Myopic Customers Research Articles

Intertemporal Price Discrimination via Randomized Promotions

Problem definition: The undesirable but inevitable consequence of running promotions is that consumers can be trained to time their purchases strategically. In this paper, we study randomized promotions, where the firm randomly offers discounts over time, as an alternative strategy of intertemporal price discrimination. Methodology/results: We consider a base model where a monopolist sells a single product to a market with a constant stream of two market segments. The segments are heterogeneous in both their product valuations and patience levels. The firm precommits to a price distribution, and in each period, a price is randomly drawn from the committed distribution. We characterize the optimal price distribution as a randomized promotion policy and show that it serves as an intertemporal price discrimination mechanism such that high-valuation customers would make a purchase immediately at a regular price upon arrival, and low-valuation customers would wait for a random promotion. Compared against the optimal cyclic pricing policy, which is optimal within the strategy space of all deterministic pricing policies, the optimal randomized pricing policy beats it if low-valuation customers are sufficiently patient and the absolute discrepancy between high and low customer valuations is large enough. We extend the model in three directions. First, we consider the case where a portion of customers are myopic and would never wait. We show that the existence of myopic customers is detrimental to the firm’s profitability, and the expected profit from an optimal randomized pricing policy decreases as the proportion of myopic customers in the population increases. Second, we consider Markovian pricing policies where prices are allowed to be intertemporally correlated in a Markovian fashion. This additional maneuver allows the firm to reap an even higher profit when low-valuation customers are sufficiently patient by avoiding consecutive promotions but, on average, running the promotion more frequently with a smaller discount size. Lastly, we consider a model with multiple customer segments and show that a two-point price distribution remains optimal, and our conclusion from the two-segment base model still holds under certain conditions that are adopted in the literature. Managerial implications: Our results imply that the firm may want to deliberately randomize promotions in the presence of forward-looking customers. Funding: This work was supported by the National Natural Science Foundation of China [Grant 72201124], the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2015-06757 and RGPIN-2021-04295], and the Youth Project of the Humanities and Social Science Foundation of the Ministry of Education of China [Grant 22YJC630006]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.1194 .

Buy now or later? New or remanufactured? How to attract strategic customers

It is common for sellers to markdown product prices late in a selling season which prompts consumers to strategically manage their purchase timing. Facing consumers’ strategic behaviour, the manufacturer should decide the prices for products carefully to ensure its profit. This paper explores the manufacturer’s optimal pricing decisions in a closed-loop supply chain by considering the customers’ type, the limited number of returns, consumers’ acceptability of the remanufactured products, as well as the discounting rate of consumers’ perceived value for a delayed purchase. The results show that the manufacturer’s retailing plan and the optimal prices depend on the unit production cost of the new and remanufactured products. In general, the consumer’s strategic behaviour hurts the manufacturer’s profit. When consumers are strategic, the manufacturer reduces the selling price of the new product and it is less likely to engage in remanufacturing when the unit production cost of the new product is high as compared to the case of myopic customers. The numerical experiments provide additional implications and show that the manufacturer can take some simple counter-measure strategies to react to either the underestimation or overestimation of the expected price by the consumer.

Inventory pooling and pricing decisions in multiple markets with strategic customers

This study considers the pricing and inventory decisions for the retailer selling in multiple markets with strategic customers. The impact of strategic customer behavior on inventory pooling is examined. The equilibrium decisions, in which strategic customers tend to purchase early, are subsequently characterized in the pooled/non-pooled systems. Our results highlight the role of the strategic customer in each market. Compared with myopic customers, the retailer is prone to reduce its inventory for strategic customers. The retailer’s optimal inventory for high-profit products is lower in the pooled system than in the non-pooled system. However, the result is reversed for low-profit products. The analytical and numerical results simultaneously demonstrate that, in the high-profit condition, the retailers’ inventory in the pooled system increases with the correlation coefficient of different markets, while the retailers’ profit decreases with the correlation coefficient. There is an opposite relationship in the low-profit condition. When the markets are less correlated, the retailer owns low inventory but high profit. Moreover, the retailers’ profit is always higher in the pooled system than in the non-pooled system.

