Pseudo-collusion in a centralized algorithmic financial market

Recent studies have increasingly explored whether reinforcement learning algorithms can give rise to cooperative behavior that results in non-competitive pricing across various market settings. In financial markets, Cartea et al. (2022) show that market makers using multi-armed bandit (MAB) algorithms generally converge to competitive pricing in quote-driven over-the-counter (OTC) markets, barring some unlikely exceptions where all market makers use a specific MAB variant and the number of competitors is small. However, theoretical reasoning suggests that a Nash equilibrium under price competition (as can be observed in quote-driven OTC markets) is inherently easier to learn than a Nash equilibrium under quantity competition, as best responses are more straightforward to identify in the former case. In this paper, we investigate whether algorithmic liquidity providers converge to a competitive equilibrium in a Kyle-style market (Kyle, 1989), where competition between them occurs through demand schedules. Beyond its analytical tractability, this market structure is supported by theoretical arguments and increasingly underlies real-world implementations such as periodic batch auctions. Our findings indicate that sub-competitive liquidity provision arises in this setting for two out of the three reinforcement learning algorithms tested, with the resulting price inefficiency persisting even as the number of competing liquidity providers grows large.