Each mechanism is a function Em(D, q̂, q0) that maps a farmer's own verified adoption D and performance q̂ to a reward
entitlement. Entitlements never depend on other farmers' current decisions; the budget constraint is applied afterwards by pro-rata
rationing. Expected rewards used in the adoption decision are computed with the same function, using a projected performance and
the payout ratio realised in the previous period — this removes any circular dependency between decisions and rewards.
S0 · No financial incentive
Control condition. Farmers decide on intrinsic propensity, perceived benefits and costs only.
Eligibility
No farmer is eligible.
Actual entitlement (after verification)
E₀(i,t) = 0
Expected reward (before the decision)
R̂(i,t) = 0
S1 · Fixed reward
Every qualifying farmer receives the same flat payment per period, independent of how much performance improves.
Eligibility
Verified adoption in period t.
Actual entitlement (after verification)
E₁(i,t) = F · 1[D(i,t)=1 ∧ q̂(i,t) ≥ q_min]
Expected reward (before the decision)
R̂(i,t) = π(t−1) · F · 1[q̃(i,t) ≥ q_min]
| Parameter | Default | Unit |
|---|---|---|
| F (fixed reward) | 100 | MU per period |
| q_min (minimum verified performance) | 0 | index 0–1 |
S2 · Performance-based reward
Payment proportional to the verified improvement of the sustainability performance index over the farmer's own baseline, up to a cap.
Eligibility
Verified adoption in period t and verified improvement q̂(i,t) − q0(i) > 0.
Actual entitlement (after verification)
E₂(i,t) = min(cap, k · max(0, q̂(i,t) − q0(i))) · 1[D(i,t)=1]
Expected reward (before the decision)
R̂(i,t) = π(t−1) · min(cap, k · max(0, q̃(i,t) − q0(i)))
| Parameter | Default | Unit |
|---|---|---|
| k (rate) | 333.33 | MU per performance-index unit |
| cap | 200 | MU per period |
S3 · Tiered reward
Payment depends on which sustainability-performance threshold the verified performance reaches; higher tiers pay more.
Eligibility
Verified adoption in period t and q̂(i,t) ≥ 0.45 (lowest tier).
Actual entitlement (after verification)
E₃(i,t) = R_k for the highest k with q̂(i,t) ≥ θ_k (0 if none) · 1[D(i,t)=1]
Expected reward (before the decision)
R̂(i,t) = π(t−1) · R_k(q̃(i,t))
| Parameter | Default | Unit |
|---|---|---|
| Tier 1: θ1 → R1 | q̂ ≥ 0.45 → 50 | MU per period |
| Tier 2: θ2 → R2 | q̂ ≥ 0.55 → 100 | MU per period |
| Tier 3: θ3 → R3 | q̂ ≥ 0.65 → 150 | MU per period |
S3R · Tiered reward, baseline-relative (v2 variant)
Same tier rewards as S3, but thresholds apply to the verified ground-cover gain over the farmer's own baseline. Baseline ground cover alone is never paid. A separately named variant: S3 is not redefined.
Eligibility
Verified participation in season t and verified gain q̂(i,t) − q0(i) ≥ 0.1 (lowest tier).
Actual entitlement (after verification)
E₃ᴿ(i,t) = R'_k for the highest k with q̂(i,t) − q0(i) ≥ θ'_k (0 if none) · 1[D(i,t)=1]
Expected reward (before the decision)
R̂(i,t) = π(t−1) · weighted mean over h < H of R'_k(q̃_h(i,t) − q0(i))
| Parameter | Default | Unit |
|---|---|---|
| Tier 1: θ'1 → R'1 | gain ≥ 0.1 → 50 | MU per season |
| Tier 2: θ'2 → R'2 | gain ≥ 0.2 → 100 | MU per season |
| Tier 3: θ'3 → R'3 | gain ≥ 0.3 → 150 | MU per season |
Entitlement as a function of verified performance
Computed by the simulation code for an adopting farmer with baseline q0 = 0.35 (default parameters)
Illustrative evaluation of the mechanism functions — not simulation results. Actual payments may be lower when the budget cap binds.
View data table
Shared rules
Notation
- D(i,t) ∈ {0,1}: adoption decision of farmer i in period t (verification of adoption assumed exact).
- q̂(i,t) = clamp(q(i,t) + ε), ε ~ N(0, σv²): verified performance.
- q̃(i,t) = q(i,t−1) + γ(qmaxi − q(i,t−1)): farmer's projected performance if adopting.
- π(t−1): realised payout ratio of the previous period (π(0) = 1).
Budget constraint
Cap(t) = Remaining(t) / (T − t + 1)
Paid(i,t) = E(i,t) · min(1, Cap(t) / Σj E(j,t))
Σ Paid ≤ Cap(t) ≤ Remaining(t) in every period, so total expenditure never exceeds the programme budget. Unspent funds carry forward.
Reward scale λ (model v2)
Every reward amount (F; k and cap; tier rewards) is multiplied by a common λ; eligibility rules and thresholds are unchanged. Model v2 compares mechanisms along a λ grid and at equal actual expenditure, not at equal nominal reward levels.
Nominal parity is not fairness
The default levels give each mechanism a mean steady-state entitlement of about M = 100 MU. As the parity profile below shows, a first-time participant expects much less under S2, S3 and S3R than under S1. Defaults were not tuned toward any ranking, but equal nominal levels do not imply equal incentives or equal spending.
First-season versus steady-state reward parity
Entitlement by consecutive seasons of participation
Mean over a SYNTHETIC reference population of 10,000 farmers (default v2 parameters, λ = 1)
Computed analytically from the mechanism functions and ground-cover dynamics — not a simulation result.
View data table
Parity diagnostics
| Mechanism | Season 1 | Forward-looking (H) | Season 12 | λ for first-season parity |
|---|---|---|---|---|
| S1 Fixed
0 % expect 0 in season 1 |
100 MU | 100 MU | 100 MU | 1.00 |
| S2 Performance-based
0 % expect 0 in season 1 |
35 MU | 54 MU | 99 MU | 2.86 |
| S3 Tiered
48 % expect 0 in season 1 |
37 MU | 60 MU | 109 MU | 2.71 |
| S3R Tiered, relative
44 % expect 0 in season 1 |
28 MU | 56 MU | 116 MU | 3.59 |