{
  "modelName": "AgriNudgex Participation \u0026 Persistence ABM",
  "modelVersion": "2.0.0",
  "modelStatus": "current",
  "codeVersion": "40177a25d7a0ff4b6056582704ac5a33c138b0b4",
  "dataOrigin": "SYNTHETIC",
  "dataOriginStatement": "All farmer data are SYNTHETIC agents generated by the AgriNudgex simulation model. They do not represent real farmers, observed behaviour, or empirical measurements. Results are model outputs conditional on stated assumptions and are not evidence of real-world effectiveness.",
  "empiricalCalibration": "None. All behavioural and population parameters are hypothetical (see \u0027evidence\u0027).",
  "monetaryUnit": "MU (abstract monetary unit)",
  "practiceScenario": {
    "crop": "Olive orchards (Olea europaea), Mediterranean rain-fed conditions",
    "practice": "Maintained inter-row ground cover (sown cover crop or managed spontaneous vegetation) during the erosion-risk season, instead of bare soil kept by tillage or herbicide",
    "periodUnit": "One agricultural season (one year)",
    "decision": "Whether to maintain inter-row ground cover in the coming season (binary, taken once per season)",
    "performanceIndicator": "Verified inter-row ground-cover fraction during the erosion-risk season (0\u20131); a single observable indicator, not an aggregate sustainability score",
    "reversibility": "Reversible-seasonal: participation can start or stop every season; cover quality builds up over consecutive seasons and degrades towards the conventional level after stopping",
    "verification": "Assumed remote sensing or field inspection; participation verified without error, ground-cover fraction with Gaussian measurement error"
  },
  "equations": [
    "P(i,t) = 1 / (1 \u002B exp(\u2212U(i,t)))",
    "U(i,t) = \u03B1_i \u002B \u03B2_B\u00B7B(i,t) \u2212 \u03B2_C\u00B7C_i/M \u002B \u03B2_R\u00B7s_i\u00B7R_exp(i,t)/M \u002B \u03B7\u00B7D(i,t\u22121)",
    "B(i,t) = clamp[0,1](B_i \u002B \u03C1\u00B7D(i,t\u22121))",
    "R_exp(i,t) = \u03C0(t\u22121) \u00B7 \u03A3_{h=0}^{H_eff\u22121} \u03C6^h \u00B7 E_m(1, q\u0303_h(i,t), q0_i) / \u03A3_{h=0}^{H_eff\u22121} \u03C6^h,  H_eff = min(H, T\u2212t\u002B1),  \u03C0(0) = \u03C00",
    "q\u0303_h(i,t): ground cover after h\u002B1 consecutive participating seasons from q(i,t\u22121)",
    "D(i,t) = 1[u(i,t) \u003C P(i,t)],  u(i,t) = U(0,1) counter-based draw keyed by (decision seed, i, t) \u2014 common to all mechanisms and reward scales",
    "q(i,t) = q \u002B \u03B3(qmax_i \u2212 q) if D(i,t)=1;  q \u2212 \u03B4(q \u2212 q0_i) otherwise;  initial participants start k0 improvement steps above q0_i",
    "q\u0302(i,t) = clamp[0,1](q(i,t) \u002B \u03B5),  \u03B5 ~ N(0, \u03C3_v\u00B2)",
    "Entitlements with reward scale \u03BB: S1 \u03BBF\u00B71[D=1 \u2227 q\u0302\u2265q_min]; S2 min(\u03BB\u00B7cap, \u03BBk\u00B7max(0, q\u0302\u2212q0)); S3 \u03BBR_j for highest \u03B8_j \u2264 q\u0302; S3R \u03BBR\u0027_j for highest \u03B8\u0027_j \u2264 q\u0302\u2212q0",
    "Cap(t) = Remaining(t)/(T\u2212t\u002B1) (\u221E if uncapped);  Paid = E\u00B7min(1, Cap/\u03A3E);  \u03C0(t) = \u03A3Paid/\u03A3E"
  ],
  "parameters": [
    {
      "symbol": "\u03B1_i",
      "name": "Baseline participation propensity",
      "category": "Agent attribute",
      "definition": "Intrinsic tendency to maintain ground cover, absorbing unobserved preferences and constraints.",
      "unit": "logit (dimensionless)",
      "defaultValue": "TN(\u03BC=\u22122.0, \u03C3=1.0; [\u22126, 2])",
      "allowedRange": "\u03BC \u2208 [\u221210, 10]",
      "sensitivityRange": "\u03BC \u2208 [\u22123, \u22121]",
      "evidence": "Hypothetical",
      "rationale": "Places participation without incentives in a low-to-moderate range so incentives can matter; heterogeneity via \u03C3.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Higher \u03BC raises participation under every mechanism and the control; reduces additionality (more deadweight)."
    },
    {
      "symbol": "B_i",
      "name": "Perceived benefit of ground cover",
      "category": "Agent attribute",
      "definition": "Farmer\u0027s perceived agronomic benefit (e.g. erosion control, soil moisture, trafficability), normalised.",
      "unit": "index [0, 1]",
      "defaultValue": "TN(0.5, 0.15; [0, 1])",
      "allowedRange": "\u03BC \u2208 [0, 1]",
      "sensitivityRange": "\u03BC \u2208 [0.3, 0.7]",
      "evidence": "Hypothetical",
      "rationale": "Symmetric mid-range perception; cover crops in olive groves are promoted mainly for soil protection (qualitative context, see references).",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Raises participation; interacts with \u03B2_B."
