set correspondences and studies how strategy availability can erode, collapse, or recover over time. It gives a representation, essential-uniqueness, and minimal-dimension theorem for observable feasibility processes; proves existence of substrate-preserving equilibria under explicit threshold regularity; and analyzes finite-time bistability, irreversibility, hysteresis, and voluntariness preservation in canonical one-substrate population models. The model is then specialized to Illichian radical monopoly, where a dominant practice can reshape the surrounding substrate until an alternative practice exits the feasible set. The paper also develops results on substrate commons, observational censoring, strategic substrate control, mechanism-design impossibility, and recovery under deterministic, noisy, and divided-jurisdiction conditions. The central contribution is the integration of regime-shift and capability-erosion dynamics with endogenous feasible-set correspondences, equilibrium choice, radical-monopoly interpretation, mechanism design, strategic substrate control, and recovery theory.