Voluntary Carbon Market in Agriculture: A Game Theory Approach

Abstract

Small and marginal farmers in India encounter significant barriers in accessing emerging carbon markets due to high transaction costs, limited bargaining power, and resource constraints. This study addresses these issues using a dual approach: (1) Cooperative Game Theory to examine coalition formation among farmers through Farmer Producer Organizations (FPOs), assessing benefits of aggregation, stability via the Core concept, and fairness through the Shapley value; (2) Mechanism Design to investigate carbon credit pricing and trading by comparing Shapley-based allocation with traditional auction mechanisms like VCG. Simulation results indicate that farmer coalitions can substantially enhance individual payoffs, with Shapley allocation consistently ensuring equitable outcomes and 100% individual rationality—unlike conventional auction methods.

Context & Motivation

Agriculture forms the backbone of India's economy, contributing ~18% to GDP and supporting over half its population. However, Indian agriculture faces mounting pressures from climate change, rising input costs, and land tenure complexities.

86%

of agricultural land cultivated by small & marginal farmers

60%

of total land area used for agriculture

The Voluntary Carbon Market Framework

The Government of India's proposed VCM framework aims to incentivize farmers to adopt sustainable practices (agroforestry, conservation tillage, reduced fertilizer use) by enabling them to generate and sell carbon credits. However, critical challenges remain:

High Transaction Costs: MRV (Monitoring, Reporting, Verification) requirements
Limited Bargaining Power: Individual farmers lack negotiation leverage
Resource Constraints: Limited technical knowledge and access to finance
Fair Revenue Distribution: How to equitably share collective benefits

Key Contributions

Coalition Analysis

Model FPOs as cooperative coalitions using characteristic functions that capture economies of scale and synergistic effects.

Shapley Value Allocation

Fair revenue distribution based on marginal contributions, ensuring equitable outcomes and individual rationality.

Core Stability

Analysis of coalition stability ensuring no subgroup has incentive to deviate from the FPO structure.

Mechanism Comparison

Comprehensive evaluation of VCG auctions, Uniform Price auctions, and cooperative game-theoretic approaches.

Dual Methodological Approach

1. Cooperative Game Theory Model

Characteristic Function

Model coalition value with baseline contributions and synergy effects:

v(S) = α Σ r_i + β (Σ r_i)²

where

                        
                            ri = standalone farmer payoff

                            α ≥ 0 = scaling parameter

                            β ≥ 0 = synergy parameter

Shapley Value Computation

Calculate fair allocation based on expected marginal contributions across all possible joining orders. Uses exact computation for small coalitions (n≤10) and Monte Carlo approximation for larger groups.

Core Stability Check

Verify no blocking coalitions exist: ensure Σ_i∈S x_i ≥ v(S) for all subsets S ⊆ N, guaranteeing coalition stability.

2. Mechanism Design Approach

VCG Auction

Vickrey-Clarke-Groves mechanism ensuring efficient allocation and strategy-proof bidding. Winners pay based on critical cost (lowest excluded bidder's cost).

Uniform Price Auction

Simple clearing mechanism where all winners receive the same market-clearing price based on total demand.

Performance Comparison

Evaluate mechanisms on farmer profitability, fairness (Gini coefficient), and individual rationality vs. standalone farming payoff.

Key Results Evidence-Based

Coalition Value Creation

Experiments with varying coalition sizes (N ∈ {3, 5, 8, 12}) using baseline parameters (α=1.0, β=0.01) demonstrate substantial value generation through aggregation:

Value Per Farmer

Coalition Size N=3 Baseline + 5%

Coalition Size N=8 Baseline + 12%

Coalition Size N=12 Baseline + 18%

Stability Analysis (N=12)

Shapley Value Core Stable

Equal Split Core Stable

Proportional Split Core Stable

Fairness Metrics

Shapley Gini 0.12

Equal Split Gini 0.00

Proportional Gini 0.12

Mechanism Comparison Results (N=250)

Mechanism	Avg Profit (INR)	IR Met (%)	Gini Coefficient	Participation
Shapley (α=1.0, β=0.0)	~20,000	100%	0.14	Full
VCG Auction	8,000 - 15,000	< 10%	0.25 - 0.32	Price-dependent
Uniform Price	< 5,000	0%	~1.0	Very Low

Critical Findings

Individual Rationality

Shapley allocation achieves 100% IR (all farmers better off than standalone) while VCG shows < 10% IR at most price points.