Pricing Decisions for a Sustainable Supply Chain in the Presence of Potential Strategic Customers

In service to sustainable development, consumers have begun to prefer green products for their special environmental characteristics, and many enterprises are introducing new products to improve their competitiveness, but this tactic may not work if customers are strategic, as they might choose to defer purchasing decisions while prices are high and wait for lower prices in the future. Considering the differences in purchase behavior, we divided customers into two groups—strategic customers and myopic customers. Furthermore, we distinguished three types of strategic customers according to their different preferences to analyze the optimal pricing and greenness strategies in sustainable supply chain in strategic customer scenarios. Our results led to the following conclusions. (1) Strategic customers’ individual preferences can affect optimum equilibrium and that a higher purchase price threshold can stimulate the manufacturer to improve greenness and set a higher price, while a higher greenness purchase threshold and purchase value threshold will force manufacturer to set a lower price. (2) We observed that strategic customers can increase demand and vender profit. As the number of strategic customers increases, selling price and greenness will experience downward trends in a price threshold scenario but upward trends in greenness threshold and value threshold scenarios. (3) A firm can take measures to mitigate the effects of strategic customers by adjusting price and greenness dynamically according to price and greenness sensitivity, which can play a leading role in actively influencing strategic customer behavior.

Robust Dynamic Pricing with Strategic Customers

We consider the canonical revenue management (RM) problem wherein a seller must sell an inventory of some product over a finite horizon via an anonymous, posted price mechanism. Unlike typical models in RM, we assume that customers are forward looking. In particular, customers arrive randomly over time and strategize about their times of purchases. The private valuations of these customers decay over time and the customers incur monitoring costs; both the rates of decay and these monitoring costs are private information. This setting has resisted the design of optimal dynamic mechanisms heretofore. Optimal pricing schemes—an almost necessary mechanism format for practical RM considerations—have been similarly elusive. The present paper proposes a mechanism we dub robust pricing. Robust pricing is guaranteed to achieve expected revenues that are at least within 29% of those under an optimal (not necessarily posted price) dynamic mechanism. We thus provide the first approximation algorithm for this problem. The robust pricing mechanism is practical, since it is an anonymous posted price mechanism and since the seller can compute the robust pricing policy for a problem without any knowledge of the distribution of customer discount factors and monitoring costs. The robust pricing mechanism also enjoys the simple interpretation of solving a dynamic pricing problem for myopic customers with the additional requirement of a novel “restricted sub-martingale constraint” on prices that discourages rapid discounting. We believe this interpretation is attractive to practitioners. Finally, numerical experiments suggest that the robust pricing mechanism is, for all intents, near optimal.

Are Strategic Customers Bad for a Supply Chain?

We consider a manufacturer serving a retailer that sells its product to customers over two periods. Each firm determines its unit price. The retailer orders the product from the manufacturer prior to the beginning of the selling periods. We consider two types of customers: (1) strategic customers who take their future options into account and time their purchases accordingly and (2) myopic customers who consider only their current options. We compare the resulting equilibria for these two scenarios and evaluate the impact of customers’ strategic behavior. We find that strategic customer behavior always benefits the manufacturer. Interestingly, it may also improve the profitability of the retailer and the entire supply chain in some cases. Strategic customer behavior and decentralization are often regarded as detriments to supply chain performance. We find that, however, the combination of these two factors may not result in the worst supply chain performance. When customers are sufficiently patient, a decentralized supply chain that faces strategic customers actually outperforms the supply chain with only one of those factors at play. Finally, we show that when customers are strategic, the retailer’s and manufacturer’s profits with price commitment, availability commitment, or quick response can be lower than those when customers are myopic. The online appendix is available at https://doi.org/10.1287/msom.2017.0651 .

Quantity Competition When Most Favored Customers are Strategic

Legal studies usually treat a policy of a manufacturer or retailer as socially harmful if it reduces product output and increases the price. We consider a two‐period model where the first‐period price is fixed and resellers endogenously decide to use meet‐the‐competition clause with a most‐favored‐customer clause (MFC) to counteract strategic customer behavior. As a result of MFC, the second‐period (reduced) price increases and resellers’ inventories decrease. However, customer surplus may increase and aggregate welfare increases in the majority of market situations. MFC can mitigate the losses in welfare and resellers’ profits due to strategic customers. Moreover, under reseller competition, MFC may even lead to higher levels of these values than with myopic customers, that is, to gain from increased strategic behavior. With growing competition, benefits or losses from MFC can be higher than losses from strategic customer behavior.

