Incentive-aware Contextual Pricing with Non-parametric Market Noise

We consider a dynamic pricing problem for repeated contextual second-price auctions with strategic buyers whose goals are to maximize their long-term time discounted utility. The seller has very limited information about buyers' overall demand curves, which depends on $d$-dimensional context vectors characterizing auctioned items, and a non-parametric market noise distribution that captures buyers' idiosyncratic tastes. The noise distribution and the relationship between the context vectors and buyers' demand curves are both unknown to the seller. We focus on designing the seller's learning policy to set contextual reserve prices where the seller's goal is to minimize his regret for revenue. We first propose a pricing policy when buyers are truthful and show that it achieves a $T$-period regret bound of $\tilde{\mathcal{O}}(\sqrt{dT})$ against a clairvoyant policy that has full information of the buyers' demand. Next, under the setting where buyers bid strategically to maximize their long-term discounted utility, we develop a variant of our first policy that is robust to strategic (corrupted) bids. This policy incorporates randomized "isolation" periods, during which a buyer is randomly chosen to solely participate in the auction. We show that this design allows the seller to control the number of periods in which buyers significantly corrupt their bids. Because of this nice property, our robust policy enjoys a $T$-period regret of $\tilde{\mathcal{O}}(\sqrt{dT})$, matching that under the truthful setting up to a constant factor that depends on the utility discount factor.