We study overpricing in a repeated game between two representative agents: a market maker, who controls market liquidity, and a market taker, who chooses trade quantities. Market prices evolve through the endogenous price impact of trades and exogenous shocks. We define overpricing relative to a counterfactual price path that holds fixed the same sequence of shocks while shutting down price impact, and characterize the set of feasible strategy profiles that generate persistent overpricing while respecting cash and inventory constraints. We provide a sufficient condition for decentralized learning to reach the overpricing region in finite time, and we show that this condition is satisfied, in particular, by projected stochastic gradient ascent. A key step in the analysis is a decomposition of the game into a competitive component, which favors zero price impact, and a collaborative component, which makes overpricing jointly profitable when aggregate inventory is positive. We further show that the same structural incentives govern both myopic and farsighted objectives. Together, these results show how decentralized learning by adaptive market agents can lead to persistent overpricing in financial markets.

翻译：我们研究了两个典型主体在重复博弈中的超价现象：一个控制市场流动性的做市商，以及一个选择交易量的市场接收者。市场价格通过交易的内生价格冲击和外生冲击共同演化。我们将超价定义为相对于一个反事实价格路径的偏离——该路径在固定相同冲击序列的同时关闭价格冲击，并刻画了在满足现金和库存约束下能够产生持续性超价的可行策略组合集合。我们提供了一个充分条件，使得去中心化学习在有限时间内能够达到超价区域，并证明该条件特别适用于投影随机梯度上升算法。分析中的一个关键步骤是将博弈分解为竞争性成分（偏向零价格冲击）与协作性成分（当总库存为正时使超价联合有利可图）。我们进一步证明，相同的结构激励既支配短视目标，也支配远见目标。这些结果表明，自适应市场主体的去中心化学习如何能够在金融市场中导致持续性超价。