Profit of a Supply Chain versus its Decentralization in the Presence of Strategic Customers

A strategic customer is the customer who can intentionally delay purchases and wait for products on sale. In the selling season of seasonal products, there is usually a sale period because product valuation drops significantly. We study the behavior of strategic customers in a supply chain selling seasonal products. Contrary to strategic customers, myopic customers buy or leave, and do not wait. Previous researches with myopic customers suggest that decentralization decreases the supply chain’s profit. We simulate supply chain members’ interaction and learning processes of decisions to investigate how decentralization of a supply chain affects its profit in the presence of strategic customers. We study the effect of customer heterogeneity over product valuation and find that: (i) The profit of the decentralized supply chain is higher than that of the centralized one when the degree of customer heterogeneity is high, the expected product valuation is low, and customers have low time sensitivity. (ii) Decentralization retards delaying purchases of strategic customers. In addition, we find that the endogenization of the sale price can weaken the negative effect of strategic customers on the supply chain’s profit.

Pricing and inventory strategies under quick response with strategic and myopic consumers

AbstractWe divide consumers in the selling period into two types according to their purchasing behavior: strategic customers and myopic customers. We address the optimal inventory and pricing decision problem of a retailer considering strategic and myopic consumers with and without a quick response. The results indicate that the retailer should establish a higher price to sell only to myopic customers if there is a sufficient presence of myopic customers in the market, and the retailer should set a lower price to sell to myopic and strategic customers if the number of myopic customers in the market is relatively low. A quick response can decrease the initial ordering quantity and increase the retailer's profit when selling only to myopic customers or selling to both myopic and strategic customers. Moreover, a quick response is beneficial for the retailer to improve the product's retail price if the retailer wishes the two types of customers to purchase the product during the selling period. We also find that the pricing strategy considering strategic and myopic consumers under a quick response will increase profits more than the pricing strategy only considering myopic customers. Finally, numerical experiments are conducted to illustrate and validate the proposed models and provide managerial insights.

Dynamic Product Rotation in the Presence of Strategic Customers

Dynamic product rotation is perceived as a useful lever to increase sales. The effect over individual customers is, however, unclear: more choice in the future may induce them to postpone a purchase if the current offer is not sufficiently appealing, hoping to buy a better product in the future; moreover, visiting a store to learn about a new product may be costly, thereby diminishing the value of product updates. We analyze a model of strategic customer behavior in the face of a rotating product offering, with variable assortment depth. We find that the customers’ visit and purchase decisions follow a relatively simple structure: a customer should visit the store only when new products have been introduced and purchase a product if the value it provides is higher than a threshold. We then use this structure to examine the retailer’s optimal product-rotation policy. The structure of the optimal policy depends on product-rotation costs and capacity constraints. When capacity constraints are tight, the retailer spreads out product introductions throughout the selling season. Strategic customers tend to become more demanding (their purchasing thresholds increase) as the frequency of product rotation increases, so the marginal benefit of each additional product rotation decreases. In contrast, the purchasing thresholds for myopic customers—who buy the first item that fits their needs—are independent of the number of products introduced in the season. As a result, when the cost of product rotation is low, the frequency of product updates is higher when the retailer sells to strategic customers, whereas the opposite is true when the cost of product rotation is high. When capacity constraints are less stringent and product-rotation costs are convex in the assortment depth, we find that the level of product variety should increase as the season progresses when the firm sells to strategic customers, while the level of product variety stays constant over the season when faced with myopic customers. Finally, when there are no capacity constraints, it is optimal to introduce all products in a single period. This paper was accepted by Serguei Netessine, operations management.

