Xuanming Su

Intertemporal Pricing with Strategic Customer Behavior

This paper develops a model of dynamic pricing with endogenous intertemporal demand. In the model, there is a monopolist who sells a finite inventory over a finite time horizon. The seller adjusts prices dynamically to maximize revenue. Customers arrive continually over the duration of the selling season. At each point in time, customers may purchase the product at current prices, remain in the market at a cost to purchase later, or exit, and they wish to maximize individual utility. The customer population is heterogeneous along two dimensions: they may have different valuations for the product and different degrees of patience (waiting costs). We demonstrate that heterogeneity in both valuation and patience is important because they jointly determine the structure of optimal pricing policies. In particular, when high-value customers are proportionately less patient, markdown pricing policies are effective because the high-value customers would buy early at high prices while the low-value customers are willing to wait (i.e., they are not lost). On the other hand, when the high-value customers are more patient than the low-value customers, prices should increase over time to discourage inefficient waiting. Contrary to intuition, we find that strategic waiting by customers may sometimes benefit the seller: when low-value customers wait, they compete for availability with high-value customers and thus increase their willingness to pay. Our results also shed light on how the composition of the customer population affects optimal revenue, consumer surplus, and social welfare. Finally, we consider the long-run problem of selecting the optimal initial stocking quantity.

Bounded Rationality in Newsvendor Models

Many theoretical models adopt a normative approach and assume that decision makers are perfect optimizers. In contrast, this paper takes a descriptive approach and considers bounded rationality, in the sense that decision makers are prone to errors and biases. Our decision model builds on the quantal choice model: While the best decision need not always be made, better decisions are made more often. We apply this framework to the classic newsvendor model and characterize the ordering decisions made by a boundedly rational decision maker. We identify systematic biases and offer insight into when overordering and underordering may occur. We also investigate the impact of these biases on several other inventory settings that have traditionally been studied using the newsvendor model as a building block, such as supply chain contracting, the bullwhip effect, and inventory pooling. We find that incorporating decision noise and optimization error yields results that are consistent with some anomalies highlighted by recent experimental findings.

Strategic Customer Behavior, Commitment, and Supply Chain Performance

This paper studies the impact of strategic customer behavior on supply chain performance. We start with a newsvendor seller facing forward-looking customers. The seller initially charges a regular price but may salvage the leftover inventory at a lower salvage price after random demand is realized. Customers anticipate future sales and choose purchase timing to maximize their expected surplus. We characterize the rational expectations equilibrium, where we find that the sellers stocking level is lower than that in the classic model without strategic customers. We show that the sellers profit can be improved by promising either that quantities available will be limited (quantity commitment) or that prices will be kept high (price commitment). In most cases, both forms of commitment are not credible in a centralized supply chain with a single seller. However, decentralized supply chains can use contractual arrangements as indirect commitment devices to attain the desired outcomes with commitment. Decentralization has generally been associated with coordination problems, but we present the contrasting view that disparate interests within a supply chain can actually improve overall supply chain performance. In particular, with strategic customer behavior, we find that (i) a decentralized supply chain with a wholesale price contract may perform strictly better than a centralized supply chain; (ii) contracts widely studied in the supply chain coordination literature (e.g., markdown money, sales rebates, and buyback contracts) can serve as a commitment device as well as an incentive-coordinating device; and (iii) some of the above contracts cannot allocate profits arbitrarily between supply chain members because of strategic customer behavior.

Consumer Returns Policies and Supply Chain Performance

This paper develops a model of consumer returns policies. In our model, consumers face valuation uncertainty and realize their valuations only after purchase. There is also aggregate demand uncertainty, captured using the conventional newsvendor model. In this environment, consumers decide whether to purchase and then whether to return the product, whereas the seller sets the price, quantity, and refund amount. Using our model, we study the impact of full returns policies (e.g., using 100% money-back guarantees) and partial returns policies (e.g., when restocking fees are charged) on supply chain performance. Next, we demonstrate that consumer returns policies may distort incentives under common supply contracts (such as manufacturer buy-backs), and we propose strategies to coordinate the supply chain in the presence of consumer returns. Finally, we explore several extensions and demonstrate the robustness of our findings.

On the Value of Commitment and Availability Guarantees When Selling to Strategic Consumers

This paper studies the role of product availability in attracting consumer demand. We start with a newsvendor model, but additionally assume that stockouts are costly to consumers. The seller sets an observable price and an unobservable stocking quantity. Consumers anticipate the likelihood of stockouts and determine whether to visit the seller. We characterize the rational expectations equilibrium in this game. We propose two strategies that the seller can use to improve profits: (i) commitment (i.e., the seller, ex ante, commits to a particular quantity) and (ii) availability guarantees (i.e., the seller promises to compensate consumers, ex post, if the product is out of stock). Interestingly, the seller has an incentive to overcompensate consumers during stockouts, relative to the first-best benchmark under which social welfare is maximized. We find that first-best outcomes do not arise in equilibrium, but can be supported when the seller uses a combination of commitment and availability guarantees. Finally, we examine the robustness of these conclusions by extending our analysis to incorporate dynamic learning, multiple products, and consumer heterogeneity.

