Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions

Abstract

Motivated by pricing in ad exchange markets, we consider the problem of robust learning of reserve prices against strategic buyers in repeated contextual second-price auctions. Buyers' valuations for an item depend on the context that describes the item. However, the seller is not aware of the relationship between the context and buyers' valuations, i.e., buyers' preferences. The seller's goal is to design a learning policy to set reserve prices via observing the past sales data, and her objective is to minimize her regret for revenue, where the regret is computed against a clairvoyant policy that knows buyers' heterogeneous preferences. Given the seller's goal, utility-maximizing buyers have the incentive to bid untruthfully in order to manipulate the seller's learning policy. We propose learning policies that are robust to such strategic behavior. These policies use the outcomes of the auctions, rather than the submitted bids, to estimate the preferences while controlling the long-term effect of the outcome of each auction on the future reserve prices. When the market noise distribution is known to the seller, we propose a policy called Contextual Robust Pricing (CORP) that achieves a T-period regret of O(d log(T d) log(T )), where d is the dimension of the contextual information.When the market noise distribution is unknown to the seller, we propose two policies whose regrets are sublinear in T .

Contextual search in the presence of irrational agents

“…Moving from the single-to the higher-dimensional case, there have been mainly two families of algorithms. The more classical approach involves statistical methods based, for example, on linear regression and the central limit theorem [1,3,4,17,18,20,32,35,38]. This line of work does not deal with adversarial contexts and tends to obtain performance loss of the order of…”

Boosted Second Price Auctions

“…In addition, define τ i = {t ∈ [T ] : b t i ≥ r i , |S t | ≥ 2} as the set of the auctions in which both b t i ≥ r i and the number of bids that clear their reserve price is at least two. 18 Let h t −i and s t −i , t ∈ τ i , be respectively the highest and second-highest 19 boosted bids of the bidders in set S t \{i}. Define r * −i and β * −i respectively as the reserve price and boost value associated with h t −i .…”

“…20 Observe that the 18 When there is only one bidder in an auction, assigning boosts does not change the allocation and payment of the auction. 19 When there are only two bidders in set S t , t ∈ τ i , then we set s t −i , to zero. 20 Let τ h i be the set of auctions in τ i in which buyer i has the highest boosted bid and his payment is governed by the the second highest boosted bid; that is,…”

“…Further, only recently, several theoretical papers have made some progress in this direction under certain assumptions; see, for example, [1,2,19,24,30]. It would be interesting to study how strategic bidders change their behavior to game the learning algorithm of BSP auctions and how this behavior impacts the seller.…”

Dynamic Pricing and Demand Learning on a Large Network of Products: A PAC-Bayesian Approach

“…The related literature in operations research and management science (OR/MS) is more recent and focuses on near-optimal or asymptotically optimal policies in more general problem settings-see, for example, Aviv and Pazgal (2005), Araman and Caldentey (2009), Besbes and Zeevi (2009), Farias and Van Roy (2010), Harrison et al (2012). This literature has been expanding in various directions, including dynamic pricing based on contextual information (Nambiar et al 2019, Chen et al 2021, Ban and Keskin 2020, Golrezaei et al 2021) and pricing in nonstationary demand environments (den Boer 2015, Zeevi 2017, Chen et al 2019). The vast majority of the aforementioned works focus on the pricing for a single product.…”