Large Language Models Can Design Game-Theoretic Objectives for Multi-Agent Planning

Game theory is a powerful paradigm to describe the interplay between participants in interactive multi-agent scenarios, and relies on the knowledge of player objectives or payoff structures for game optimal decision making. However, designing such objectives for games is challenging as it requires evaluating the impact of an agent’s actions on the behavior of others, and understanding the effect of changes in one's policy on the behavior of others. Indeed, aligning objective representations with a desired multi-agent behavior is achieved via tedious and impractical heuristics or human trial-and-error. This work aims to ease this process and proposes a multi-agent planning architecture that relies on a large language model (LLM) as the game formulation designer. First, we exhibit the zero-shot proficiency of the more capable LLMs (such as GPT-4) in tuning continuous objective function parameters in accordance with a specified high-level goal for autonomous driving examples. We then develop a planner which uses an LLM as a matrix game designer, for scenarios with discrete and finite action spaces. Given a scene history, the actions available to each agent, and high-level objectives (expressed in natural language), the LLM evaluates the payoffs associated with each combination of actions. From the game structure obtained, agents execute Nash optimal actions, the scene is re-evaluated, and the process is repeated. We evaluate our approach on a heterogeneous robot planning task inspired by wildlife conservation, as well as a household multi-humanoid transport task, and show the superiority of our LLM-based approach to other baselines