Personalized pricing, which involves tailoring prices based on individual
characteristics, is commonly used by firms to implement a consumer-specific
pricing policy. In this process, buyers can also strategically manipulate their
feature data to obtain a lower price, incurring certain manipulation costs.
Such strategic behavior can hinder firms from maximizing their profits. In this
paper, we study the contextual dynamic pricing problem with strategic buyers.
The seller does not observe the buyer's true feature, but a manipulated feature
according to buyers' strategic behavior. In addition, the seller does not
observe the buyers' valuation of the product, but only a binary response
indicating whether a sale happens or not. Recognizing these challenges, we
propose a strategic dynamic pricing policy that incorporates the buyers'
strategic behavior into the online learning to maximize the seller's cumulative
revenue. We first prove that existing non-strategic pricing policies that
neglect the buyers' strategic behavior result in a linear $\Omega(T)$ regret
with $T$ the total time horizon, indicating that these policies are not better
than a random pricing policy. We then establish that our proposed policy
achieves a sublinear regret upper bound of $O(\sqrt{T})$. Importantly, our
policy is not a mere amalgamation of existing dynamic pricing policies and
strategic behavior handling algorithms. Our policy can also accommodate the
scenario when the marginal cost of manipulation is unknown in advance. To
account for it, we simultaneously estimate the valuation parameter and the cost
parameter in the online pricing policy, which is shown to also achieve an
$O(\sqrt{T})$ regret bound. Extensive experiments support our theoretical
developments and demonstrate the superior performance of our policy compared to
other pricing policies that are unaware of the strategic behaviors.

个性化定价策略探讨了与策略性购买者的上下文动态定价问题，并提出了一个战略动态定价策略，该策略能够最大化卖方的累积收入，并能同时估计估值参数和成本参数，从而达到 O (sqrt (T)) 的遗憾上界。

具有战略买家的情境动态定价

Contextual Dynamic Pricing with Strategic Buyers

We study revenue optimization learning algorithms for posted-price auctions
with strategic buyers. We analyze a very broad family of monotone regret
minimization algorithms for this problem, which includes the previously best
known algorithm, and show that no algorithm in that family admits a strategic
regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new
algorithm that achieves a strategic regret differing from the lower bound only
by a factor in $O(\log T)$, an exponential improvement upon the previous best
algorithm. Our new algorithm admits a natural analysis and simpler proofs, and
the ideas behind its design are general. We also report the results of
empirical evaluations comparing our algorithm with the previous state of the
art and show a consistent exponential improvement in several different
scenarios.

该研究针对公告价格拍卖中存在的策略买家，研究了收入最优化的学习算法，提出了一种新的算法，相较于之前最好的算法，在减小策略遗憾度方面有指数级改善，且表现优于现有技术。