The price of new brand-name prescription drugs has been rising fast in the United States. For example, the Amgen cholesterol drug Repatha had an initial list price of $14,523 per year. Patients, even with insurance coverage, must pay out of pocket a significant portion of this price. The treatment might not be successful, and this possibility reduces risk-sensitive patients’ incentives to purchase the drug. The high price together with the chance of negative treatment outcomes may lead payers to deny coverage for the drug. Outcome-based pricing has been proposed as a way to reallocate the risks and improve both payer resource allocation and patient access to drugs. According to an outcome-based rebate contract between Amgen and Harvard Pilgrim Healthcare, if a patient on Repatha suffers a heart attack or a stroke, both patient and insurer are refunded the cost of the drug. We use a stylized model to analyze the effect of outcome-based pricing via rebates. Our model captures the interaction between heterogenous, price-sensitive, risk-sensitive patients who decide whether to purchase the drug; a payer deciding whether to provide coverage for the drug; and a price-setting pharmaceutical firm seeking to maximize expected profits. We find that, in many cases, a pharmaceutical firm and payer cannot simultaneously benefit from outcome-based pricing, and who will benefit is determined by the probability of treatment success. Outcome-based pricing thus appears unlikely to solve the issues of high drug prices and high payer expenditures. However, supplementing outcome-based pricing with a transfer payment from firm to payer can make payer and firm (but not necessarily the patients) better off than under uniform pricing when the drug has a low chance of success.

Problem definition: The Centers for Medicare & Medicaid Services launched the Primary Care First (PCF) initiative in January 2021. The initiative builds upon prior innovative payment models and aims at incentivizing a redesign of primary care delivery, including new modes of delivery, such as remote care. To achieve this goal, the initiative blends capitation and fee-for-service (FFS) payments and includes performance-based adjustments linked to service quality and health outcomes. We analyze a model motivated by this new payment system, and its impact on the different stakeholders, and derive insights on how to design it to reach the best possible outcome. Methodology/results: We propose an analytical model that captures patient heterogeneity in terms of health complexity, provider choice of care-delivery mode (referral to a specialist, in-person visit, or remote care), and quality of service (health outcomes and wait time). We analyze the provider decision on the mode of care delivery under both FFS and PCF and study whether PCF can be designed to yield a socially optimal outcome. We characterize analytically when patients, payer, and providers are better off under PCF and show that, in many cases, PCF can be designed to yield a socially optimal outcome. We numerically calibrate our model for 14 states in the United States. We observe that the average health status in a state is a source of heterogeneity that crucially drives the performance of PCF. We find that the model motivated by the current PCF implementation results in too much adoption of referral care and too little adoption of remote care. In addition, states with poor average health status may use more in-person care than socially optimal under a baseline (low) level of capitation. Moreover, relying on high levels of capitation leads to low adoption of in-person care. Managerial implications: Our results have health policy implications by shedding light on how PCF might impact patients, payer, and providers. Under the current performance-based adjustments, low levels of capitation should be preferred. PCF has the potential to be designed to achieve socially optimal outcomes. However, the fee per visit may need to be tailored to the local population’s health status. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.1207 .

In this paper, we study the role of capacity on the efficiency of a two-tier supply chain with two suppliers (leaders, first tier) and one retailer (follower, second tier). The suppliers compete via pricing (Bertrand competition) and, as one would expect in practice, are faced with production capacity. We consider a model with differentiated substitutable products where the suppliers are symmetric differing only by their production capacity. We characterize the prices, production amounts and profits in three cases: (1) the suppliers compete in a decentralized Nash equilibrium game, (2) the suppliers “cooperate” to optimize the total suppliers’ profit, and (3) the two tiers of the supply chain are centrally coordinated. We show that in a decentralized setting, the supplier with a lower capacity may benefit from restricting her capacity even when additional capacity is available at no cost. We also show that the loss of total profit due to decentralization cannot exceed 25 % of the centralized chain profits. Nevertheless, the loss of total profit is not a monotonic function of the “degree of asymmetry” of the suppliers’ capacities. Furthermore, we provide an upper bound on the supplier profit loss at equilibrium (compared with the cooperation setting) that depends on the “market power” of the suppliers as well as their market size. We show that there is less supplier profit loss as the asymmetry (in terms of their capacities) increases between the two suppliers. The worst case arises when the two suppliers are completely symmetric.

