Rational Addiction without Irrationality: Institutional Erosion, Statistical Camouflage, and Engagement Traps

The paper develops a mechanism by which a fully rational, dynamically consistent Bayesian agent can be trapped into dependence on an institution without any irrationality, present bias, or naivety. The institution provides a current-period surplus but erodes the agent's outside option over time at a rate the institution controls. The agent observes own autonomy only through Gaussian noise and updates optimally about whether hidden active erosion is occurring alongside the known passive decline. The baseline model establishes core counterproductivity implications. One-period welfare equals current autonomy plus the net benefit of institutional engagement, which combines an institutional output benefit and a passive degradation cost. The optimal scale from the agent's myopic perspective is interior and can be found explicitly. Under constant scale, the exit option is foreclosed in finite time when degradation is sufficiently aggressive, an exact formula gives the foreclosure date, and welfare follows a path that first rises before it falls. A growth ratchet result shows that output-based measurement cannot identify the welfare-maximizing scale because any monotone accountability scheme that rewards reported output falls victim to a boundary argument showing the optimal scale lies at a corner of every admissible mechanism's support. Benign neighborhoods around the optimal scale exist but shrink as institutional ambition grows. The strategic erosion section solves the institution's reduced-form degradation problem. The institution chooses a per-period active erosion intensity subject to a cap and a total budget, discounting its own future payoffs. Under an affine continuation value the optimal policy is a threshold rule: zero active erosion far from the lock-in boundary and maximal feasible erosion inside the capture region. A patience comparison result shows that greater institutional patience expands the active-erosion region and weakly hastens lock-in, with strict acceleration under a standard arithmetic condition. The full dynamic erosion problem admits a contraction Bellman operator with a unique fixed point. The detection section solves the associated statistical problems. A regulator observes autonomy through Gaussian noise. With known initial autonomy and constant decline the Neyman-Pearson power frontier and the earliest detectable date are explicit and expressed in terms of a cumulative sum statistic. With unknown initial autonomy, projecting out the intercept yields the optimal translation-invariant likelihood ratio, which reduces to the OLS slope statistic under constant decline, with explicit power and detection formulas. For general active-erosion paths, delaying known-state detection is equivalent to minimizing the squared prefix sums of cumulative decline. Among feasible paths with fixed total decline and a per-period cap, the back-loaded path that concentrates erosion near the lock-in deadline is detection-optimal. A detection gap result shows that if known-state detection is slower than the lock-in deadline, the exit option can be destroyed before decline can be reliably detected, and this gap survives the unknown-initial-autonomy nuisance parameter. The rational engagement section endogenizes participation. The agent updates a posterior over a hidden binary regime using the projected likelihood ratio from the detection section. A one-step continuation bound shows that if the posterior probability of active erosion is below an explicit threshold, continuation is sufficient for the exact dynamically consistent agent. The exact finite-horizon problem admits an exact Bellman recursion in the two-dimensional posterior state, and the value function is proved affine in the posterior mean of current autonomy, so the exact free boundary is horizontal in that coordinate. The main theorem, the rational addiction via statistical camouflage result, proves that for an open parameter region satisfying four explicit conditions — a lock-in wedge separating passive from active foreclosure, continuation cutoffs strictly above the prior, small total crossing probability under the back-loaded path, and negative commitment value under full information — a fully rational Bayesian agent remains engaged through lock-in with probability at least one minus epsilon, while the same dynamically consistent agent would reject the institution at date zero under full information. The admissible parameter set is nonempty and open, established constructively via a numerical calibration. The union bound used in the crossing probability condition is shown to be conservative by comparing it to exact recursive exit probabilities computed from the Bellman recursion. Comparative statics are proved analytically. Noisier self-monitoring strictly reduces the threshold-crossing probability and expands the trap region. Greater agent patience shrinks the sufficient continuation region. A precision-targeting appendix characterizes heterogeneous agents by self-monitoring quality and shows that the institution can screen them through scale menus. The companion executed Jupyter notebook implements all numerical results in 35 cells using NumPy, SciPy, pandas, and Matplotlib. The IllichModel dataclass encodes the baseline calibration with power-law benefit and degradation functions. Cells verify the counterproductivity threshold, the finite-time foreclosure formulas, the growth ratchet, and the output-based accountability impossibility numerically. The strategic-erosion section implements the threshold policy and verifies the patience comparison across three discount factors. The detection section computes Neyman-Pearson power frontiers and back-loaded camouflage path performance for both known and unknown initial autonomy. The rational-addiction section implements the back-loaded path, computes the union-bound crossing probability, verifies all four conditions of the main theorem at the baseline calibration, and runs a Monte Carlo simulation of exact exit probabilities confirming that the union bound exceeds the exact probability by a factor of 1.011 at the baseline. The exact Bellman section solves the finite-horizon Bellman recursion on a dense grid in the posterior state, verifies that the continuation premium is monotone decreasing in the posterior probability of active erosion, and scans the full five-dimensional grid in monitoring noise, discount factor, total erosion, erosion cap, and horizon, finding the admissible region and decomposing which of the four conditions binds first at the feasible boundary. A validation summary cell records pass-fail status for every analytical check. All cells are executed with outputs preserved.