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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.

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 seller's stocking level is lower than that in the classic model without strategic customers. We show that the seller's 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.

We study a dynamic pricing problem for a class of products with stable consumption patterns (e.g., household items, staple foods). Consumers may stock up the product at current prices for future consumption, but they incur inventory holding costs. We model this situation as a dynamic game over an infinite time horizon: in each period, the seller sets a price, and each consumer chooses how many units to buy. We develop a solution methodology based on rational expectations. By endowing each player with beliefs, we decouple the dynamic game into individual dynamic programs for each player. We solve for the rational expectations equilibrium, where all players make optimal dynamic decisions given correct beliefs about others' behavior. In equilibrium, the seller may either charge a constant fixed price or offer periodic price promotions at predictable time intervals. We show that promotions are useful when frequent shoppers are willing to pay more for the product than are occasional shoppers. We also develop several model extensions to study the impact of consumer stockpiling on the seller's inventory, production, and rationing strategies.

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.

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 firm's 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.

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. Customers strategically make channel choices. The BOPS option affects customer 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. This paper was accepted by Vishal Gaur, operations management .

We consider a supply chain with a single supplier and two retailers. The retailers choose their orders strategically, and if their orders exceed the supplier's capacity, quantities are allocated proportionally to the orders. We experimentally study the capacity allocation game using subjects motivated by financial incentives. We find that the Nash equilibrium, which assumes that players are perfectly rational, substantially exaggerates retailers' tendency to strategically order more than they need. We propose a model of bounded rationality based on the quantal response equilibrium, in which players are not perfect optimizers and they face uncertainty in their opponents' actions. We structurally estimate model parameters using the maximum-likelihood method. Our results confirm that retailers exhibit bounded rationality, become more rational through repeated game play, but may not converge to perfect rationality as assumed by the Nash equilibrium. Finally, we consider several alternative behavioral theories and show that they do not explain our experimental data as well as our bounded rationality model. This paper was accepted by loana Popescu, guest editor, operations management.

People exhibit peer-induced fairness concerns when they look to their peers as a reference to evaluate their endowments. We analyze two independent ultimatum games played sequentially by a leader and two followers. With peer-induced fairness, the second follower is averse to receiving less than the first follower. Using laboratory experimental data, we estimate that peer-induced fairness between followers is two times stronger than distributional fairness between leader and follower. Allowing for heterogeneity, we find that 50 percent of subjects are fairness-minded. We discuss how peer-induced fairness might limit price discrimination, account for low variability in CEO compensation, and explain pattern bargaining.

Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the \"centipede game,\" however, players frequently violate this principle. An alternative is a \"dynamic level- k \" model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level- k rule is a best response to the level- (k-1) rule, and the level- ∞ rule corresponds to backward induction. Players choose rules based on their best guesses of others' rules and use historical plays to improve their guesses. The model captures two systematic violations of backward induction in centipede games, limited induction and repetition unraveling. Because the dynamic level- k model always converges to backward induction over repetition, the former can be considered to be a tracing procedure for the latter. We also examine the generalizability of the dynamic level- k model by applying it to explain systematic violations of backward induction in sequential bargaining games. We show that the same model is capable of capturing these violations in two separate bargaining experiments. This paper was accepted by Peter Wakker, decision analysis.

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.