Can no-regret learners survive in markets with Bayesians?
Learning in Markets with Heterogeneous Agents: Dynamics and Survival of Bayesian vs. No-Regret Learners
February 13, 2025
https://arxiv.org/pdf/2502.08597This paper analyzes how different AI learning strategies perform in a simulated asset market. It compares "Bayesian learners," which maintain beliefs about market behavior and update them based on observations, with "no-regret learners," which adapt their strategies based on past performance.
Key findings relevant to LLM-based multi-agent systems:
- Survival depends on relative regret: An agent's long-term success depends not just on minimizing its own regret, but on having consistently lower regret than other agents. Even small differences in regret can lead to one agent dominating the market.
- Bayesian learning is fragile: While optimal when correct, Bayesian agents are sensitive to errors in their initial beliefs (priors) or update rules. Small inaccuracies can be exploited by no-regret learners.
- No-regret learning is robust: No-regret learners, while not always optimal, are less sensitive to model errors and can exploit weaknesses in Bayesian agents.
- Connection to LLM agents: The paper's market setting, though simplified, parallels multi-agent interactions where LLMs act as agents making decisions based on learned models of their environment, highlighting the importance of robustness and relative performance in such systems. The fragility of Bayesian updates emphasizes the challenge of maintaining accurate beliefs in dynamic environments where LLMs might be susceptible to manipulation or misinformation.