We incorporate the effects of multi-unit purchases into consumer choice models and investigate the associated joint assortment and pricing problems. Under the proposed two-stage choice framework, consumers first form a consideration set, and then select a product with the optimal quantity from the consideration set  to maximize their utility.  For the joint assortment and pricing problem with homogeneous consumers, we find that a multi-purchase-willingness-ordered assortment is optimal under certain technical conditions, and propose a polynomial-time algorithm to find the optimal assortment and prices for general cases. We further show that the optimal prices and assortment size are not monotone in the multi-purchase-willingness. For the joint assortment and pricing problem with heterogeneous consumers, we first prove that this problem is NP-hard. We then consider a scenario with discrete prices and develop a fully polynomial-time approximation scheme by considering a finite number of consumer segments and nested consideration sets. We conduct an empirical study on the JD.com dataset and show that the new choice framework can improve model fitting and prediction accuracy compared with existing choice models with multiple purchases. We reveal that our model is especially suitable for datasets exhibiting a strong diminishing marginal effect for product variety.  We further extend our analysis to price competition and establish the existence and uniqueness of a Nash equilibrium. For the joint optimization with fixed costs, we develop an algorithm that can find a solution guaranteeing at least half of the optimal expected profit.

Artificial intelligence (AI) is increasingly being used in the development of clinical algorithms to support clinical decision making. Their potential bias, as reflected in disparities in accuracy across patient populations, has received growing attention. The U.S. Centers for Medicare and Medicaid Services (CMS) recently proposed an anti-bias liability rule stating that providers may be liable for erroneous medical decisions made in reliance on biased algorithms. In this paper, we model and analyze how such anti-discrimination liability rules affect both upstream AI development decisions (by an AI firm) and downstream AI deployment decisions (by a physician). The AI firm first decides on the algorithm's accuracy for two types of patients, where training the algorithm for the disadvantaged patients requires higher development costs; in response, the physician decides whether and how to use the algorithm, which may be biased against the disadvantaged patient, when prescribing a treatment plan. Using a biased algorithm can help reduce clinical uncertainty, but may expose the physician to legal liability in the event of a treatment error. We show several results with important policy implications. First, anti-discrimination liability can lead to discriminatory use of AI by inducing the physician to (1) underuse AI and (2) disproportionately reject AI recommendations for disadvantaged patients. Second, we show a non-monotonic effect of liability on the physician's decision to use AI: as liability increases, the physician is  less likely to use AI for disadvantaged patients and then more likely to use it.  Finally, we show mandating equal accuracy can make all patients worse off, because it removes liability concerns and leads to more AI use, but the physician may overuse AI for disadvantaged patients.

We consider one supplier that decides the production quantity to serve two manufacturers, who contract with the supplier for raw materials and sell their finished products to the same uncertain market under Cournot competition. The manufacturers can either contract with the supplier by a push contract or by a pull contract. We first establish the supplier's production decision, and the manufacturers' ordering and selling decisions, given both manufacturers' contracting strategies, i.e., push contract or pull contract. We characterize the first-mover advantage of a push contract under competition, and find that when a competitor chooses a pull contract, the manufacturer with a push contract will possibly reduce his order quantity even when the supplier reduces supply to his competitor. Then, we investigate manufacturers' equilibrium contracting strategies, and the supplier's contracting preference. Interestingly, we find that completely symmetric manufacturers can choose different contracting strategies even when the wholesale prices for both contracts are identical. Finally, we numerically characterize how competition influences the value of pull and push contracts. From the perspective of the whole supply chain, we find that a pull contract alone cannot achieve Pareto improvement, and only a mixed contract can possibly achieve Pareto improvement under reasonable wholesale prices.

E-retailing often involves displaying advertised products during a search, with additional unadvertised products recommended when consumers click on a specific advertised product page. We model this process as a two-stage choice behavior with product revisitation: (1) A consumer is initially attracted to either an advertised product or the outside option. (2) She can observe unadvertised products if and only if attracted to an advertised product, then she revisits the advertised product and compares it with all unadvertised options to make a final selection. Our empirical study using JD.com data demonstrates that our proposed model can outperform a mixture of multinomial logit models in both fitting and prediction. For assortment planning, we prove the problem is NP-complete and propose an algorithm that includes some high-revenue and low-preference advertised products and some high-revenue unadvertised products, guaranteeing at least half of the optimal expected profit. We also devise a fully polynomial-time approximation scheme (FPTAS). For pricing, we derive the optimal pricing strategy and show that prices for unadvertised products may exhibit non-monotonic changes as their total preference increases. We next incorporate advertising costs for advertised products and devise an FPTAS for the corresponding assortment optimization problem. Finally, we extend our analysis to a Stackelberg game framework, examining two competing firms engaged in assortment planning and pricing strategies.