The reference effect in newsvendor model with strategic customers

PurposeThe purpose of this paper is to discuss the role of reference effect on newsvendor’s decision behavior in a market with strategic customers and work out the newsvendor’s optimal pricing policy and ordering quantity.Design/methodology/approachThis study utilizes the prospect theory and strategic customer framework to analyze the decision-making behavior on the newsvendor’s optimal pricing policy and ordering quantity. The paper further presents an extension of newsvendor model and provides the model’s properties. The paper finally analyzes the results with various parameters on the model and reports on the insights generated by the model.FindingsThe paper indicates that the ordering quantity is not altered with the changing proportion of strategic customers and myopic customers, but the ordering quantity and the pricing strategy are influenced in terms of newsvendor’s reference effect, loss aversion, product cost, and salvage price.Practical implicationsThe research findings have important implications for decision makers. Previous researches have studied the incomplete rationality newsvendor’s decision-making behavior mainly by analyzing the vendor’s risk preferences or loss aversion, but the effect of reference point also plays an important role in analyzing the decision-maker’s behavior. The paper provides the optimal pricing policy and ordering quantity with the reference effect considering the strategic customers behavior. This model is also a valid complementarity to behavioral operations management research area.Originality/valueThe paper examines the role of reference effect in newsvendor problem with the strategic customers and analyzes the impact of parameters such as loss aversion on the newsvendor’s decision behavior.

Research on Pricing Decision-Making for Fresh Agricultural Products with Strategic Customers and Value Decreasing Rate

With the strategic customers and decreasing value taken into consideration, the study establishes the model to express how the retailer makes pricing decision when facing the strategic and myopic customers at the same time. In order to describe the effect of the value decreasing rate of products and the proportion of strategic customers, we assume the product value decreases in certain rate, than we investigate the decision-making process in two-stage sequence. The results show different effects between the excess supply and insufficient supply status in the market. Retailers’ optimal price will increase with the value decreasing rate, and will be unrelated with the proportion of strategic customers in former status, while retailers’ optimal price will increase with the value decreasing rate and the proportion of strategic customers in latter status. The computational studies show the conclusion and provide the reasonable advices for agricultural product retailers.

Intertemporal Pricing Under Minimax Regret

We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a finite time horizon. Customers’ types differ along two dimensions: (i) their willingness-to-pay for the product and (ii) their arrival time during the selling season. We assume that the seller knows only the support of the customers’ valuations and do not make any other distributional assumptions about customers’ willingness-to-pay or arrival times. We consider a robust formulation of the seller’s pricing problem that is based on the minimization of her worst-case regret. We consider two distinct cases of customers’ purchasing behavior: myopic and strategic customers. For both of these cases, we characterize optimal price paths. For myopic customers, the regret is determined by the price at a critical time. Depending on the problem parameters, this critical time will be either the end of the selling season or it will be a time that equalizes the worst-case regret generated by undercharging customers and the worst-case regret generated by customers waiting for the price to fall. The optimal pricing strategy is not unique except at the critical time. For strategic consumers, we develop a robust mechanism design approach to compute an optimal policy. Depending on the problem parameters, the optimal policy might lead some consumers to wait until the end of the selling season and might price others out of the market. Under strategic customers, the optimal price equalizes the regrets generated by different customer types that arrive at the beginning of the selling season. We show that a seller that does not know if the customers are myopic should price as if they are strategic. We also show there is no benefit under myopic consumers to having a selling season longer than a certain uniform bound, but that the same is not true with strategic consumers.

Are Strategic Customers Bad for a Supply Chain?

We consider a manufacturer serving a retailer who sells its product to customers over two periods. Each firm determines its unit price. The retailer orders the product from the manufacturer prior to the beginning of the selling periods. We consider two types of customers: strategic customers who take their future options into account and time their purchases accordingly, and myopic customers who consider only their current options. We compare the resulting equilibria for these two scenarios and evaluate the impact of customers' strategic behavior. We find that strategic customer behavior always benefits the manufacturer. Interestingly, it may also improve profitability of the retailer and the entire supply chain in some cases. Strategic customer behavior and decentralization are often regarded as detriments to supply chain performance. We find that, however, the combination of these two factors may not result in the worst supply chain performance. When customers are sufficiently patient, a decentralized supply chain that faces strategic customers actually outperforms the supply chain with only one of those factors at play. Finally, we show that when customers are strategic, the retailer's and manufacturer's profits with price commitment, availability commitment or quick response can be lower than those when customers are myopic.