    },
    {
      "symbol": "C_i",
      "name": "Additional seasonal cost of maintaining cover",
      "category": "Agent attribute",
      "definition": "Extra cost per season (seed, mowing, water competition, management).",
      "unit": "MU per season",
      "defaultValue": "TN(80, 25; [10, 200])",
      "allowedRange": "\u03BC \u2208 [0, 1000]",
      "sensitivityRange": "\u03BC \u2208 [40, 120]",
      "evidence": "Hypothetical",
      "rationale": "Expressed relative to M = 100 MU; no olive-specific cost data were used.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Higher costs lower participation and raise the reward needed for additional participation."
    },
    {
      "symbol": "s_i",
      "name": "Individual incentive sensitivity",
      "category": "Agent attribute",
      "definition": "Multiplier of \u03B2_R for farmer i.",
      "unit": "dimensionless",
      "defaultValue": "TN(1.0, 0.25; [0.1, 2.0])",
      "allowedRange": "[0, 10]",
      "sensitivityRange": "\u03C3 scaled by h",
      "evidence": "Hypothetical",
      "rationale": "Heterogeneous responsiveness to money with population mean \u2248 1.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Spreads the response to rewards across farmers; affects payment concentration."
    },
    {
      "symbol": "q0_i",
      "name": "Baseline inter-row ground cover",
      "category": "Agent attribute",
      "definition": "Ground-cover fraction under conventional (tillage/herbicide) management.",
      "unit": "fraction [0, 1]",
      "defaultValue": "TN(0.35, 0.10; [0.05, 0.80])",
      "allowedRange": "[0, 1]",
      "sensitivityRange": "correlation with C via r",
      "evidence": "Hypothetical",
      "rationale": "Residual vegetation varies across groves; value not calibrated.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Determines who reaches absolute S3 thresholds without improvement (baseline qualifiers)."
    },
    {
      "symbol": "g_i",
      "name": "Attainable ground-cover gain",
      "category": "Agent attribute",
      "definition": "qmax_i = min(1, q0_i \u002B g_i): cover reachable under sustained participation.",
      "unit": "fraction",
      "defaultValue": "TN(0.30, 0.10; [0.05, 0.60])",
      "allowedRange": "[0, 1]",
      "sensitivityRange": null,
      "evidence": "Hypothetical",
      "rationale": "Site-dependent potential (soil, rainfall, slope) represented as heterogeneity.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Larger gains raise S2/S3/S3R rewards for sustained participants."
    },
    {
      "symbol": "D(i,0)",
      "name": "Initial participation",
      "category": "Agent attribute",
      "definition": "Participation status before season 1.",
      "unit": "binary",
      "defaultValue": "Bernoulli(0.10)",
      "allowedRange": "[0, 1]",
      "sensitivityRange": null,
      "evidence": "Hypothetical",
      "rationale": "A minority already maintain cover.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "With \u03B7 \u003E 0, initial participants are more likely to continue; they receive non-additional payments."
    },
    {
      "symbol": "\u03B2_B",
      "name": "Benefit coefficient",
      "category": "Behaviour",
      "definition": "Utility per unit of perceived benefit.",
      "unit": "utility per index unit",
      "defaultValue": "2.0",
      "allowedRange": "[0, 20]",
      "sensitivityRange": "via B\u0304 range",
      "evidence": "Hypothetical",
      "rationale": "Unchanged from v1.0.0.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Scales the influence of perceived benefits."
    },
    {
      "symbol": "\u03B2_C",
      "name": "Cost coefficient",
      "category": "Behaviour",
      "definition": "Utility per unit of normalised cost C/M.",
      "unit": "utility per M",
      "defaultValue": "1.5",
      "allowedRange": "[0, 20]",
      "sensitivityRange": "via C\u0304 range",
      "evidence": "Hypothetical",
      "rationale": "Unchanged from v1.0.0.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Scales cost deterrence; \u03B2_R/\u03B2_C is the money-equivalence of rewards."
    },
    {
      "symbol": "\u03B2_R",
      "name": "Reward coefficient (incentive sensitivity)",
      "category": "Behaviour",
      "definition": "Utility per unit of normalised expected reward R_exp/M.",
      "unit": "utility per M",
      "defaultValue": "1.5 (= \u03B2_C)",
      "allowedRange": "[0, 20]",
      "sensitivityRange": "[0.5, 3.0]",
      "evidence": "Hypothetical",
      "rationale": "\u03B2_R = \u03B2_C means 1 MU of expected reward offsets 1 MU of cost.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Main driver of the response to every incentive."
    },
    {
      "symbol": "\u03C1",
      "name": "Experience effect",
      "category": "Behaviour",
      "definition": "Perceived benefit increase after participating in the previous season.",
      "unit": "index units",
      "defaultValue": "0.10",
      "allowedRange": "[0, 1]",
      "sensitivityRange": null,
      "evidence": "Hypothetical",
      "rationale": "Learning-by-doing, unchanged from v1.0.0.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Weak persistence channel."
