Markets with Heterogeneous Agents: Dynamics and Survival of Bayesian vs. No-Regret Learners

This paper examines the performance of Bayesian learners and no-regret learners in competitive asset markets, identifying conditions for their survival or vanishing. It contrasts the economic focus on Bayesian learning with the computer science emphasis on no-regret learning, highlighting that low regret doesn't always guarantee market survival against a perfect Bayesian, while Bayesian learning can be fragile to slight errors. The research proposes a robust Bayesian update strategy that combines the advantages of both approaches, achieving constant regret in stable environments and logarithmic regret during distribution shifts, offering a more adaptable solution for algorithmic trading. The document also bridges the theoretical frameworks of regret minimization and Bayesian learning in asset markets, contributing to a deeper understanding of heterogeneous learning agents' dynamics and their impact on markets.