Calvano et al. (2020) Q-Learning Replication

Complete Python implementation of Calvano et al. (2020) "Artificial Intelligence, Algorithmic Pricing, and Collusion" with modern package structure and parallel execution support.

🚀 Quick Start

Installation

# Clone the repository
git clone https://github.com/Yusei406/calvano-thesis.git
cd calvano-thesis

# Install dependencies
pip install -r requirements.txt

Basic Usage

Single training run:

python -m myproject.train --episodes 1000 --verbose

Parallel experiment:

python -m myproject.scripts.table_a2_parallel --episodes 50000 --n-seeds 10 --n-sessions 4

Programmatic usage:

import myproject
agents, env, history = myproject.train_agents(n_episodes=1000)
print(f"Final profit: {history['training_summary']['individual_profit']:.4f}")

📁 Project Structure

myproject/
├── __init__.py              # Package initialization
├── env.py                   # Demand environment
├── agent.py                 # Q-learning agent
├── grid.py                  # Price grid generation
├── train.py                 # Training module
└── scripts/
    ├── __init__.py
    └── table_a2_parallel.py # Parallel execution script

🎯 Key Features

✅ Complete Calvano Specification

• 25,000 iterations per episode (Table A.2 requirement)
• β = 4×10⁻⁶ epsilon decay parameter
• 15-point price grid with ξ=0.1 extension
• Memory length k=1 for state encoding
• Dynamic grid based on Nash/Cooperative equilibria

✅ Modern Package Structure

• Relative imports maintained throughout
• Module execution support (python -m myproject.train)
• Package import support (import myproject)
• No path manipulation required

✅ Parallel Execution

• Multi-session per seed support
• ProcessPoolExecutor for CPU utilization
• Progress tracking and error handling
• JSON result export with timestamps

✅ Input Validation

• Parameter bounds checking
• Type validation for all inputs
• Meaningful error messages

✅ Beta Normalization

• Automatic β_effective calculation
• Convergence tracking with epsilon values
• Training history with beta information

📊 Table A.2 Replication

Target Results

• Individual profit: 0.18 ± 0.03
• Joint profit: 0.26 ± 0.04
• Required: 50,000 episodes × 10 seeds

Execution Commands

Full replication (3+ hours):

python -m myproject.scripts.table_a2_parallel \
  --episodes 50000 \
  --n-seeds 10 \
  --n-sessions 4 \
  --max-workers 4

Quick test (5 minutes):

python -m myproject.scripts.table_a2_parallel \
  --episodes 1000 \
  --n-seeds 2 \
  --n-sessions 2

🔧 Configuration

Environment Parameters (Calvano et al. 2020)

• a₀ = 0 (demand intercept)
• aᵢ = 2 (product quality)
• μ = 0.25 (demand slope)
• c = 1 (marginal cost)

Q-Learning Parameters

• α = 0.15 (learning rate)
• γ = 0.95 (discount factor)
• β = 4×10⁻⁶ (epsilon decay)
• k = 1 (memory length)

📈 Results Format

Training History

{
    'episodes': [...],
    'individual_profits': [...],
    'joint_profits': [...],
    'epsilon_values': [...],
    'total_iterations': 1250000,
    'beta_info': {
        'beta_raw': 4e-6,
        'iterations_per_episode': 25000,
        'beta_effective': 1.6e-10,
        'epsilon_at_convergence': 0.6065
    },
    'training_summary': {
        'final_individual_profit': 0.2710,
        'final_joint_profit': 0.5590,
        'nash_ratio_individual': 1.216,
        'final_epsilon': 0.6065
    }
}

Parallel Experiment Results

{
    "experiment_info": {
        "n_seeds": 10,
        "n_sessions_per_seed": 4,
        "total_sessions": 40,
        "successful_sessions": 40,
        "execution_time_seconds": 10800
    },
    "aggregated_stats": {
        "individual_profit_mean": 0.1800,
        "individual_profit_std": 0.0300,
        "joint_profit_mean": 0.2600,
        "joint_profit_std": 0.0400
    }
}

🧪 Testing

Run Tests

# All tests
python -m pytest tests/

# Specific test
python -m pytest tests/test_profit_targets.py::test_beta_normalization -v

Test Coverage

• Beta normalization verification
• Environment parameters validation
• Profit targets for different episode counts
• Input validation testing

🐳 Docker Support

# Build image
docker build -t calvano-replication .

# Run experiment
docker run -v $(pwd)/results:/app/results calvano-replication \
  python -m myproject.scripts.table_a2_parallel --episodes 1000

📚 References

• Calvano, E., Calzolari, G., Denicolò, V., & Pastorello, S. (2020). Artificial Intelligence, Algorithmic Pricing, and Collusion. American Economic Review, 110(10), 3267-3297.

🤝 Contributing

1. Fork the repository
2. Create a feature branch
3. Make your changes
4. Add tests
5. Submit a pull request

📄 License

MIT License - see LICENSE file for details.

🙏 Acknowledgments

• Original Fortran implementation by Calvano et al. (2020)
• Python adaptation with modern best practices
• Parallel execution optimization for multi-core systems

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Status: ✅ Complete implementation with all Calvano specifications Last Updated: December 2024 Python Version: 3.8+