提出无遗憾市场做市策略，适配价格与估值的多种动态场景。
Market Making without Regret
- 基于序列决策框架，设计可自适应的买卖价差策略。
- 在独立同分布假设下，首次证明理论最小后悔值下界。
- 揭示做市与第一价格拍卖的深层联系，适合算法交易研究者。
我们研究一种序贯决策场景：每轮中，做市商设定买入价 $B_t$ 和卖出价 $A_t$，面对具有私有估值的交易者（做市客）。若估值低于买入价或高于卖出价，则发生交易（买入或卖出）。若交易发生，令 $M_t$ 为当轮市场成交价（仅在本轮末观测到），做市商收益为 $M_t - B_t$（买入时）或 $A_t - M_t$（卖出时）。本文在多种假设（对抗性、独立同分布及其变体）下刻画了做市商相对于最优固定报价对的后悔值。上界分析揭示了做市与第一价格拍卖及动态定价之间的深刻关联。主要技术贡献是针对利普希茨分布且价格与估值独立情形的下界证明。分析难点源于奖励与反馈函数的独特结构，使得算法可任意调节探索成本。
原文摘要 · Abstract (English)
We consider a sequential decision-making setting where, at every round $t$, a market maker posts a bid price $B_t$ and an ask price $A_t$ to an incoming trader (the taker) with a private valuation for one unit of some asset. If the trader's valuation is lower than the bid price, or higher than the ask price, then a trade (sell or buy) occurs. If a trade happens at round $t$, then letting $M_t$ be the market price (observed only at the end of round $t$), the maker's utility is $M_t - B_t$ if the maker bought the asset, and $A_t - M_t$ if they sold it. We characterize the maker's regret with respect to the best fixed choice of bid and ask pairs under a variety of assumptions (adversarial, i.i.d., and their variants) on the sequence of market prices and valuations. Our upper bound analysis unveils an intriguing connection relating market making to first-price auctions and dynamic pricing. Our main technical contribution is a lower bound for the i.i.d. case with Lipschitz distributions and independence between prices and valuations. The difficulty in the analysis stems from the unique structure of the reward and feedback functions, allowing an algorithm to acquire information by graduating the "cost of exploration" in an arbitrary way.
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