Amit Pazgal

Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers

We study the optimal pricing of a finite quantity of a fashion-like seasonal good in the presence of forward-looking (strategic) customers. We distinguish between two classes of pricing strategies: contingent and announced fixed-discount. In both cases, the seller acts as a Stackelberg leader announcing his pricing strategy, while consumers act as followers taking the sellers strategy as given and determining their purchasing behavior. In each case, we identify a subgame-perfect Nash equilibrium and show that given the sellers strategy, the equilibrium in the consumer subgame is unique and consists of symmetric threshold purchasing policies. For both cases, we develop a benchmark model in which customers are nonstrategic (myopic). We conduct a comprehensive numerical study to explore the impact of strategic consumer behavior on pricing policies and expected revenue performance. We show that strategic customer behavior suppresses the benefits of price segmentation, particularly under medium-to-high values of heterogeneity and modest rates of decline in valuations. However, when the level of consumer heterogeneity is small, the rate of decline is medium-to-high, and the seller can optimally choose the time of discount in advance, segmentation can be used quite effectively even with strategic consumers. We find that the seller cannot avoid the adverse impact of strategic consumer behavior even under low levels of initial inventory. We argue that while the seller expects customers to be more concerned about product availability at discount time, he cannot use high-price “betting” strategies as he would in the case of low inventory and myopic customers. Under certain qualifications, announced fixed-discount strategies perform essentially the same as contingent pricing policies in the case of myopic consumers. However, under strategic consumer behavior, announced pricing policies can be advantageous to the seller, compared to contingent pricing schemes. Interestingly, those cases that announced discount strategies offer a significant advantage compared to contingent pricing policies. They appear to offer only a minimal advantage in comparison to fixed-pricing policies. Finally, when the seller incorrectly assumes that strategic customers are myopic in their purchasing decisions, it can be quite costly, reaching potential revenue losses of about 20%.

Optimal Markdown Pricing: Implications of Inventory Display Formats in the Presence of Strategic Customers

We propose a game-theoretical model of a retailer who sells a limited inventory of a product over a finite selling season by using one of two inventory display formats: display all (DA) and display one (DO). Under DA, the retailer displays all available units so that each arriving customer has perfect information about the actual inventory level. Under DO, the retailer displays only one unit at a time so that each customer knows about product availability but not the actual inventory level. Recent research suggests that when faced with strategic consumers, the retailer could increase expected profits by making an upfront commitment to a price path. We focus on such pricing strategies in this paper, and study the potential benefit of DO compared to DA, and its effectiveness in mitigating the adverse impact of strategic consumer behavior. We find support for our hypothesis that the DO format could potentially create an increased sense of shortage risk, and hence it is better than the DA format. However, although potentially beneficial, a move from DA to DO is typically very far from eliminating the adverse impact of strategic consumer behavior. We observe that, generally, it is not important for a retailer to modify the level of inventory when moving from a DA to a DO format; a change in the display format, along with an appropriate price modification, is typically sufficient. Interestingly, across all scenarios in which a change in inventory is significantly beneficial, we observed that only one of the following two actions takes place: either the premium price is increased along with a reduction in inventory, or inventory is increased along with premium price reduction. We find that the marginal benefit of DO can vary dramatically as a function of the per-unit cost to the retailer. In particular, when the retailers per-unit cost is relatively high, but not too high to make sales unprofitable or to justify exclusive sales to high-valuation customers only, the benefits of DO appear to be at their highest level, and could reach up to 20% increase in profit. Finally, we demonstrate that by moving from DA to DO, while keeping the price path unchanged, the volatility of the retailers profit decreases.

A Partially Observed Markov Decision Process for Dynamic Pricing

In this paper, we develop a stylized partially observed Markov decision process (POMDP) framework to study a dynamic pricing problem faced by sellers of fashion-like goods. We consider a retailer that plans to sell a given stock of items during a finite sales season. The objective of the retailer is to dynamically price the product in a way that maximizes expected revenues. Our model brings together various types of uncertainties about the demand, some of which are resolvable through sales observations. We develop a rigorous upper bound for the sellers optimal dynamic decision problem and use it to propose an active-learning heuristic pricing policy. We conduct a numerical study to test the performance of four different heuristic dynamic pricing policies in order to gain insight into several important managerial questions that arise in the context of revenue management.

Behavior-Based Discrimination: Is It a Winning Play, and If So, When?

With advances in technology, the collection of information from consumers at the time of purchase is common in many categories. This information allows a firm to straightforwardly classify consumers as either “new” or “past” consumers. This opens the door for firms to implement marketing that a discriminates between new and past consumers and b entails making offers to them that are significantly different. Our objective is to examine the competitive effects of marketing that tailors offers to consumers based on their past buying behavior. In a two-period model with two competing firms, we assume that each firm is able to commit about whether or not to implement behavior-based discrimination BBD, i.e., to add benefits to its offer for past consumers in the second period. When the firms are identical in their ability to add value to the second-period offer, BBD generally leads to lower profits for both firms. Past customers are so valuable in the second period that BBD leads to cutthroat competition in the first period. As a result, the payoffs associated with the implementation of BBD form a prisoners dilemma. Interestingly, when a firm has a significant advantage over its competitor one firm has the capability to add more benefits for its past customers than the other, it can increase its profit versus the base case even when there is significant competition in the second period. Moreover, the firm at a disadvantage sometimes finds that the best response to BBD by a strong competitor is to respond with a uniform price and avoid the practice completely.