Joint Pricing and Inventory Management with Strategic Customers

We consider a joint pricing and inventory management problem wherein a seller sells a single product over an infinite horizon via dynamically determining anonymous posted prices and inventory replenishment quantities. Customers arrive over time with a deterministic arrival rate but heterogeneous product valuations. Unlike typical inventory models, we assume that customers are forward-looking, who can strategize their times of purchases. A customer incurs waiting and monitoring cost if he delays his time of purchase anticipating a lower future price. The seller incurs fixed ordering cost and inventory holding cost. The seller seeks a joint pricing and inventory policy that maximizes her long-run average profit. We show that the optimal policy is cyclic, i.e., the seller repeats the pricing and ordering decisions over cycles of the same length. Under this optimal policy, strategic customer equilibrium behaviors are proven to be myopic. The seller's optimal long-run average profit in the presence of strategic customers is the same as her optimal profit in an auxiliary classical backlogging model wherein customers are myopic that they make their purchasing decisions immediately upon their arrivals. Remarkably, this implies that solving the (seemingly very hard) model with strategic customers is as easy and tractable as solving the above auxiliary model with myopic customers. Our results settle the open debate whether incorporating strategic customer behaviors significantly complicates the model. The answer is surprisingly appealing. Our results allow firms to incorporate strategic customer behaviors with little modeling and computational overhead. We develop a novel approach to prove the optimality of our proposed policy in the presence of strategic customers. In particular, we establish a benchmark profit that is the seller's optimal profit in the joint mechanism design and inventory control problem. We show that this benchmark serves as an upper bound of all joint pricing and inventory policies. We then show that this benchmark is upper bounded by the seller's profit under our proposed policy, which then implies the optimality of our policy.

Trade-In Remanufacturing, Strategic Customer Behavior, and Government Subsidies

Remanufacturing has been increasingly used in industry. To facilitate the collection of cores for remanufacturing, many firms offer rebates that allow repeat customers to trade in used products for upgraded ones at a discounted price. This paper studies the impact of strategic customer behavior on the economic and environmental values of such trade-in remanufacturing practice. There are several major findings. First, under trade-in remanufacturing, a firm may earn a higher profit with strategic customers than with myopic customers, which differs from the common belief that firms dislike forward-looking customer behavior due to its detrimental effect on profit. This is because strategic customers can anticipate the future price discount brought by the trade-in option, so when the revenue-generating effect of remanufacturing is strong enough, they might be willing to pay a higher first-period price than the myopic customers. Second, we show that strategic customer behavior may create a tension between profitability and sustainability: On one hand, by exploiting the forward-looking customer behavior, trade-in remanufacturing is more valuable to the firm with strategic customers than with myopic customers; on the other hand, with strategic customers, trade-in remanufacturing may have a negative impact on the environment and also on social welfare, since it may give rise to a significantly higher production quantity without improving customer surplus. Therefore, our research demonstrates that it is important to understand the interaction between trade-in remanufacturing and strategic customer behavior. Finally, to resolve the above tension, we study how a social planner (e.g., the government) should design a public policy to maximize social welfare. It has been shown that subsidizing remanufactured products alone may lead to undesired outcomes; however, the social optimum can be achieved by using a simple linear subsidy and tax scheme for all product versions.

