The Recursive Feasibility Game: When Optimization Consumes Its Own Futures

This paper presents a structural framework for evaluating when strategic optimization is a valid mode of reasoning under constraint, and when it is not.

Rather than treating strategy as universally applicable, the framework specifies the structural conditions under which strategic reasoning remains admissible, the endogenous mechanisms by which those conditions fail in move-exhausting systems, and the precise boundary at which strategic optimization becomes invalid as a way of reasoning about action.

The analysis centers on a single governing question:
Does there exist at least one executable action that expands future reachability within a fixed system boundary and remaining coordination capacity, over a finite evaluation horizon?
Strategic optimization is structurally admissible if and only if the answer is affirmative.

The paper introduces several core contributions:

• Playability Conditions: the necessary and jointly sufficient structural conditions under which strategic reasoning is coherent

• Strategic Exhaustion: a unique invalidation boundary at which no action can expand future reachability, reversals exceed remaining coordination capacity, and leverage exists only via boundary redefinition

• Reasoning-Mode Routing: an exhaustive classification of which modes of reasoning remain admissible once strategic optimization becomes invalid

• The Strategy Viability Audit: a conservative, observer-executable diagnostic procedure for determining reasoning admissibility without appeal to outcomes, intent, or authority

A key result is the separation of continued activity from continued leverage, and execution quality from reasoning validity. In systems with finite coordination capacity and persistent commitments, strategic optimization can become invalid even while coordination, performance, and execution remain strong. Because most indicators track performance conditional on the remaining option-space rather than the structure of that space itself, the loss of strategic leverage is often unobservable as it occurs—a phenomenon formalized here as feasibility signal lag.

The framework is explicitly diagnostic rather than prescriptive. It does not recommend actions, rank outcomes, justify interventions, or define success. Its sole function is to determine which modes of reasoning remain structurally admissible within a declared system boundary. Explicit falsifiers, applicability limits, and a hard stop condition are provided to prevent overreach or misuse.

The framework applies across organizational, institutional, technical, and socio-technical systems wherever action consumes future optionality under constraint. It is falsifiable by counterexample and requires no calibrated measurement, relying instead on explicit boundary specification and structural comparison.