We examine the dynamics of informational efficiency in a market with asymmetrically informed, boundedly rational traders who adaptively learn optimal strategies using simple multiarmed bandit (MAB) algorithms. The strategies available to the traders have two dimensions: on the one hand, the traders must endogenously choose whether to acquire a costly information signal, on the other, they must determine how aggressively they trade by choosing the share of their wealth to be invested in the risky asset. Our study contributes to two strands of literature: the literature comparing the effects of competitive and strategic behavior on asset price efficiency under costly information as well as the actively growing literature on algorithmic tacit collusion and pseudo-collusion in financial markets. We find that for certain market environments (with low information costs) our model reproduces the results of Kyle [1989] in that the ability of traders to trade strategically leads to worse price efficiency compared to the purely competitive case. For other environments (with high information costs), on the other hand, our results show that a market with strategically acting traders can be more efficient than a purely competitive one. Furthermore, we obtain novel results on the ability of independently learning traders to coordinate on a pseudo-collusive behavior, leading to non-competitive pricing. Contrary to some recent contributions (see e.g. [Cartea et al. 2022]), we find that the pseudo-collusive behavior in our model is robust to a large number of agents, demonstrating that even in the setting of financial markets with a large number of independently learning traders non-competitive pricing and pseudo-collusive behavior can frequently arise.

翻译：本文研究了一个市场中信息效率的动态变化，该市场中的交易者信息不对称且有限理性，他们使用简单的多臂老虎机（MAB）算法自适应地学习最优策略。交易者可用的策略有两个维度：一方面，交易者必须内生地选择是否获取一个成本高昂的信息信号；另一方面，他们必须通过选择投资于风险资产的财富比例来决定交易的激进程度。我们的研究对两个文献分支做出了贡献：一是比较在信息成本下竞争性与战略性行为对资产价格效率影响的文献，二是关于金融市场中算法默示合谋与伪合谋的活跃增长文献。我们发现，对于某些市场环境（信息成本较低），我们的模型再现了Kyle [1989]的结果，即交易者进行战略性交易的能力会导致价格效率比纯竞争情况更差。另一方面，对于其他环境（信息成本较高），我们的结果表明，具有战略性行为交易者的市场可能比纯竞争市场更有效率。此外，我们获得了关于独立学习交易者协调形成伪合谋行为能力的新结果，这导致了非竞争性定价。与近期的一些研究（例如[Cartea等人，2022]）相反，我们发现我们模型中的伪合谋行为对大量智能体具有稳健性，这表明即使在拥有大量独立学习交易者的金融市场环境中，非竞争性定价和伪合谋行为也经常出现。