Trade-in Remanufacturing, Customer Purchasing Behavior, and Government Policy

Trade-in remanufacturing is a commonly adopted business practice under which firms collect used products for remanufacturing by allowing repeat customers to trade in used products for upgraded ones at a discount price. This paper studies how customer purchasing behavior and remanufacturing efficiency affect the economic and environmental values of such a business practice. We demonstrate a new benefit of trade-in remanufacturing: it helps exploit the forward-looking behavior of strategic customers, which could be much more significant than the widely recognized revenue-generating and environmental benefits of remanufacturing. High remanufacturing efficiency does not necessarily benefit a firm. With overly high remanufacturing efficiency, product durability is so high that repeat customers are reluctant to trade in and upgrade their used products. When customers are highly strategic, trade-in remanufacturing creates a tension between profitability and sustainability: on one hand, by exploiting the intensive forward-looking customer behavior, trade-in remanufacturing is quite valuable to the firm; on the other hand, with highly strategic customers, trade-in remanufacturing has a substantial negative impact on the environment and social welfare, since it may induce significantly higher production quantities without improving customer surplus. With nearly myopic customers, however, trade-in remanufacturing benefits both the firm and the environment. Therefore, understanding the interactions between customer purchasing behavior and trade-in remanufacturing is important to both firms and policy makers. Finally, to resolve the above tension, we study how a social planner (e.g., government) should design a public policy to maximize social welfare. The social optimum can be achieved by using a simple linear subsidy/tax scheme for both new production and remanufacturing. The proposed policy can also induce the firm to set the socially optimal remanufacturing efficiency. The online appendix is available at https://doi.org/10.1287/msom.2017.0696 .

Intertemporal Pricing Without Priors

We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a finite time horizon. Customers are heterogeneous along two dimensions: (i) willingness-to-pay for the product and (ii) arrival time during the selling season. We assume that the seller knows only the support of the customers' valuations and do not make any other distributional assumptions about customers' willingness-to-pay or arrival times. We consider a robust formulation of the seller's pricing problem which is based on the minimization of her worst-case regret, a framework first proposed by Bergemann and Schlag (2008) in the context of static pricing. We consider two distinct cases of customers' purchasing behavior: myopic and strategic customers. For both of these cases, we characterize optimal price paths. For myopic customers, the regret is determined by the price at a critical time. Depending on the problem parameters, this critical time will be either the end of the selling season or it will be a time that equalizes the worst-case regret generated by undercharging customers and the worst-case regret generated by customers waiting for the price to fall. The optimal pricing strategy is not unique except at the critical time. For strategic consumers, we develop a robust mechanism design approach to compute an optimal policy. Depending on the problem parameters, the optimal policy might lead some consumers to wait until the end of the selling season and might price others out of the market. Under strategic customers, the optimal price equalizes the regrets generated by different customer types that arrive at the beginning of the selling season. We show that a seller that does not know if the customers are myopic should price as if they are strategic. We also show there is no benefit under myopic consumers to having a selling season longer than a certain uniform bound, but that the same is not true with strategic consumers.

Dynamic pricing with strategic customers

This paper provides an overview of the literature on dynamic pricing with strategic customers. In the past, research on dynamic pricing was mostly concerned with optimally pricing products over time in a market with myopic customers. In recent years, the consideration of strategic customers, who can delay a purchase to take advantage of a future discount, has dramatically increased. This paper’s main contribution is the development of a comprehensive classification scheme to structure the field of research and, based upon this, a systematic overview of all relevant papers. We then present in detail the various aspects considered in the literature together with their motivation from industry and state the major findings of the most relevant papers. Further attention is given to important problem extensions proposed in the literature that have been considered in only a few papers and are usually motivated by specific practical applications. Finally, promising directions for future research are indicated.

Risk-Averse Newsvendor Model with Strategic Consumer Behavior

The classic newsvendor problem focuses on maximizing the expected profit or minimizing the expected cost when the newsvendor faces myopic customers. However, it ignores the customer’s bargain-hunting behavior and risk preference measure of the newsvendor. As a result, we carry out the rational expectation (RE) equilibrium analysis for risk-averse newsvendor facing forward-looking customers who anticipate future sales and choose purchasing timing to maximize their expected surplus. We propose the equations satisfied by the RE equilibrium price and quantity for the risk-averse retailer in general setting and the explicit equilibrium decisions for the case where demand follows the uniform distribution and utility is a general power function. We identify the impacts of the system parameters on the RE equilibrium for this specific situation. In particular, we show that the RE equilibrium price for some risk-averse newsvendors is lower than for a risk-neutral retailer and the RE equilibrium stocking quantity for some risk-averse newsvendors is higher than for a risk-neutral retailer. We also find that the RE equilibrium sale price for a risk-averse newsvendor is decreasing in salvage price in some situations.