Contextual Dynamic Pricing with Strategic Buyers
Pangpang Liu Zhuoran Yang Zhaoran Wang Will Wei Sun
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.