    },
    {
      "symbol": "\u03B7",
      "name": "Persistence strength (habit / switching cost)",
      "category": "Behaviour (new in v2)",
      "definition": "Utility bonus for continuing last season\u0027s practice; equivalently a switching cost of \u03B7/\u03B2_C\u00B7M MU.",
      "unit": "utility units",
      "defaultValue": "2.0",
      "allowedRange": "[0, 10]",
      "sensitivityRange": "[0, 4]",
      "evidence": "Hypothetical",
      "rationale": "Represents habit, sunk establishment effort and management routines; \u03B7 = 2 \u2248 switching cost of 133 MU. \u03B7 = 0 reproduces the memoryless v1 rule.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Raises continuation and sustained participation; favours mechanisms that sustain participation over time."
    },
    {
      "symbol": "H",
      "name": "Expectation horizon",
      "category": "Behaviour (new in v2)",
      "definition": "Seasons over which a farmer anticipates rewards along a path of continued participation.",
      "unit": "seasons (integer)",
      "defaultValue": "3",
      "allowedRange": "[1, 12]",
      "sensitivityRange": "{1, \u2026, 5}",
      "evidence": "Hypothetical",
      "rationale": "Farmers deciding on a multi-season practice plausibly look beyond one season; H = 1 reproduces v1 myopia.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Larger H raises the anticipated value of accumulation-based rewards (S2, S3, S3R) relative to S1."
    },
    {
      "symbol": "\u03C6",
      "name": "Expectation discount",
      "category": "Behaviour (new in v2)",
      "definition": "Weight per season on anticipated future rewards within H.",
      "unit": "fraction",
      "defaultValue": "0.9",
      "allowedRange": "[0, 1]",
      "sensitivityRange": null,
      "evidence": "Hypothetical",
      "rationale": "Moderate discounting of future seasons.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Lower \u03C6 approaches myopia."
    },
    {
      "symbol": "\u03C00",
      "name": "Initial payout expectation",
      "category": "Behaviour (new in v2)",
      "definition": "Payout ratio expected before any payment is observed.",
      "unit": "fraction",
      "defaultValue": "1.0",
      "allowedRange": "[0, 1]",
      "sensitivityRange": "[0.5, 1.0]",
      "evidence": "Hypothetical",
      "rationale": "Announced rewards believed in full (v1); lower values represent distrust of a new programme.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Affects season-1 participation and early over-subscription under binding caps."
    },
    {
      "symbol": "k0",
      "name": "Prior practice of initial participants",
      "category": "Behaviour (new in v2)",
      "definition": "Improvement steps applied to initial participants\u0027 starting ground cover.",
      "unit": "seasons",
      "defaultValue": "1",
      "allowedRange": "[0, 20]",
      "sensitivityRange": null,
      "evidence": "Hypothetical",
      "rationale": "Initial participants have practised at least one season; k0 = 0 reproduces v1.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Raises payments to initial participants under S2/S3/S3R (deadweight)."
    },
    {
      "symbol": "M",
      "name": "Monetary reference",
      "category": "Normalisation",
      "definition": "Scale used to normalise costs and rewards in utility.",
      "unit": "MU",
      "defaultValue": "100",
      "allowedRange": "[1, 10^6]",
      "sensitivityRange": null,
      "evidence": "Normalisation",
      "rationale": "MU is an abstract monetary unit; no currency conversion is implied.",
      "source": "Convention.",
      "expectedInfluence": "Changes the meaning of \u03B2_C and \u03B2_R only."
    },
    {
      "symbol": "h",
      "name": "Heterogeneity scale",
      "category": "Population (new in v2)",
      "definition": "Multiplier of the standard deviations of \u03B1, B, C and s.",
      "unit": "dimensionless",
      "defaultValue": "1.0",
      "allowedRange": "[0, 3]",
      "sensitivityRange": "[0.5, 1.5]",
      "evidence": "Hypothetical",
      "rationale": "Tests sensitivity to farmer heterogeneity (RQ3).",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "More heterogeneity widens participation and payment dispersion."
    },
    {
      "symbol": "r",
      "name": "Cost\u2013baseline correlation",
      "category": "Population (new in v2)",
      "definition": "Gaussian-copula correlation between C_i and q0_i.",
      "unit": "correlation",
      "defaultValue": "0",
      "allowedRange": "[\u22120.95, 0.95]",
      "sensitivityRange": "[\u22120.5, 0.5]",
      "evidence": "Hypothetical",
      "rationale": "Independence is a strong assumption (audit M3); the sign is unknown and is therefore varied symmetrically.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Changes who qualifies for absolute S3 tiers and the cost profile of participants."
    },
    {
      "symbol": "\u03B3",
      "name": "Cover establishment rate",
      "category": "Ground cover",
      "definition": "Share of the gap to qmax closed per participating season.",
      "unit": "fraction per season",
      "defaultValue": "0.35",
      "allowedRange": "[0, 1]",
      "sensitivityRange": "[0.15, 0.55]",
      "evidence": "Hypothetical",
      "rationale": "Cover quality builds over several seasons.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Faster establishment raises early S2/S3/S3R rewards."
    },
    {
      "symbol": "\u03B4",
      "name": "Cover degradation rate",
      "category": "Ground cover",
      "definition": "Share of the gain above q0 lost per non-participating season.",
      "unit": "fraction per season",
      "defaultValue": "0.25",
      "allowedRange": "[0, 1]",
      "sensitivityRange": "[0.10, 0.50]",
      "evidence": "Hypothetical",
      "rationale": "Stopping (tillage/herbicide) degrades cover towards the conventional level.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Higher \u03B4 penalises interrupted participation under accumulation-based mechanisms."
