How can LLMs learn strategies in multi-leader Stackelberg games?
LEARNING IN CONJECTURAL STACKELBERG GAMES
This paper introduces Conjectural Stackelberg Games (CSG), a game-theoretic model where multiple leader agents make decisions while anticipating the reactions of a follower agent, and also anticipate each other's actions through learned conjectures. A two-stage algorithm called COSTAL is presented, where agents first learn conjectures about other agents' responses and then iteratively update their own strategies based on these learned conjectures. Key points for LLM-based multi-agent systems include: agents don't need perfect knowledge of other agents' behaviors; conjectures, learned from training data, can replace best-response calculations; convergence guarantees are provided for the learning algorithm; and the approach is computationally tractable, even with many agents. This opens possibilities for using CSGs as a framework for LLM-based multi-agent applications, where accurate prediction of others' behavior is difficult or expensive.