A Generative Model for Game Theory with Flow Equilibrium

Zhiyu Zhao, David Henry Mguni, Yali Du, Kaiyang Guo, Haifeng Zhang, Jun Wang

Keywords: Generative Model, Variational Inference, Game Theory

TL;DR: This paper introduces a balanced approach to handling strategy uncertainty using game theory and variational inference.

Abstract:

In recent years, generative models have emerged as a groundbreaking development in the field of artificial intelligence, transforming various domains such as image synthesis, natural language processing, and data generation. While recent studies have integrated generative models into multi-agent scenarios, their game-theoretical implications have remained largely unexplored. Specifically, the relationship between solutions derived from generative models and game theoretical equilibrium concepts lacks rigorous investigation.
This paper aims to bridge the gap between generative models and game theory by introducing a novel probabilistic framework for modelling multi-agent decision-making problems. This innovative framework reinterprets these problems as generative processes. Furthermore, we introduce a training objective known as "flow equilibrium" and establish a theoretical connection between flow equilibrium and Nash equilibrium. To analyse the theoretical properties of our framework, we present a tabular version algorithm along with a convergence proof. Additionally, we propose an extended algorithm incorporating neural networks to handle more complex environments. Notably, our framework naturally incorporates opponent modelling. Harnessing the capabilities of generative models, our framework excels in capturing the intricate dynamics of strategic interactions among agents. We validate our approach through testing on various multi-agent tasks, including cooperative and general-sum games. The empirical results consistently support our theoretical findings, demonstrating that our framework consistently outperforms existing methods in terms of solution quality.

Primary Area: general machine learning (i.e., none of the above)

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Submission Number: 7790