    },
    {
      "symbol": "\u03C3_v",
      "name": "Verification error",
      "category": "Ground cover",
      "definition": "SD of the measurement error of verified ground cover.",
      "unit": "fraction (SD)",
      "defaultValue": "0.02",
      "allowedRange": "[0, 0.5]",
      "sensitivityRange": null,
      "evidence": "Hypothetical",
      "rationale": "Assumed remote-sensing/inspection precision; not validated.",
      "source": "No verified source; value chosen by the modellers.",
      "expectedInfluence": "Noise matters near S3/S3R thresholds."
    },
    {
      "symbol": "F",
      "name": "S1 fixed reward",
      "category": "Mechanism",
      "definition": "Flat payment per verified participating season.",
      "unit": "MU per season",
      "defaultValue": "100 (= M)",
      "allowedRange": "[0, 10^6]",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "Steady-state nominal parity rule of v1.0.0 (kept for continuity).",
      "source": "Design.",
      "expectedInfluence": "Level of S1; varied jointly with others through \u03BB."
    },
    {
      "symbol": "k, cap",
      "name": "S2 rate and cap",
      "category": "Mechanism",
      "definition": "Payment per unit of verified ground-cover gain over q0; per-season cap.",
      "unit": "MU per cover unit; MU",
      "defaultValue": "333.33; 200",
      "allowedRange": "[0, 10^7]; [0, 10^6]",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "k = M / E[g] gives M at the mean attainable gain (steady-state parity).",
      "source": "Design.",
      "expectedInfluence": "Level of S2."
    },
    {
      "symbol": "\u03B8_j \u2192 R_j",
      "name": "S3 absolute tiers",
      "category": "Mechanism",
      "definition": "Reward of the highest absolute ground-cover threshold reached.",
      "unit": "fraction \u2192 MU",
      "defaultValue": "0.45\u219250, 0.55\u2192100, 0.65\u2192150",
      "allowedRange": "increasing",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "Unchanged from v1.0.0.",
      "source": "Design.",
      "expectedInfluence": "Pays baseline qualifiers (farmers with q0 \u2265 0.45) without improvement."
    },
    {
      "symbol": "\u03B8\u0027_j \u2192 R\u0027_j",
      "name": "S3R relative tiers",
      "category": "Mechanism (new in v2)",
      "definition": "Reward of the highest threshold of verified gain q\u0302 \u2212 q0 reached.",
      "unit": "fraction \u2192 MU",
      "defaultValue": "0.10\u219250, 0.20\u2192100, 0.30\u2192150",
      "allowedRange": "increasing",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "S3 thresholds minus the mean baseline (0.35); a separately named variant, S3 is not redefined.",
      "source": "Design.",
      "expectedInfluence": "Pays only improvement; removes baseline windfalls."
    },
    {
      "symbol": "\u03BB",
      "name": "Common reward scale",
      "category": "Protocol (new in v2)",
      "definition": "Multiplier of all reward amounts (thresholds unchanged).",
      "unit": "dimensionless",
      "defaultValue": "{0.25, 0.5, 0.75, 1, 1.25, 1.5, 2, 2.5, 3}",
      "allowedRange": "[0, 20]",
      "sensitivityRange": "{0.5, 1, 1.5, 2, 3} in E3",
      "evidence": "DesignChoice",
      "rationale": "Traces each mechanism\u0027s cost\u2013participation frontier; \u03BB = 0 equals the control.",
      "source": "Design.",
      "expectedInfluence": "Determines the expenditure range over which matched comparisons are possible."
    },
    {
      "symbol": "T",
      "name": "Horizon",
      "category": "Design",
      "definition": "Number of seasons.",
      "unit": "seasons",
      "defaultValue": "12",
      "allowedRange": "[1, 36]",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "Unchanged.",
      "source": "Design.",
      "expectedInfluence": "Longer horizons favour accumulation-based rewards."
    },
    {
      "symbol": "N",
      "name": "Population size",
      "category": "Design",
      "definition": "Number of synthetic farmers.",
      "unit": "farmers",
      "defaultValue": "250 (E2), 200 (E3)",
      "allowedRange": "[2, 1000]",
      "sensitivityRange": "precision check only (E4)",
      "evidence": "DesignChoice",
      "rationale": "Agents do not interact and budgets are per farmer, so N affects Monte Carlo precision, not expected outcomes.",
      "source": "Design.",
      "expectedInfluence": "Precision only."
    },
    {
      "symbol": "R",
      "name": "Repetitions",
      "category": "Design",
      "definition": "Independent Monte Carlo repetitions.",
      "unit": "count",
      "defaultValue": "100 (E1, E2, E4), 20 per point (E3)",
      "allowedRange": "[1, 200]",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "",
      "source": "Design.",
      "expectedInfluence": "Precision only."
    },
    {
      "symbol": "Budget",
      "name": "Nominal budget cap",
      "category": "Design",
      "definition": "Maximum expenditure per farmer over the horizon (E1); uncapped in E2/E3.",
      "unit": "MU per farmer",
      "defaultValue": "Low 200 / Medium 400 / High 800; uncapped",
      "allowedRange": "[0, 10^6]",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "A cap is not an expenditure level; actual expenditure is reported separately.",
      "source": "Design.",
      "expectedInfluence": "Binding caps ration payments pro rata."