Limited Memory, Categorization, and Competition

This paper investigates the effects of a limited consumer memory on the price competition between firms. It studies a specific aspect of memory---namely, the categorization of available price information that the consumers may need to recall for decision making. This paper analyzes competition between firms in a market with uninformed consumers who do not compare prices, informed consumers who compare prices but with limited memory, and informed consumers who have perfect memory. Consumers, aware of their memory limitations, choose how to encode the prices into categories, whereas firms take the limitations of consumers into account in choosing their pricing strategies. Two distinct types of categorization processes are investigated: (1) a symmetric one in which consumers compare only the labels of price categories from the competing firms and (2) an asymmetric one in which consumers compare the recalled price of one firm with the actual price of the other. We find that the equilibrium partition for the consumers calls for finer categorization toward the bottom of the price distribution. Thus consumers have a motivation to invest in greater memory resources in encoding lower prices to induce firms to charge more favorable prices. The interaction between the categorization strategies of the consumers and the price competition between the firms is such that small initial improvements in recall move the market outcomes quickly toward the case of perfect recall. Even with few memory categories, the expected price consumers pay and their surplus is close to the case of perfect recall. There is thus a suggestion in this model that market competition adjusts to the memory limitations of consumers.

Comparison of customer balking and reneging behavior to queueing theory predictions: An experimental study

In this paper, we study customer decision-making while in a queuing situation. Customers can either join a queue or balk and return at a later time. Customers who join can renege and also return later. Our objective is to determine whether people seem to follow the benchmarks provided by queuing theory or whether psychological costs and perceptions of time invalidate these benchmarks. We use a computerized experiment where participants face explicit financial rewards and penalties for their decisions in a between subjects, fully crossed design with two experimental factors-clock data, and information about expected waiting time, each at two levels, presence and absence. Evaluated against the queuing theory benchmark, decision-making is quite good. Reneging is very rare, as queuing theory requires. Most participants follow a consistent rule for balking. They balk at every line longer than some critical value, as prescribed by queueing theory. But, even when corrected for heterogeneity in time perception, this critical value is greater than the one that minimizes expected waiting time. The large critical value may be due to risk-aversion or participants overestimating the switching cost. The results are supported by a second experiment using different parameters. Information improved decisions for most participants by increasing the precision of waiting time estimates. In addition, information helps participants who underestimate waiting time to correctly leave the line and those who over-estimate to stay. Providing clock time had almost no impact on decision-making.

Dynamic Influences on Individual Choice Behavior

Research examining the process of individual decision making over time isbriefly reviewed. We focus on two major areas of work in choice dynamics:research that has examined how current choices are influenced by the historyof previous choices, and newer work examining how choices may be made toexploit expectations about options available in the future. A central themeof the survey is that if a general understanding of choice dynamics is toemerge, it will come through the development of boundedly-rational models ofdynamic problem solving that lie on the interface between economics andpsychology.

Profit-Increasing Consumer Exit

This paper examines the phenomenon of profit-increasing consumer exit and the related phenomenon of profit-decreasing consumer entry. We demonstrate that firms can be better off in shrinking markets and worse off in growing markets, even in the absence of competitive entry or exit. Specifically, firms may benefit if a segment of consumers who are relatively indifferent about consuming any product in the category leave the market. Profits can increase for all firms even if the exiting consumers have strong preferences for only one of the products in the market. In shrinking markets, it is reasonable to assume that the people who are likely to exit the market first are people who are “least committed” to the category. In particular, people who are the least satisfied with the existing offers are the most likely to change their behavior by finding an alternative or adopting a new technology. Similarly, in growing markets, consumers who enter the market late are generally the least committed to the category. Such exiting can relax the competitive pressure between firms and lead to increased profitability. Our findings provide an explanation for profit growth that has been observed in product industries exhibiting slow and predictable declines over time, including vacuum tubes, cigarettes, and soft drinks.

Cumulative Discrete Choice

We present a discrete choice model in which a consumers impression of each alternative is based on her memory of past experience with this choice, and is stochastically updated whenever the alternative is chosen. The consumer remembers a cumulative utility index per alternative, and, when an alternative is chosen, the index is updated by the addition of a random variable, interpreted as instantaneous utility. We prove that the frequencies of choice converge, with probability 1, to limit frequencies, which can be computed from the models parameters.

Price Adjustment Policy with Partial Refunds

Have you ever purchased an item only to notice a short while later that its price was reduced? Many retailers offer to refund customers the full price difference as long as the discount occurred within a short period of time after the original purchase. Such policy looks attractive to consumers as it shields them from future price fluctuations. But can this policy be advantageous for the retailer? In this paper we investigate the price difference refund policy (commonly referred to as price adjustment) and demonstrate how it can result in a higher profit even if all consumers request and receive a price adjustment. Further, the existing literature and practice both assume that if a price adjustment policy is employed, the consumers should get the full price difference refunded. In this paper we endogenize the refund amount, allowing the retailer to determine the optimal percentage of the price difference to be returned to consumers. We fully characterize the conditions under which it is optimal to offer a partial or greater than full price adjustment to customers as well as the optimal refund percentage. Additionally, we demonstrate that the practice of limiting the price adjustment option to a short period after the purchase incident is not necessarily in the best interest of retailers.