A Computer-Aided Approach for Approximate Nash Equilibria

Xiaotie Deng, Dongchen Li, Hanyu Li

Abstract: Ever since the landmark PPAD-completeness result for Nash equilibria in two-player normal-form games, significant research has focused on developing polynomial-time algorithms for \(\epsilon \)-approximate Nash equilibria (\(\epsilon \)-NE). The challenge of establishing the optimal approximation guarantee in polynomial time remains pivotal. While advancements have been made for two-player games, progress in multi-player games is still limited. Difficulties arise due to the increased sophistication of multi-player games and the lack of tools for analyzing approximation bounds. This paper presents a method that allows machines to perform approximation analysis for multi-player games using a domain-specific language called LegoNE. LegoNE enables researchers to design algorithms with only high-level intuitions, while it automatically uncovers the underlying structures and proves the approximation bounds on its own. Using LegoNE, we design a new algorithm for three-player games that achieves a \((0.5+\delta )\)-NE, improving the previous best bound \((0.6+\delta )\). This shows that human-machine collaboration allows us to obtain higher-level understandings and better results.

External IDs:doi:10.1007/978-3-032-08560-3_18