Markdown as a pricing modality is ubiquitous in retail whereas everyday low price (EDLP) remains relatively rare (despite its several advantages, such as simplicity). This paper explores whether and why retailers can use either of these pricing modalities as an effective defense against a competitor entering the market with the alternative pricing modality. Various studies have shown that consumers are strategic and heterogeneous in their valuation of a product. Consumers are also shown to be regret-prone, and anticipation of regret affects their purchase decisions. Consumers experience availability regret when they are unable to purchase products due to stockouts and high-price regret when they miss an opportunity to purchase products at low prices. Considering such factors, consumers decide whether, when, and from which retailer to purchase the product. In such a market environment, we find that the possible entry of a competitor should deter retailers from using the EDLP pricing modality but not markdown. We also identify a new reason for the markdown retailer to ration stock (in addition to the reason for discouraging consumers to wait for the markdown). In particular, we show that the markdown retailer can use inventory rationing to preclude a cutthroat competition and bankruptcy after the entry of an EDLP retailer. We also quantify how consumer regret affects both retailers' decisions and resulting profits. In particular, in a competitive market, the EDLP retailer cannot simply disregard consumers' availability and high-price regret (even when it stocks ample inventory and does not discount prices). We show that high-price regret and availability regret have complementary effects on the markdown retailer's rationing strategy and the EDLP retailer's price decision. Finally, using a proprietary price data set from a large department store, we show that ignoring regret factors causes the markdown retailer to leave up to 20% of its profits on the table. In addition, in a competitive market, the markdown retailer rations too aggressively when regret is ignored and, as a result, leaves some of the forgone profit to its competitor-the EDLP retailer. The retail industry is often characterized by its slim profit margins. In such an environment, the aforementioned results also suggest that retailers should seriously consider investing in developing the capacity to estimate and quantify the role of regret in consumers' purchase decisions.

We study competition and coordination in a supply chain in which a single supplier both operates a direct channel and sells its product through multiple differentiated retailers. We study analytically the supply chain with symmetric retailers and find that the supplier prefers to have as many retailers as possible in the market, even if the retailers' equilibrium retail price is lower than that of the supplier, and even if the number of retailers and their cost or market advantage prevent sales through the direct channel. We find that the two-channel supply chain may be subject to inefficiencies not present in the single-channel supply chain. We show that several contracts known to coordinate a single-channel supply chain do not coordinate the two-channel supply chain; thus we propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the two-channel supply chain with symmetric retailers. We provide some analytical results for the supply chain with asymmetric retailers and propose an efficient solution approach for finding the equilibrium. We find numerically that the supplier still benefits from having more retailers in the market and that linear quantity discount contracts can mitigate supply chain inefficiency, though they no longer achieve perfect coordination.

This work focuses on the business-to-business interaction between a service requester and a service provider in a healthcare environment. The requester is the primary caregiver responsible for managing the health of a population of patients. When a patient requires advanced care outside of the requester's expertise, the requester refers the patient to a provider and pays for the referral services. Treatment may succeed or fail, and in the case of failure, the requester incurs further follow-up costs. The requester may exert preventive effort to reduce the volume of referrals. The provider may exert nonreimbursable effort to reduce the chance of treatment failure. We analyze payment contracts between the two firms. We find that fee-for-service (FFS) induces neither system nor social optimum effort outcomes. However, a penalty contract can generally coordinate the effort decisions with either the system optimum or the social optimum. Furthermore, we find that patients may benefit from having a coordinating contract replace FFS. However, the types of procedures that make a coordinating contract most advantageous for the requester and provider are not necessarily the same as those that make the patients better off than under FFS. Yet, in most cases, the coordinating contract improves social welfare, as compared to FFS, and brings it close to the social optimum. Hence, the requester provider coordinating contract can be considered as an improvement over FFS for the entire system.

