We analyze the performance of heterogeneous learning agents in asset markets with stochastic payoffs. Our main focus is on comparing Bayesian learners and no-regret learners who compete in markets and identifying the conditions under which each approach is more effective. We formally relate the notions of survival and market dominance studied in economics and the framework of regret minimization, thereby bridging these theories. A central finding is that regret plays a key role in market selection, but low regret alone does not guarantee survival: surprisingly, an agent may achieve even logarithmic regret and yet be driven out of the market when competing against a Bayesian learner with a finite prior that assigns positive probability to the correct model. At the same time, we show that Bayesian learning is highly fragile, while no-regret learning requires less knowledge of the environment and is therefore more robust. Motivated by this contrast, we propose two simple hybrid strategies that incorporate Bayesian updates while improving robustness and adaptability to distribution shifts, taking a step toward a best-of-both-worlds learning approach. More broadly, our work contributes to the understanding of dynamics of heterogeneous learning agents and their impact on markets.

翻译：我们分析了具有随机收益的资产市场中异质学习代理的表现。主要关注点是比较在市场中竞争的贝叶斯学习者与无遗憾学习者，并确定每种方法更为有效的条件。我们正式建立了经济学中研究的生存与市场主导概念与遗憾最小化框架之间的联系，从而桥接了这些理论。一个核心发现是，遗憾在市场选择中扮演关键角色，但低遗憾本身并不能保证生存：令人惊讶的是，即使代理实现了对数级遗憾，当与具有有限先验且该先验对正确模型赋予正概率的贝叶斯学习者竞争时，该代理仍可能被逐出市场。同时，我们表明贝叶斯学习高度脆弱，而无遗憾学习对环境知识的需求较少，因此更为稳健。受这一对比的启发，我们提出了两种简单的混合策略，这些策略结合了贝叶斯更新，同时提高了对分布变化的稳健性和适应性，朝着“两全其美”的学习方法迈进了一步。更广泛地说，我们的工作有助于理解异质学习代理的动态及其对市场的影响。