    },
    {
      "symbol": "X",
      "name": "Expenditure targets for matching",
      "category": "Analysis (new in v2)",
      "definition": "Actual expenditure per farmer at which mechanisms are compared.",
      "unit": "MU per farmer over horizon",
      "defaultValue": "100, 200, 300, 400 (primary 200)",
      "allowedRange": "\u003E 0",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "Pre-specified before running the protocol; no extrapolation beyond observed spending.",
      "source": "Design.",
      "expectedInfluence": "Outcome differences are reported per target."
    },
    {
      "symbol": "k_s",
      "name": "Sustained-participation threshold",
      "category": "Analysis (new in v2)",
      "definition": "Minimum consecutive participating seasons counted as sustained.",
      "unit": "seasons",
      "defaultValue": "4",
      "allowedRange": "[1, T]",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "One third of the horizon; reported alongside the full set of longitudinal metrics.",
      "source": "Design.",
      "expectedInfluence": "Defines endpoint P2."
    },
    {
      "symbol": "K, seed_LHS",
      "name": "Latin Hypercube design",
      "category": "Analysis (new in v2)",
      "definition": "Number of design points and design seed.",
      "unit": "points; integer",
      "defaultValue": "64; 20270101",
      "allowedRange": "K \u2265 8",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "Global sensitivity design (Marino et al. 2008).",
      "source": "Design.",
      "expectedInfluence": "Resolution of RQ3 analysis."
    },
    {
      "symbol": "B_boot",
      "name": "Bootstrap resamples",
      "category": "Analysis (new in v2)",
      "definition": "Resamples for percentile intervals.",
      "unit": "count",
      "defaultValue": "1000 (500 within E3 points)",
      "allowedRange": "[200, 10000]",
      "sensitivityRange": null,
      "evidence": "DesignChoice",
      "rationale": "",
      "source": "Design.",
      "expectedInfluence": "Interval precision only."
    }
  ],
  "metrics": [
    {
      "key": "meanParticipation",
      "label": "Horizon-mean participation (P1)",
      "group": "Participation",
      "role": "Primary",
      "direction": "Higher",
      "unit": "share of farmers (0\u20131)",
      "definition": "Mean over seasons 1..T of the share of farmers participating.",
      "undefinedWhen": "Never."
    },
    {
      "key": "sustainedShare",
      "label": "Sustained participation (P2)",
      "group": "Sustained participation",
      "role": "Primary",
      "direction": "Higher",
      "unit": "share of farmers (0\u20131)",
      "definition": "Share of farmers with at least one spell of \u2265 k consecutive participating seasons (k = 4 by default).",
      "undefinedWhen": "Never."
    },
    {
      "key": "meanParticipationImprovement",
      "label": "\u0394 horizon-mean participation vs control",
      "group": "Participation",
      "role": "Primary",
      "direction": "Higher",
      "unit": "percentage points",
      "definition": "P1(m) \u2212 P1(S0), paired within repetition (common random numbers).",
      "undefinedWhen": "For S0."
    },
    {
      "key": "sustainedShareImprovement",
      "label": "\u0394 sustained participation vs control",
      "group": "Sustained participation",
      "role": "Primary",
      "direction": "Higher",
      "unit": "percentage points",
      "definition": "P2(m) \u2212 P2(S0), paired within repetition.",
      "undefinedWhen": "For S0."
    },
    {
      "key": "firstPeriodParticipation",
      "label": "Initial participation (season 1)",
      "group": "Participation",
      "role": "Secondary",
      "direction": "Higher",
      "unit": "share of farmers (0\u20131)",
      "definition": "Share participating in the first simulated season.",
      "undefinedWhen": "Never."
    },
    {
      "key": "finalParticipation",
      "label": "Final-season participation",
      "group": "Participation",
      "role": "Secondary",
      "direction": "Higher",
      "unit": "share of farmers (0\u20131)",
      "definition": "Share participating in season T (single-season snapshot).",
      "undefinedWhen": "Never."
    },
    {
      "key": "everParticipated",
      "label": "Ever participated",
      "group": "Participation",
      "role": "Secondary",
      "direction": "None",
      "unit": "share of farmers (0\u20131)",
      "definition": "Share of farmers participating in at least one season.",
      "undefinedWhen": "Never."
    },
    {
      "key": "continuationProbability",
      "label": "Continuation probability",
      "group": "Sustained participation",
      "role": "Secondary",
      "direction": "Higher",
      "unit": "probability (0\u20131)",
      "definition": "\u03A3_{t\u22652} D(t\u22121)D(t) / \u03A3_{t\u22652} D(t\u22121): probability of participating again after a participating season.",
      "undefinedWhen": "No participation in seasons 1..T\u22121."
    },
    {
      "key": "disadoptionRate",
      "label": "Dis-adoption rate",
      "group": "Sustained participation",
      "role": "Secondary",
      "direction": "Lower",
      "unit": "probability (0\u20131)",
      "definition": "1 \u2212 continuation probability: probability of stopping after a participating season.",
      "undefinedWhen": "No participation in seasons 1..T\u22121."
    },
    {
      "key": "meanSpellLength",
      "label": "Mean consecutive participation duration",
      "group": "Sustained participation",
      "role": "Secondary",
      "direction": "Higher",
      "unit": "seasons",
      "definition": "Mean length of maximal runs of consecutive participating seasons within 1..T (right-censored at T).",
      "undefinedWhen": "No participation."
    },
    {
      "key": "allPeriodsShare",
      "label": "Participated in every season",
      "group": "Sustained participation",
      "role": "Secondary",
      "direction": "Higher",
      "unit": "share of farmers (0\u20131)",
      "definition": "Share of farmers participating in all T seasons.",
      "undefinedWhen": "Never."