Recipient Choice Can Address the Efficiency-Equity Trade-off in Kidney Transplantation: A Mechanism Design Model

In kidney allocation, transplant candidates may have private information about their propensity to enjoy good outcomes after transplantation or about their relative expected improvement in quality of life after transplantation. This paper develops a mechanism design model to investigate the effect of such information asymmetry on the kidney allocation system. In this model, there are n transplant queues corresponding to n candidate types. Candidate types are only observed by the candidates, and each candidate chooses the queue to join by reporting a type. Kidneys have heterogeneous types, and each kidney will be assigned to one of the queues depending on its type. Candidates report their type strategically to join the queue that maximizes their utility. Candidate utility depends on the type of kidney received and the expected waiting time, which is calculated using fluid approximations. We consider two alternative social welfare functions: aggregate utility (emphasizing efficiency) and minimum utility across all candidates (emphasizing equity). The kidney allocation problem is to divide the organ supply among the different queues so that social welfare is maximized, and this problem is solved explicitly under both objective functions. There are three findings: (1) The allocation mechanism induces truth telling by ensuring that candidates who wait longer receive better kidneys; (2) Information rents are earned by high-risk candidates under the efficiency objective and by low-risk candidates under the equity objective; (3) a choice-based kidney allocation system in which candidates choose the type of queue to join leads to outcomes in the middle of the efficiency-equity spectrum.

Optimal Pricing with Speculators and Strategic Consumers

This paper studies a monopolist firm selling a fixed capacity. The firm sets a price before demand uncertainty is resolved. Speculators may enter the market purely with the intention of resale, which can be profitable if demand turns out to be high. Consumers may strategically choose when to purchase, and they may also choose to purchase from the firm or from the speculators. We characterize equilibrium prices and profits and analyze the long-run capacity decisions of the firm. There are three major findings. First, the presence of speculators increases the firms expected profits even though the resale market competes with the firm. Second, by facilitating resale, the firm can mimic dynamic pricing outcomes and enjoy the associated benefits while charging a fixed price. Third, speculative behavior may generate incentives for the seller to artificially restrict supply, and thus may lead to lower capacity investments. We also explore several model extensions that highlight the robustness of our results.

Distributional and Peer-Induced Fairness in Supply Chain Contract Design

Members of a supply chain often make profit comparisons. A retailer exhibits peer-induced fairness concerns when his own profit is behind that of a peer retailer interacting with the same supplier. In addition, a retailer exhibits distributional fairness when his suppliers share of total profit is larger than his own. While existing research focuses exclusively on distributional fairness concerns, this study investigates how both types of fairness might interact and influence economic outcomes in a supply chain. We consider a one-supplier and two-retailer supply chain setting, and we show that (i) in the presence of distributional fairness alone, the wholesale price offer is lower than the standard wholesale price offer; (ii) in the presence of both types of fairness, the second wholesale price is higher than the first wholesale price; and (iii) in the presence of both types of fairness, the second retailer makes a lower profit and has a lower share of the total supply chain profit than the first retailer. We run controlled experiments with subjects motivated by substantial monetary incentives and show that subject behaviors are consistent with the model predictions. Structural estimation on the data suggests that peer-induced fairness is more salient than distributional fairness.

A Model of Consumer Inertia with Applications to Dynamic Pricing

This paper introduces a model to capture the behavioral phenomenon of inertia in inter-temporal consumer purchase decisions. We define inertia as the inherent tendency to refrain from making any purchase. This is represented by a utility premium that is required to trigger purchases. Inertia may induce consumers to wait even when it is optimal to buy immediately. We show that our model of inertia is consistent with well-established behavioral regularities, such as loss aversion and probability weighting in the sense of prospect theory, and hyperbolic time preferences. We embed this decision model within a dynamic pricing context. The firm has a fixed capacity of a particular product and sells it over two time periods to a market consisting of both rational and inertial consumers. We find that the depth of inertia (i.e., strength of inertial effects) always hurts seller profits but the breadth of inertia (i.e., the proportion of inertial consumers) may sometimes be beneficial. We offer practical recommendations for firms to influence both depth and breadth of consumer inertia.

Omnichannel Retail Operations with Buy-Online-and-Pick-up-in-Store

Many retailers have recently started to offer customers the option to buy online and pick up in store (BOPS). We study the impact of the BOPS initiative on store operations. We build a stylized model where a retailer operates both online and offline channels. Consumers strategically make channel choices. The BOPS option affects consumer choice in two ways: by providing real-time information about inventory availability and by reducing the hassle cost of shopping. We obtain three findings. First, not all products are well-suited for in-store pickup; specifically, it may not be profitable to implement BOPS on products that sell well in stores. Second, BOPS enables retailers to reach new customers, but for existing customers, the shift from online fulfillment to store fulfillment may decrease profit margins when the latter is less cost effective. Finally, in a decentralized retail system where store and online channels are managed separately, BOPS revenue can be shared across channels to alleviate incentive conflicts; it is rarely efficient to allocate all the revenue to a single channel.