Models of influenza transmission have focused on the ability of vaccination, antiviral therapy, and social distancing strategies to mitigate epidemics. Influenza transmission, however, may also be interrupted by hygiene interventions such as frequent hand washing and wearing masks or respirators. We apply a model of influenza disease transmission that incorporates hygiene and social distancing interventions. The model describes population mixing as a Poisson process, and the probability of infection upon contact between an infectious and susceptible person is parameterized by p. While social distancing interventions modify contact rates in the population, hygiene interventions modify p. Public health decision making involves tradeoffs, and we introduce an objective function that considers the direct costs of interventions and new infections to determine the optimum intervention type (social distancing versus hygiene intervention) and population compliance for epidemic mitigation. Significant simplifications have been made in these models. However, we demonstrate that the method is feasible, provides plausible results, and is sensitive to the selection of model parameters. Specifically, we show that the optimum combination of nonpharmaceutical interventions depends upon the probability of infection, intervention compliance, and duration of infectiousness. Means by which realism can be increased in the method are discussed.

Problem definition: The traditional payment system between an insurer and providers does not incentivize providers to limit their prices, nor patients to choose less expensive providers, hence contributing to high insurer expenditures. Reference pricing has been proposed as a way to better align incentives and control the rising costs of healthcare. In this payment system, the insurer determines the maximum amount that can be reimbursed for a procedure (reference price). If a patient selects a provider charging more than the reference price, the patient is responsible for the entire portion above it. Our goal is to understand how reference pricing performs relative to more traditional payment systems. Academic/practical relevance: Our results can help healthcare leaders understand when reference pricing has the potential to be a successful alternative payment mechanism, what its impact on the different stakeholders is, and how to best design it. Methodology: We propose a game-theoretical model to analyze the reference pricing payment scheme. Our model incorporates an insurer that chooses the reference price, multiple competing price-setting providers, and heterogeneous patients who select a provider based on a multinomial logit choice model. Results: We find that the highest-priced providers reduce their prices under reference pricing. Moreover, reference pricing often outperforms the fixed and the variable payment systems both in terms of expected patient utility and insurer cost but incurs a loss in the highest-priced providers’ profit. Furthermore, we show that in general the insurer utility is often higher under reference pricing unless the insurer is a public nonprofit insurer that weighs the providers’ utility as much as its own cost. Managerial implications: Overall, our findings indicate that reference pricing constitutes a promising payment system for “shoppable” healthcare services as long as the insurer does not act similar to a public nonprofit insurer.

One of the most important concerns for managing public health is the prevention of infectious diseases. Although vaccines provide the most effective means for preventing infectious diseases, there are two main reasons why it is often difficult to reach a socially optimal level of vaccine coverage: (i) the emergence of operational issues (such as yield uncertainty) on the supply side, and (ii) the existence of negative network effects on the consumption side. In particular, uncertainties about production yield and vaccine imperfections often make manufacturing some vaccines a risky process and may lead the manufacturer to produce below the socially optimal level. At the same time, negative network effects provide incentives to potential consumers to free ride off the immunity of the vaccinated population. In this research, we consider how a central policy-maker can induce a socially optimal vaccine coverage through the use of incentives to both consumers and the vaccine manufacturer. We consider a monopoly market for an imperfect vaccine; we show that a fixed two-part subsidy is unable to coordinate the market, but derive a two-part menu of subsidies that leads to a socially efficient level of coverage.

We identify market conditions under which intermediaries can thrive in retailer-driven supply chains. Our main finding is that, as a consequence of the retailers' leadership position, intermediaries prefer products for which the supply base (existing production capacity) is neither too narrow nor too broad; that is, less existing capacity can result in more intermediary profit. We also show that our main finding is robust to (i) the presence of horizontal competition among retailers and intermediaries, (ii) the existence of exclusive suppliers, and (iii) the ability of the retailers to source directly from the suppliers. Nevertheless, we find that horizontal competition between intermediaries encourages them to carry products with relatively smaller production capacity, whereas exclusive suppliers and direct sourcing encourage intermediaries to carry products with relatively larger installed capacity.