Can I find robust Nash equilibria efficiently in data-driven games?
Nash equilibrium seeking for a class of quadratic-bilinear Wasserstein distributionally robust games
This paper addresses decision-making in multi-agent systems under uncertainty, where each agent has private data and differing levels of risk aversion. It focuses on a specific class of games with quadratic-bilinear cost functions affected by uncertainty and uses Wasserstein ambiguity sets to model the uncertainty in each agent's private data. The core contribution is a reformulation of this complex distributionally robust game into a more computationally tractable variational inequality problem, making it easier to find stable solutions (Nash equilibria) where no agent can improve their outcome by unilaterally changing their strategy.
For LLM-based multi-agent systems, this research offers a way to model agents with different "personalities" regarding risk and data interpretation. The reformulation provides a scalable approach for finding stable solutions in such systems, even with large datasets and complex interactions between agents. The paper's focus on individual, data-driven uncertainty sets is particularly relevant to personalized LLMs and their integration into multi-agent environments. The data-driven nature of the approach aligns well with the data-centric paradigm of LLMs. The focus on finding equilibrium solutions could impact LLM multi-agent system design, shifting from simply generating responses to strategically optimizing actions within a group of diverse agents.