Superior Fairness

Shapley demonstrates excellent fairness (Gini ≈ 0.14) compared to VCG (0.25-0.32) and Uniform Price (≈ 1.0).

Parameter Sensitivity

When α < 1.0, all farmers worse off (0% IR). When α ≥ 1.0 with β > 0, significant gains achieved with maintained fairness.

Aggregator Impact

Commission rates > 20% cause participation collapse. Critical balance needed between aggregator viability and farmer incentives.

Impact of Farmer Heterogeneity

Simulations with mixed coalitions (N=15: 10 small farmers, 5 large farmers) under different parameter settings reveal:

Scenario 1: α=1.0, β=0.0 (No Synergy)

Shapley returns exactly standalone payoff to each farmer (φ_i = r_i)
No strict incentive to join, but no one made worse off

Scenario 2: α=1.25, β=0.0 (Baseline Scaling Only)

Uniform percentage gain: All farmers receive exactly 25% increase (φ_i = 1.25 × r_i)
Absolute gains differ: Large farmers gain more in INR, but relative benefit identical
Result: Equitable incentive structure for both small and large farmers

This demonstrates that Shapley allocation doesn't disadvantage small farmers when working with heterogeneous coalitions, maintaining proportional fairness.

Aggregator-Mediated Model

Extended analysis modeling the FPO/aggregator as a strategic player with operational costs and commission structure:

Model Components

Net Value for Farmers:

V_F(S) = (1 - δ) × V_net(S)

where

                Vnet(S) = max(0, V(S) - CA(S)) 

                CA(S) = Cbase + Cvar × |S|

                δ = aggregator commission rate

Key Findings (C_base=10,000 INR, C_var=300 INR/farmer)

Commission δ = 0-15%

IR Satisfaction 100%

Core Stability Stable

Farmer Participation Full

Commission δ = 20%+

IR Satisfaction 0%

Core Stability Stable (but irrelevant)

Farmer Participation Collapse

Critical Insight: A threshold exists (~15-20% commission) beyond which voluntary participation collapses, even with fair internal allocation. VCM design must balance aggregator sustainability with sufficient farmer incentives.

Policy Implications & Recommendations

1. Prioritize FPO Formation

Government should strongly incentivize farmer aggregation through FPOs. Simulations show 18%+ value increase for N=12 coalitions with modest synergy (β=0.01).

2. Adopt Shapley-Based Distribution

Implement Shapley value or similar cooperative game-theoretic allocation for internal FPO revenue sharing to ensure fairness and 100% IR satisfaction.

3. Regulate Aggregator Commissions

Set commission rate caps (< 15-20%) for aggregators/FPOs to maintain farmer participation incentives while ensuring operational sustainability.

4. Hybrid Mechanism Design

Consider hybrid approaches combining VCG-style price discovery for external markets with Shapley-based internal distribution within FPOs.

Implementation Recommendations

Capacity Building: Train FPO managers on fair allocation mechanisms and their computational implementation
Transparency: Make allocation rules clear and verifiable to build farmer trust
Parameter Calibration: Conduct pilot studies to empirically estimate α and β for different regions/crop types
Cost Subsidies: Government support for MRV costs to reduce C_base and C_var, improving overall participation
Digital Infrastructure: Develop platforms for automated Shapley computation and transparent credit trading

Experimental Methodology

Synthetic Data Generation

Created representative dataset of N=250 farmers with heterogeneous characteristics:

Farm Size: Gamma distribution (shape=2, scale=1.5) to reflect small farm prevalence
Carbon Credits (q_i): Gamma distribution (shape=2.5, scale=1.8), minimum 0.1 tCO2e
Standalone Payoff (r_i): Normal distribution (μ=20,000 INR, σ=5,000), minimum 5,000 INR
True Cost (c_i): Gamma distribution (shape=3, scale=800) + 500 INR base, minimum 100 INR

Computational Approaches

Exact Methods (n ≤ 10)

Complete enumeration of all permutations or coalitions for precise Shapley value calculation and Core verification.

