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 the best-known strategic robustness guarantee. At a technical level, our results are established via a simple relation that bridges Myerson's auction theory and standard no-regret learning theory. This showcases the potential of translating standard regret guarantees into strategic robustness guarantees for specific games, without explicitly minimizing any form of swap regret.

翻译：在贝叶斯单物品拍卖中，单调竞价策略——即对更高估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，当通过分位数表示更新单调竞价策略时，灵活在线梯度下降（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灵活OGD时，无论拍卖者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灵活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，都具有策略鲁棒性——即使拍卖形式每轮发生变化，只要该形式满足分配单调性和自愿参与条件。特别地，乘性权重更新（MWU）算法同时实现了最优悔值保证和最知名的策略鲁棒性保证。在技术层面，我们的结果通过一个简洁的关系式建立，该关系式连接了Myerson拍卖理论与标准无悔学习理论。这展示了将标准悔值保证转化为特定博弈的策略鲁棒性保证的潜力，而无需显式最小化任何形式的交换悔值。