    },
    {
      "key": "readoptionShare",
      "label": "Re-adopters",
      "group": "Sustained participation",
      "role": "Secondary",
      "direction": "None",
      "unit": "share of farmers (0\u20131)",
      "definition": "Share of farmers who start a new participation spell after an earlier spell ended within the horizon.",
      "undefinedWhen": "Never."
    },
    {
      "key": "readoptionsPerFarmer",
      "label": "Re-adoption frequency",
      "group": "Sustained participation",
      "role": "Secondary",
      "direction": "None",
      "unit": "events per farmer",
      "definition": "Number of re-adoption events divided by N.",
      "undefinedWhen": "Never."
    },
    {
      "key": "expenditurePerFarmer",
      "label": "Actual expenditure per farmer",
      "group": "Spending \u0026 cost-effectiveness",
      "role": "Secondary",
      "direction": "None",
      "unit": "MU per farmer over the horizon",
      "definition": "Rewards actually paid \u00F7 N. Distinct from the nominal budget cap.",
      "undefinedWhen": "Never."
    },
    {
      "key": "totalExpenditure",
      "label": "Total expenditure",
      "group": "Spending \u0026 cost-effectiveness",
      "role": "Descriptive",
      "direction": "None",
      "unit": "MU",
      "definition": "\u03A3 rewards actually paid after budget rationing.",
      "undefinedWhen": "Never."
    },
    {
      "key": "budgetUtilization",
      "label": "Budget utilisation",
      "group": "Spending \u0026 cost-effectiveness",
      "role": "Descriptive",
      "direction": "None",
      "unit": "share of nominal budget (0\u20131)",
      "definition": "Actual expenditure \u00F7 nominal budget cap.",
      "undefinedWhen": "Uncapped budget, zero budget, or S0."
    },
    {
      "key": "costPerAdditionalParticipantPeriod",
      "label": "Cost per additional participant-season (per-run ratio)",
      "group": "Spending \u0026 cost-effectiveness",
      "role": "Secondary",
      "direction": "Lower",
      "unit": "MU per participant-season",
      "definition": "Expenditure \u00F7 net additional participant-seasons in that repetition. Secondary estimator; the primary estimator is the pooled ratio.",
      "undefinedWhen": "Net additional participant-seasons \u2264 0, and S0."
    },
    {
      "key": "additionalParticipantPeriods",
      "label": "Net additional participant-seasons",
      "group": "Additionality (synthetic counterfactual)",
      "role": "Secondary",
      "direction": "Higher",
      "unit": "farmer-seasons",
      "definition": "\u03A3 D(m) \u2212 \u03A3 D(S0) over farmers and seasons, paired. = gross additional \u2212 displaced.",
      "undefinedWhen": "For S0."
    },
    {
      "key": "grossAdditionalParticipantPeriods",
      "label": "Gross additional participant-seasons",
      "group": "Additionality (synthetic counterfactual)",
      "role": "Descriptive",
      "direction": "None",
      "unit": "farmer-seasons",
      "definition": "Farmer-seasons with D(m) = 1 and D(S0) = 0 in the paired control.",
      "undefinedWhen": "For S0."
    },
    {
      "key": "displacedParticipantPeriods",
      "label": "Displaced participant-seasons",
      "group": "Additionality (synthetic counterfactual)",
      "role": "Descriptive",
      "direction": "None",
      "unit": "farmer-seasons",
      "definition": "Farmer-seasons with D(m) = 0 and D(S0) = 1 (path divergence under persistence).",
      "undefinedWhen": "For S0."
    },
    {
      "key": "deadweightShare",
      "label": "Deadweight share of payments",
      "group": "Additionality (synthetic counterfactual)",
      "role": "Secondary",
      "direction": "Lower",
      "unit": "share of expenditure (0\u20131)",
      "definition": "Share of payments made in farmer-seasons in which the same farmer also participates in the paired control (synthetic counterfactual).",
      "undefinedWhen": "Nothing paid, or S0."
    },
    {
      "key": "deadweightPayments",
      "label": "Deadweight payments",
      "group": "Additionality (synthetic counterfactual)",
      "role": "Descriptive",
      "direction": "None",
      "unit": "MU",
      "definition": "Payments in farmer-seasons that would also be participating under the paired control.",
      "undefinedWhen": "For S0."
    },
    {
      "key": "rewardGini",
      "label": "Payment Gini (all farmers)",
      "group": "Distribution \u0026 equity",
      "role": "Secondary",
      "direction": "None",
      "unit": "index (0\u20131)",
      "definition": "Gini of cumulative payments over all farmers, zeros included.",
      "undefinedWhen": "Nothing paid."
    },
    {
      "key": "recipientRewardGini",
      "label": "Payment Gini (recipients)",
      "group": "Distribution \u0026 equity",
      "role": "Secondary",
      "direction": "None",
      "unit": "index (0\u20131)",
      "definition": "Gini of cumulative payments among farmers paid at least once.",
      "undefinedWhen": "Nobody paid."
    },
    {
      "key": "shareRewarded",
      "label": "Share of farmers paid",
      "group": "Distribution \u0026 equity",
      "role": "Secondary",
      "direction": "None",
      "unit": "share of farmers (0\u20131)",
      "definition": "Share of farmers receiving a positive payment at least once.",
      "undefinedWhen": "Never."
