design coupon allocation algorithms

This paper investigates how recommendation algorithms affect market transaction efficiency and buyer welfare, focusing on designing mechanisms that maximize buyers’ expected utility. Using game-theoretic modeling and mechanism design, we propose the first recommendation framework optimized for buyer utility, rigorously characterizing the optimal strategy: the algorithm can strategically introduce recommendation bias to incentivize price reductions by sellers, while preserving buyers’ aggregate expected utility under full seller information. A key contribution is the revelation that information transparency—contrary to conventional wisdom—does not harm buyer welfare; instead, it significantly improves fairness in utility distribution between high- and low-value buyers. Extending the framework to multi-seller settings yields Pareto improvements. Our results demonstrate that recommendation systems can enhance distributive justice through structured information interventions—without compromising allocative or transactional efficiency.

This work addresses exposure inequality, reduced diversity, and regulatory risks in online platform recommendations caused by algorithmic bias toward popular items. We propose FAIR, the first combinatorial item-selection framework explicitly enforcing *pairwise fairness*: it ensures approximately equal exposure probabilities for any pair of items via linear programming. Methodologically, we introduce a provably 1/2-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS), integrating the ellipsoid method, parameterized knapsack approximation, and a dual separation oracle. Experiments on MovieLens and synthetic datasets validate FAIR’s effectiveness, quantify the “fairness cost” (i.e., the trade-off between fairness and utility), and demonstrate its ability to jointly optimize fairness, diversity, and recommendation revenue.

This paper studies the joint assortment and ranking optimization problem for matching platforms, where the goal is to maximize the expected number of matches by selecting and ordering product categories shown to both demand and supply sides under general choice models (e.g., the Multinomial Logit model). Methodologically, it characterizes the optimal adaptivity gaps among non-adaptive, semi-adaptive, and fully adaptive policies—establishing tight bounds of 2 and $e/(e-1)$, respectively. It further proposes the first polynomial-time $1/4$-approximation algorithm for fully adaptive policies and extends it to settings with cardinality-constrained assortments. All theoretical guarantees are tight. Experiments on real-world datasets confirm the algorithm’s robust empirical performance.

This paper studies the multi-stage dynamic assortment optimization problem under knapsack-style inventory constraints: a retailer must dynamically adjust its product assortment each period—based on the multinomial logit (MNL) choice model—to maximize cumulative profit as inventory depletes over time. Since the problem is NP-hard and conventional approaches (e.g., static planning or greedy heuristics) lack theoretical performance guarantees, we propose the first epoch-based re-optimization algorithm with provable bounds. Our key innovation lies in reformulating the denominator structure of the MNL objective as linear constraints, enabling tractable fluid approximations and rigorous stochastic analysis. The algorithm achieves an $O(log(TC))$ regret bound—logarithmic in the time horizon $T$ and total capacity $C$—while maintaining computational efficiency and asymptotic optimality. It significantly outperforms existing methods both theoretically and empirically.

This study investigates how advertising displays—such as “featured recommendations”—on digital platforms influence consumers’ stochastic choice behavior. By extending the Luce multinomial logit model, the authors propose a hybrid attention mechanism wherein consumers either focus on advertised items or consider the full choice set, and they develop a generalized framework in which advertising simultaneously affects both attention and preference. The work innovatively disentangles these dual effects for the first time, establishing identification conditions and a data-driven decomposition method based on observed choices. Building on random utility theory and integrating parameter identification, econometric inference, and optimization algorithms, the model primitives are uniquely identified, enabling clear separation of attention and preference effects. This approach yields implementable rules for optimizing the design of advertising subsets to maximize platform profit.

This work addresses the decision uncertainty inherent in stochastic policies commonly used in dynamic assortment optimization. We propose a derandomization algorithm that transforms inventory-agnostic, sampling-based stochastic policies into deterministic assortment sequences, eliminating randomness without sacrificing expected revenue and even uncovering superior solutions beyond the support of the original policy. We establish, for the first time, that any locally optimal deterministic policy achieves a $(1/2 - \varepsilon)$-approximation guarantee relative to the optimal stochastic policy. An efficient implementation framework is developed by integrating a static assortment optimizer with local optimality analysis. Experimental results demonstrate that the resulting deterministic policies not only match but often exceed the expected revenue of the original stochastic policies while substantially reducing decision uncertainty.

This paper addresses the problem of enhancing social welfare in two-sided matching platforms without degrading existing high-quality matches, while respecting budget and resource constraints. It proposes a selective constraint-relaxation mechanism wherein only a subset of agents—e.g., those with overly restrictive preferences or eligibility criteria—are guided to moderately loosen their constraints. To ensure fairness and efficiency, the authors introduce a hierarchical participation guarantee framework and a customizable social welfare objective function. They formulate the problem as a combinatorial optimization model and design polynomial-time algorithms applicable to both one-to-one and many-to-one matching settings. Extensive experiments on three real-world datasets demonstrate that the proposed approach significantly improves matching efficiency and aggregate social welfare. Quantitative analysis further reveals how different participation guarantees affect system performance, empirically validating the method’s effectiveness and practical applicability.

This study addresses the generalized coupon collector problem, which involves computing statistical quantities—such as the expectation, variance, and second moment—of the number of draws required to collect a specified number of coupons of certain types under arbitrary drawing probabilities. The work proposes the first polynomial-time algorithm applicable to any probability distribution over coupon types, establishing a unified framework that accommodates both targeted subsets and multi-copy collection requirements. By leveraging a tailored Markov model combined with dynamic programming, the method efficiently traverses the high-dimensional state space to enable exact computation of these moments. Under the uniform distribution, the algorithm achieves polynomial time complexity in the number of coupon types $n$, substantially enhancing computational feasibility compared to prior approaches.

Existing evaluation methods struggle to effectively assess large language models (LLMs) on multi-constraint combinatorial shopping tasks, which require simultaneous adherence to semantic plausibility and hard constraints—such as budget limits, coupon applicability, and item availability—and often admit multiple valid solutions. This work proposes the first evaluation framework that jointly accounts for semantic reasonableness and verifiable compliance with hard constraints. Leveraging a “witness basket” mechanism, the framework automatically generates user queries, constraint specifications, and evaluation criteria within simulated e-commerce and food-delivery environments. It combines semantic scoring with deterministic rule-based validation for comprehensive assessment. Experimental results reveal that state-of-the-art LLM agents perform poorly on this benchmark, highlighting significant deficiencies in their ability to perceive constraints and make reliable combinatorial decisions.