5  Limitations

Demand-side instruments are unrepresentable. The fine lever serves as a negative control: it halves A’s households’ wealth each turn it fires (converging to zero by \(t_{22}\)) but leaves P and B unchanged. Bardi’s model has no demand \(\to\) production channel — players and capital compete only for R — so a consumption-side instrument is structurally inexpressible. This does not imply that demand-side instruments (carbon taxes, ETS, behavioural nudges) are ineffective in the real world; it isolates mechanically the supply-side channel in this model and shows that the only effective point of leverage on this substrate is the production rate (capital \(C\)). Extending the model with a demand-to-production feedback would be necessary to evaluate demand-side policy instruments.

Exclusion is moot here. It is another player-targeted lever; like fine it would lack the autonomous-capital channel needed to decouple production, so it cannot beat the leading-indicator result already established in Section 3.3. We therefore report it as a Limitations note rather than running it as an experiment.

Integration-step boundary. The full win-win (saving both the emitter and the downwind victim) holds for \(dt \leq 3.0\); the baseline runs at dt = 3.0, inherited from the cascade calibration where this step size produces the canonical Seneca cliff within the 25–30-turn game window. This places the baseline at the upper edge of the win-win region: had the baseline been calibrated at \(dt = 3.5\), the headline claim would have been “partial win-win (downwind saved, emitter sacrificed)” rather than “full win-win”. The Pareto-improving claim is therefore conditional on a governance sampling cadence within the effective coupling window (\(dt \leq 3.0\) in this parametrisation). Under coarser sampling, the claim degrades gracefully to “downwind-only” — never to “no effect” — because cap-leading continues to strictly dominate all reactive baselines at every tested \(dt\) (Chapter 4).