    },
    {
      "key": "meanNetPositionParticipants",
      "label": "Net financial position of participants",
      "group": "Distribution \u0026 equity",
      "role": "Secondary",
      "direction": "None",
      "unit": "MU per farmer over the horizon",
      "definition": "Mean over farmers who ever participated of \u03A3(payments \u2212 practice costs incurred). Excludes non-monetary perceived benefits.",
      "undefinedWhen": "Nobody participated."
    },
    {
      "key": "shareParticipantsNetGain",
      "label": "Participants with non-negative net financial position",
      "group": "Distribution \u0026 equity",
      "role": "Secondary",
      "direction": "None",
      "unit": "share of participants (0\u20131)",
      "definition": "Share of ever-participants whose payments cover their practice costs.",
      "undefinedWhen": "Nobody participated."
    },
    {
      "key": "paymentShareBaselineQualifiers",
      "label": "Payments to farmers already above the lowest S3 threshold at baseline",
      "group": "Distribution \u0026 equity",
      "role": "Secondary",
      "direction": "None",
      "unit": "share of expenditure (0\u20131)",
      "definition": "Share of payments received by farmers whose baseline ground cover q0 already meets the lowest absolute S3 threshold (diagnoses rewards for baseline levels).",
      "undefinedWhen": "Nothing paid."
    },
    {
      "key": "meanPerformanceGain",
      "label": "Mean ground-cover gain",
      "group": "Ground cover",
      "role": "Secondary",
      "direction": "Higher",
      "unit": "ground-cover fraction",
      "definition": "Mean over farmers of q(i,T) \u2212 q0_i (true ground cover).",
      "undefinedWhen": "Never."
    }
  ],
  "references": [
    {
      "key": "ODD\u002BD",
      "citation": "M\u00FCller, B., Bohn, F., Dre\u00DFler, G., Groeneveld, J., Klassert, C., Martin, R., Schl\u00FCter, M., Schulze, J., Weise, H., Schwarz, N. (2013). Describing human decisions in agent-based models \u2013 ODD\u002BD, an extension of the ODD protocol. Environmental Modelling \u0026 Software 48, 37\u201348.",
      "link": "https://doi.org/10.1016/j.envsoft.2013.06.003",
      "usedFor": "Structure of docs/ODD_D_PROTOCOL.md."
    },
    {
      "key": "ODD2020",
      "citation": "Grimm, V., Railsback, S.F., Vincenot, C.E., et al. (2020). The ODD protocol for describing agent-based and other simulation models: A second update to improve clarity, replication, and structural realism. JASSS 23(2), 7.",
      "link": "https://doi.org/10.18564/jasss.4259",
      "usedFor": "Model description standard."
    },
    {
      "key": "LHS-PRCC",
      "citation": "Marino, S., Hogue, I.B., Ray, C.J., Kirschner, D.E. (2008). A methodology for performing global uncertainty and sensitivity analysis in systems biology. Journal of Theoretical Biology 254(1), 178\u2013196.",
      "link": "https://doi.org/10.1016/j.jtbi.2008.04.011",
      "usedFor": "Latin Hypercube Sampling and PRCC (experiment E3)."
    },
    {
      "key": "xoshiro",
      "citation": "Blackman, D., Vigna, S. (2021). Scrambled linear pseudorandom number generators. ACM Transactions on Mathematical Software 47(4), 36:1\u201336:32.",
      "link": "https://doi.org/10.1145/3460772",
      "usedFor": "Sequential generator xoshiro256** used for populations, LHS and bootstrap."
    },
    {
      "key": "SplitMix",
      "citation": "Steele, G.L., Lea, D., Flood, C.H. (2014). Fast splittable pseudorandom number generators. OOPSLA \u002714, 453\u2013472.",
      "link": "https://doi.org/10.1145/2660193.2660195",
      "usedFor": "SplitMix64 mixing for seed derivation and counter-based draws."
    },
    {
      "key": "Olive-cover-2009",
      "citation": "Guzm\u00E1n, G., Fereres, E., Gir\u00E1ldez, J.V., G\u00F3mez, J.A. (2009). Conference abstract, ASA-CSSA-SSSA Annual Meetings, Paper 55723 (cover crops in olive orchards of southern Spain).",
      "link": "https://a-c-s.confex.com/crops/2009am/webprogram/Paper55723.html",
      "usedFor": "Qualitative scenario context only: cover crops promoted as an alternative to bare soil kept by tillage or herbicide."
    },
    {
      "key": "Olive-cover-2021",
      "citation": "G\u00F3mez, J.A., Guzm\u00E1n, G. (2021). EGU General Assembly 2021, abstract EGU21-606 (cover crops vs tillage in an olive orchard, 2008\u20132019).",
      "link": "https://meetingorganizer.copernicus.org/EGU21/EGU21-606.html",
      "usedFor": "Qualitative context only; the authors caution against extrapolating plot results to real-world conditions. No parameter is derived from it."
