The widespread use of market-making algorithms in electronic over-the-counter markets may give rise to unexpected effects resulting from the autonomous learning dynamics of these algorithms. In particular the possibility of “tacit collusion” among market makers has increasingly received regulatory scrutiny. We model the interaction of market makers in a dealer market as a stochastic differential game of intensity control with partial information and study the resulting dynamics of bid-ask spreads. Competition among dealers is modeled as a Nash equilibrium, while collusion is described in terms of Pareto optima. Using a decentralized multi-agent deep reinforcement learning algorithm to model how competing market makers learn to adjust their quotes, we show that the interaction of market making algorithms via market prices, without any sharing of information, may give rise to tacit collusion, with spread levels strictly above the competitive equilibrium level.

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经销商市场做市算法的动态：学习与默契共谋

做市算法在电子场外交易市场中的广泛使用可能会因这些算法的自主学习动态而产生意想不到的效果。尤其是做市商之间“默契合谋”的可能性越来越受到监管部门的审查。我们将经销商市场中做市商的相互作用建模为具有部分信息的强度控制的随机微分博弈，并研究由此产生的买卖价差动态。经销商之间的竞争被建模为纳什均衡，而共谋则被描述为帕累托最优。使用去中心化多智能体深度强化学习算法来模拟竞争做市商如何学习调整其报价，我们表明，做市算法通过市场价格进行交互，在没有任何信息共享的情况下，可能会导致默契共谋，从而产生价差水平严格高于竞争均衡水平。