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.

翻译：几乎所有基于仿真的博弈都包含环境参数，这些参数会影响交互中的激励因素，但并未显式纳入博弈模型。为理解这些参数对战略激励的影响，典型的博弈论分析会选取少量代表性数值，针对每个数值构建并分析独立的博弈模型。我们提出一种新技术，用于学习一个代表具有相近联系、但对称玩家数量或其他序数环境参数不同的博弈族模型。先前研究通过训练多头神经网络输出混合策略偏离收益，这些收益可用于计算对称ε-纳什均衡。我们在此基础上进行扩展，将环境参数作为回归器的输入维度，使单一模型能够学习跨参数空间泛化的模式。对于连续和离散参数，实验结果表明，这类泛化模型优于现有方法，能以更少数据实现更高精度。该技术使参数空间的全面分析更为易行，并促进了能够捕捉参数与激励间关系的分析方法。