DeepEWA: Approximating Learning Dynamics in 2 × 2 Games with Neural Networks

This project implements a neural network approach to predict convergence characteristics of Experience-Weighted Attraction (EWA) learning dynamics in 2×2 games, based on Pangallo et al. (2022). This project was the final assignment for the course ''Computational Game Theory'', taught by Prof. Davide Grossi, and was graded 9.7/10. Please refer to DeepEWA_GitHub.pdf for our paper.

Overview

Experience Weighted Attraction generalizes various learning algorithms in game theory:

Attraction updating function:

$$Q_{i}^{a}(t) = \frac{(1-\alpha) \mathcal{N}(t-1) Q_{i}^{a}(t-1)}{\mathcal{N}(t)} + \frac{\left[ \delta + (1-\delta) \mathbb{I}(s_i^a,s_{-i}(t)) \right] \Pi_i(s_i^a, s_{-i}(t))}{\mathcal{N}(t)}$$

Action selection:

$$\mu_i(t)=\frac{e^{\beta Q_1 (t)}}{e^{\beta Q_1^a (t)} + e^{\beta Q_2^b (t)}}$$

Special cases include:

• Best Response Dynamics (α=1, β=∞, δ=1)
• Fictitious Play (α=0, β=∞, δ=1, κ=0)
• Reinforcement Learning (δ=0)
• Replicator Dynamics (β→0, α=0, δ=1)
• Logit Dynamics (α=1, δ=1, κ=1)

We train a deep neural network to classify convergence outcomes of learning dynamics on 2×2 games into four categories:

1. Limit cycles/chaos
2. Mixed strategy fixed points
3. Pure strategy fixed points
4. Pure Nash equilibria

Project Structure

DeepEWA/
├── ProbsEWA.jl           # Core EWA algorithm and convergence classification
├── DataGen.jl            # Data generation for neural network training (also included in notebook)
├── DeepEWA.ipynb         # Main Jupyter notebook with analysis
├── dependencies.jl       
├── data/                 # Training and test datasets
│   ├── train_data.csv
│   └── test_data.csv
├── images/               # Generated plots
├── notebooks EWA/        # Testing notebooks
├── notebooks NN/         # NN experiments
├── versions EWA/         # Older versions
├── literature/           # References
└── paper/                # Paper

Installation

1. Install Julia (v1.11 or higher): https://julialang.org/downloads/

Quick start

Run the following notebook:

jupyter notebook DeepEWA.ipynb

For custom 2×2 games, modify the payoff matrices:

# Example coordination game: 
custom_game = [[7 2; 2 3], [7 2; 2 3]]

EWA Parameters

• α (memory loss): [0, 1]
• κ (discount rate): [0, 1]
• δ (foregone payoffs): [0, 1]
• β (temperature): [0, ∞]

Model Architecture

• Input: 12 features (4 EWA parameters + 8 payoff matrix entries)
• Hidden layers: 3 layers with 32 ReLU units each
• Output: 4-class softmax for convergence classification
• Optimizer: AdaGrad with learning rate adaptation
• Training: 2500 epochs with batch size 64

Example accuracy results:

• Overall accuracy: ~85-95% depending on game type

References

• Pangallo, M., et al. (2022). "Towards a taxonomy of learning dynamics in 2 × 2 games"
• Camerer, C., & Ho, T. H. (1999). "Experience-weighted attraction learning in normal form games"

License

This project is licensed under the MIT License - see the LICENSE file for details.

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