Approximation (n > 10)

Monte Carlo sampling with 10,000 random permutations for Shapley estimation. Core checks limited to n ≤ 15 due to O(2ⁿ) complexity.

Evaluation Metrics

Metric	Definition	Interpretation
Individual Rationality (IR)	% of farmers with payoff ≥ standalone	Measures voluntary participation incentive
Gini Coefficient	Inequality measure (0=perfect equality, 1=maximum inequality)	Assesses fairness of payoff distribution
Core Stability	No blocking coalitions exist	Ensures coalition long-term viability
Average Farmer Profit	Mean payoff across all farmers	Overall welfare indicator
Total Surplus	Buyer value - Total true costs	Market efficiency measure

Limitations & Future Work

Current Limitations

Synthetic Data: Results based on simulated farmer profiles; empirical validation with real FPO data needed
Simplified Characteristic Function: v(S) model assumes specific functional form; reality may be more complex
Computational Scalability: Core stability verification limited to small coalitions (n ≤ 15)
Static Analysis: Doesn't model dynamic effects, repeated interactions, or learning over time
Single-Stage Market: Doesn't capture multi-tier market structures or secondary trading

Future Research Directions

Empirical Calibration

Partner with existing FPOs to calibrate characteristic function parameters (α, β) using real-world data on costs, revenues, and synergies.

Strategic Aggregators

Model aggregators as strategic players optimizing member recruitment, cost management, and market interactions.

Scalable Algorithms

Develop approximate Core verification methods and efficient Shapley computation for large coalitions (n > 100).

Mechanism Automation

Design automated mechanism discovery using machine learning to optimize for multiple objectives in complex environments.

Conclusions

Note: These results are based on synthetic data experiments and should be treated as indicative rather than conclusive pending empirical validation.

Key Takeaways

FPOs are Essential: Farmer aggregation through FPOs is not merely beneficial but likely essential for VCM viability for smallholders, with simulations showing 5-18% value increases based on coalition size.
Shapley Value Excels: Among allocation mechanisms tested, Shapley value consistently provides the best combination of fairness (Gini ≈ 0.14), individual rationality (100% vs. standalone), and Core stability.
Auction Mechanisms Fall Short: Standard VCG and Uniform Price auctions, while efficient for surplus maximization, fail to guarantee participation incentives relative to farmers' baseline agricultural activities (< 10% IR).
Critical Parameter Sensitivity: Outcomes highly sensitive to α (baseline scaling) and β (synergy effects). Ensuring α ≥ 1.0 is crucial; positive β dramatically improves farmer welfare.
Aggregator Balance Required: A critical commission threshold exists (15-20%) beyond which voluntary participation collapses. Policy must balance aggregator sustainability with farmer incentives.
Heterogeneity Handled Well: Shapley allocation maintains proportional fairness across small and large farmers, with uniform percentage gains preventing domination by larger players.
Game Theory as Policy Tool: This work demonstrates that game-theoretic and mechanism design frameworks provide actionable, quantitative insights for real-world policy implementation beyond theoretical analysis.

Practical Impact

This research provides evidence-based guidance for policymakers designing India's agricultural VCM framework. By integrating cooperative game theory insights on internal FPO dynamics with mechanism design principles for external market interactions, the study offers a unified framework to achieve dual goals: enhancing farmer welfare while advancing national climate objectives.

Acknowledgments

I would like to express my sincere gratitude to Prof. Y. Narahari, Prof. Siddharth Barman, and the members of the Game Theory Lab for their invaluable guidance, insightful feedback, and continuous encouragement throughout this project for the E1 254 Game Theory and Mechanism Design course at IISc Bangalore.

Use of AI Tools

In preparing this document, AI language models (GPT, BERT/Gemini) were utilized to enhance writing quality, provide summaries, and gain additional insights. Large Language Models also assisted in exploring statistical distributions and parameter ranges for synthetic data generation. All AI-generated content was carefully verified for accuracy and factual integrity.

Key Algorithms Implemented

Exact Shapley Value Calculation (Permutation & Coalition Methods)
Monte Carlo Shapley Value Approximation
Core Stability Verification
VCG Auction Mechanism with Price Threshold
Uniform Price Auction Clearing
Characteristic Function with Synergy Modeling
Aggregator-Mediated Coalition Analysis

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