In Bayesian single-item auctions, a monotone bidding strategy--one that prescribes a higher bid for a higher value type--can be equivalently represented as a partition of the quantile space into consecutive intervals corresponding to increasing bids. Kumar et al. (2024) prove that agile online gradient descent (OGD), when used to update a monotone bidding strategy through its quantile representation, is strategically robust in repeated first-price auctions: when all bidders employ agile OGD in this way, the auctioneer's average revenue per round is at most the revenue of Myerson's optimal auction, regardless of how she adjusts the reserve price over time. In this work, we show that this strategic robustness guarantee is not unique to agile OGD or to the first-price auction: any no-regret learning algorithm, when fed gradient feedback with respect to the quantile representation, is strategically robust, even if the auction format changes every round, provided the format satisfies allocation monotonicity and voluntary participation. In particular, the multiplicative weights update (MWU) algorithm simultaneously achieves the optimal regret guarantee and a strong strategic robustness guarantee in this auction setting. At a technical level, our results are established via a simple relation that bridges Myerson's auction theory and standard no-regret learning theory.

翻译：在贝叶斯单物品拍卖中，单调竞价策略——即对更高价值类型规定更高出价的策略——可以等价地表示为将分位数空间划分为连续区间，每个区间对应递增的出价。Kumar等人（2024）证明，当通过其分位数表示形式更新单调竞价策略时，敏捷在线梯度下降（OGD）在重复第一价格拍卖中具有策略鲁棒性：当所有竞拍者均以这种方式采用敏捷OGD时，无论拍卖人如何随时间调整保留价格，其每轮平均收益至多为Myerson最优拍卖的收益。本研究表明，这种策略鲁棒性保证并非敏捷OGD或第一价格拍卖所独有：任何无悔学习算法，在接收关于分位数表示的梯度反馈时，均具有策略鲁棒性——即使拍卖形式每轮发生变化，只要该形式满足分配单调性与自愿参与条件。特别地，乘性权重更新（MWU）算法在此拍卖设定中同时实现了最优悔值保证与强策略鲁棒性保证。在技术层面，我们的结果通过一个连接Myerson拍卖理论与标准无悔学习理论的简单关系式得以建立。