    }
  ],
  "defaultConfiguration": {
    "name": "E2 \u00B7 Cost\u2013participation frontiers and matched-spending comparison",
    "description": "Primary v2 protocol. Mechanisms are compared at equal actual expenditure per farmer (100\u2013400 MU over 12 seasons; primary 200 MU) by interpolation along each mechanism\u0027s reward-scale frontier.",
    "masterSeed": 20270202,
    "periods": 12,
    "repetitions": 100,
    "populationSizes": [
      250
    ],
    "budgetLevels": [
      {
        "label": "Uncapped",
        "budgetPerFarmer": 0,
        "uncapped": true
      }
    ],
    "sensitivityLevels": [
      {
        "label": "Medium",
        "betaR": 1.5
      }
    ],
    "mechanisms": [
      "S0",
      "S1",
      "S2",
      "S3",
      "S3R"
    ],
    "budgetAllocation": "PerPeriodWithCarryOver",
    "behavior": {
      "betaB": 2,
      "betaC": 1.5,
      "experienceEffect": 0.1,
      "monetaryReference": 100
    },
    "population": {
      "initialAdoptionRate": 0.1,
      "baselinePropensity": {
        "mean": -2,
        "sd": 1,
        "min": -6,
        "max": 2
      },
      "perceivedBenefit": {
        "mean": 0.5,
        "sd": 0.15,
        "min": 0,
        "max": 1
      },
      "adoptionCost": {
        "mean": 80,
        "sd": 25,
        "min": 10,
        "max": 200
      },
      "incentiveSensitivity": {
        "mean": 1,
        "sd": 0.25,
        "min": 0.1,
        "max": 2
      },
      "baselinePerformance": {
        "mean": 0.35,
        "sd": 0.1,
        "min": 0.05,
        "max": 0.8
      },
      "performanceGainPotential": {
        "mean": 0.3,
        "sd": 0.1,
        "min": 0.05,
        "max": 0.6
      }
    },
    "performance": {
      "improvementRate": 0.35,
      "decayRate": 0.25,
      "verificationNoiseSd": 0.02
    },
    "mechanismSettings": {
      "fixedReward": 100,
      "fixedRewardMinimumPerformance": 0,
      "performanceRate": 333.3333333333333,
      "performanceRewardCap": 200,
      "tiers": [
        {
          "threshold": 0.45,
          "reward": 50
        },
        {
          "threshold": 0.55,
          "reward": 100
        },
        {
          "threshold": 0.65,
          "reward": 150
        }
      ]
    },
    "modelVersion": "2.0.0",
    "v2": {
      "protocol": "Frontier",
      "practice": {
        "crop": "Olive orchards (Olea europaea), Mediterranean rain-fed conditions",
        "practice": "Maintained inter-row ground cover (sown cover crop or managed spontaneous vegetation) during the erosion-risk season, instead of bare soil kept by tillage or herbicide",
        "periodUnit": "One agricultural season (one year)",
        "decision": "Whether to maintain inter-row ground cover in the coming season (binary, taken once per season)",
        "performanceIndicator": "Verified inter-row ground-cover fraction during the erosion-risk season (0\u20131); a single observable indicator, not an aggregate sustainability score",
        "reversibility": "Reversible-seasonal: participation can start or stop every season; cover quality builds up over consecutive seasons and degrades towards the conventional level after stopping",
        "verification": "Assumed remote sensing or field inspection; participation verified without error, ground-cover fraction with Gaussian measurement error"
      },
      "persistenceStrength": 2,
      "expectationHorizon": 3,
      "expectationDiscount": 0.9,
      "initialPayoutExpectation": 1,
      "initialParticipantPerformanceSteps": 1,
      "heterogeneityScale": 1,
      "costBaselineCorrelation": 0,
      "sustainedSpellLength": 4,
      "bootstrapResamples": 1000,
      "relativeTiers": [
        {
          "threshold": 0.1,
          "reward": 50
        },
        {
          "threshold": 0.2,
          "reward": 100
        },
        {
          "threshold": 0.3,
          "reward": 150
        }
      ],
      "rewardScales": [
        0.25,
        0.5,
        0.75,
        1,
        1.25,
        1.5,
        2,
        2.5,
        3
      ],
      "spendingTargets": [
        100,
        200,
        300,
        400
      ],
      "primarySpendingTarget": 200,
      "sensitivity": {
        "points": 64,
        "seed": 20270101,
        "rewardScales": [
          0.5,
          1,
          1.5,
          2,
          3
        ],
        "factors": [
          {
            "factor": "BetaR",
            "min": 0.5,
            "max": 3,
            "isInteger": false
          },
          {
            "factor": "CostMean",
            "min": 40,
            "max": 120,
            "isInteger": false
          },
          {
            "factor": "BenefitMean",
            "min": 0.3,
            "max": 0.7,
            "isInteger": false
          },
          {
            "factor": "PropensityMean",
            "min": -3,
            "max": -1,
            "isInteger": false
          },
          {
            "factor": "Persistence",
            "min": 0,
            "max": 4,
            "isInteger": false
          },
          {
            "factor": "ImprovementRate",
            "min": 0.15,
            "max": 0.55,
            "isInteger": false
          },
          {
            "factor": "DecayRate",
            "min": 0.1,
            "max": 0.5,
            "isInteger": false
          },
          {
            "factor": "InitialPayoutExpectation",
            "min": 0.5,
            "max": 1,
            "isInteger": false
          },
          {
            "factor": "ExpectationHorizon",
            "min": 1,
            "max": 5,
            "isInteger": true
          },
          {
            "factor": "HeterogeneityScale",
            "min": 0.5,
            "max": 1.5,
            "isInteger": false
          },
          {
            "factor": "CostBaselineCorrelation",
            "min": -0.5,
            "max": 0.5,
            "isInteger": false
          }
        ]
      }
    }
  }
}