online retailers

Abstract: A pricing page can walk the posted price up to the last amount a buyer still accepts, a recommender can hold back a better item for a barely acceptable promoted one, and a classifier can shift its boundary once applicants change their features. The system predicts the response and then picks the menu that serves its own objective, so the surplus above the user's cutoff is taken. Playing the single best action publishes that cutoff, while noise on actions the user would never take throws away payoff and teaches the platform that a worse menu is still acceptable. We study unpredictable near-optimal policies (UNOP), which mix uniformly on near-best actions that remain individually rational. The mixture is a commitment about the response. On a finite price grid, when the best sure-demand price strictly out-earns the randomized band, a seller who already knows the curve posts below the band, and the purchase that occurs is deterministic. Knowing that curve is not the same as predicting the next draw. The mixture can be learned and the optimizer can match its best response, while the user's payoff stays higher because the mixture changes which action is targeted. In pricing and in policy-aware recommendation this leaves more surplus than greedy play when the platform optimizes against the curve and more than one action is acceptable. The gain goes away under quality ranking, a singleton near-optimal set, a wrong utility estimate, or a short-horizon explorer. That is also where mixing should be turned off if the other side is trying to cooperate.

Abstract: Personalised pricing maximises expected revenue from a market but requires detailed information about individual customers. How much of this revenue can be recovered using a simple posted price based on a finite number of samples from the underlying value distribution? We answer this question by maximising the worst-case ratio between the expected revenues of posted and personalised pricing over the fundamental class of $λ$-regular value distributions. Our results reveal a structural transition as a function of $λ$. For the class of monotone hazard rate (MHR) distributions, corresponding to $λ= 0$, the sample mean is an optimal statistic: the entire sample can be compressed into its average without any loss of revenue. Beyond the MHR class, corresponding to $λ> 0$, this property disappears. We show that the sample mean is no longer optimal, revealing that optimal sample-based pricing rules become substantially more intricate. Nevertheless, we show that a remarkably simple order-statistic based pricing rule is asymptotically optimal as the number of samples $n$ grows, achieving the optimal approximation ratio up to a tight error of order $1/n$. Our analysis combines techniques from probability, approximation theory and optimization, including doubly infinite linear programming, hypergeometric functions, and combinatorial identities involving incomplete Beta functions.

Abstract: Group recommender systems typically rely on either aggregating individual preferences or treating groups as distinct meta-users. However, these methods often suffer from static aggregation strategies or data sparsity issues within group histories. This paper introduces a novel approach, that relies on a GNN-based architecture to learn a dual representation of each user's preferences, capturing their behavior as an independent individual from one side and as a member of a collective from the other side. By performing a differential analysis of these individual and group-oriented preferences, our system then determines the behavioral profile of each user when joining a group. Finally, specific preference aggregation strategies are defined to cope with the behavioral profiles of the users composing a group. Consequently, the system is equally capable of delivering precise recommendations to individuals and to arbitrary groups, effectively unifying the two traditional paradigms of recommendation. Experiments on synthetic data simulating diverse group settings and behaviors confirm the flexibility and relevance of the proposed approach compared to state-of-the-art methods.