# Learning Parameterized Families of Games

## TL;DR

This paper presents a neural network-based method to learn a unified model of game families with varying environment parameters, improving analysis efficiency and accuracy.

## Contribution

It introduces a novel approach that incorporates environment parameters into the model inputs, enabling generalization across game variations.

## Key findings

- Generalized models outperform existing methods in accuracy.
- Models require less data to learn patterns across parameters.
- Facilitates more comprehensive analysis of game parameter spaces.

## Abstract

Nearly all simulation-based games have environment parameters that affect incentives in the interaction but are not explicitly incorporated into the game model. To understand the impact of these parameters on strategic incentives, typical game-theoretic analysis involves selecting a small set of representative values, and constructing and analyzing separate game models for each value. We introduce a novel technique to learn a single model representing a family of closely related games that differ in the number of symmetric players or other ordinal environment parameters. Prior work trains a multi-headed neural network to output mixed-strategy deviation payoffs, which can be used to compute symmetric $\varepsilon$-Nash equilibria. We extend this work by making environment parameters into input dimensions of the regressor, enabling a single model to learn patterns which generalize across the parameter space. For continuous and discrete parameters, our results show that these generalized models outperform existing approaches, achieving better accuracy with far less data. This technique makes thorough analysis of the parameter space more tractable, and promotes analyses that capture relationships between parameters and incentives.