How Can Sellers React to Consumers’ Anticipated Regret in an Online Markdown Policy?

The purpose of this study is to understand consumers’ anticipated regret in online purchase decisions and provide a realistic method for sellers to determine their markdown policy to optimize their revenue. This paper presented a mathematical model of a seller’s markdown policy under consumers’ anticipated regret and conducted a laboratory experiment to justify the existence of consumers’ anticipated regret in the markdown context. Consumers’ behavioral data were collected and used to estimate the values of the anticipated regret parameters in the markdown policy. Two interesting findings are achieved. First, the behavioral experiment justifies that consumers’ online purchase decisions will be affected by their anticipated regret behavior. Second, the seller’s optimal markdown policy that considers consumers’ anticipated regret performs better than the general markdown policy at maximizing revenue. This study can help sellers to better understand consumers’ anticipated regret in online purchase decisions and protect them from the negative consequences of miscalibrating the behavioral parameters in practice. It establishes a bridge between the mathematical modeling and behavioral laboratory experiment used to determine a seller’s optimal markdown policy. It also incorporates the impact of the product category and characteristics on consumers’ anticipated regret, which is a novel perspective. Finally, some valuable managerial insights are discussed.

SECTION I. Introduction

Markdown pricing is a popular two-period pricing strategy adopted by sellers to decrease inventory and increase revenue [12], [25], [30], and [38]. Especially during some famous shopping festivals such as “Black Friday” in the US and “Single’s Day” in China, sellers are competing to attract consumers’ attentions with a variety of price-cutting strategies.

In the e-commerce era, online sellers are becoming increasingly more adept at using markdown pricing policies to influence consumers’ purchase behaviors by adjusting prices at any time [16] and [33].

They can also disclose product availability to influence consumer decisions as a form of pressure selling to compel consumers to rush into a purchase [7]. Regarding consumers, through websites or apps, they can easily keep track of sellers’ price adjustments and remaining inventory information. They have gradually become very sophisticated and have learned to utilize retailers’ disclosed promotion information and other consumers’ shared shopping experiences to anticipate and avoid potential future regret [24] and [38]. These are the unique characteristics of online retail for both sellers and consumers.

In the markdown context, consumers always face two different choices, i.e., buying goods at a full price with sure availability and buying goods at a discounted price with shortage risk. If consumers choose the former option but find later that the latter alternative offers a better result, or if they choose the latter option but find later that the former alternative offers a better result, consumers may regret their purchase decisions [35]. In this study, we call the first type of anticipated regret high-price regret, and call the second type of anticipated regret stock-out regret. Consumers experience both types of anticipated regret in online and offline purchases in the markdown context. However, it is not easy for consumers to observe the price reduction process and inventory shortage information in physical stores. Compared with offline consumers, online consumers’ anticipated regret is relatively more significant, so it is necessary and important to provide valuable managerial insights for online sellers’ pricing and inventory strategies. Therefore, in this study, on the premise that online sellers realize that online consumers are sophisticated and afraid of regret and owing to the unique features of online retail, we focus on how online sellers can deliberately arouse online consumers’ anticipated regret to promote their online sales and make profits.

Anticipated regret has been studied extensively in the marketing and psychology domains; however, most of the relevant studies are focused on investigating the effects of consumers’ anticipated regret on pricing and marketing strategies, and they have not further analyzed the impacts of consumers’ anticipated regret on their online product purchase decisions, especially for different types and characteristics of products. Moreover, how to parameterize anticipated regret has not yet been studied or reported either. In light of these research gaps, the main objective of this article is to understand consumers’ anticipated regret in online product purchase decisions and provide a realistic method for a seller to determine its markdown policy to optimize its revenue in the long run.

Some existing studies note that different types and characteristics of products will motivate different regret emotions [9], [10], [17], [18], and [14]. This paper investigates the purchase demand and purchase intention of consumers by considering the degree of anticipated regret evoked by consumers and divides the products into two categories. Namely, products that are more likely to evoke consumers’ low high-price regret $\alpha$ and high stock-out regret $\beta$ , such as the limited-edition sneakers, signed copies of a book by a famous writer, etc., are called Type-A products. Moreover, products that are more likely to invoke consumers’ high high-price regret $\alpha$ and low stock-out regret $\beta$ , such as household appliances, fashions, etc., are called Type-B products. Therefore, two research questions are proposed.

• How should the seller optimally determine the initial price of the product, and should the markdown strategy be different for the two types of products?

• How can the sellers parameterize consumers’ anticipated regret values in the optimal markdown model?

This paper contributes in three respects. First, two types of consumers’ anticipated regret behaviors are considered in a markdown model in the online context. Second, a behavioral experiment is conducted in order to justify the existence of consumers’ anticipated regret in the markdown context and estimate the parameters of anticipated regret in the analytical model. Third, the theoretical bases are provided for e-commerce sellers to determine their concrete optimal markdown pricing policies in practice, such as the markdown strategies for different types and characteristics of products that will evoke different levels of consumer’s anticipated high-price and stock-out regrets.

The remainder of this paper is organized as follows. We review the related works in Section 2. Then, we propose an optimal markdown model considering consumers’ anticipated regret in Section 3. In Section 4, we parameterize the anticipated regret values in a behavioral laboratory experiment, and we discuss the findings and summarize the main conclusions in Section 5.

SECTION II. Related Works

Anticipated regret refers to the psychological effect of various worries that beset a decision maker before any losses actually materialize [23]. Bell [4] and Loomes and Sugden [22] explicitly incorporated the anticipatory aspects of regret in their decision making models. Simonson [32] is the earliest researcher to find evidence that anticipated regret influences consumers’ purchase timing decisions. Table 1 summarizes some research progress on anticipated regret and its applications to consumer purchases.

TABLE 1 Research on Anticipated Regret and Its Application in Consumer Purchases

As indicated in Table 1, some researchers justified that consumers’ anticipated regret can influence their purchase decisions. They found that the provision and the structure of feedback can in turn influence the extent of their anticipated regret. Some of them have mentioned that different types and characteristics of products will motivate different regret emotions [9], [10], [17], [18], and [14].

Regarding considering consumers’ anticipated regret in the markdown context, Tsiros and Hardesty [34] compare the purchase likelihoods and potential revenue among three pricing strategies, namely, steadily decreasing discounting (SDD), everyday low pricing and hi-lo pricing. They simulate each strategy by providing a sequence of prices and they observe the purchase decisions from the participants in an experiment. They find that consumers’ anticipation of increasing prices in SDD increases the likelihood of purchases and generates more revenue for the seller. The findings provide evidence that real-life sellers are aware of consumers’ anticipated regret and its effects on their revenue; therefore, they would like to use this behavioral regularity to improve their revenue by setting appropriate pricing schemes. Some researchers characterize consumers’ anticipated regret using analytic pricing models. Nasiry and Popescu [27] assume that consumers prefer advanced purchases and will even buy products at a negative surplus because doing so causes less emotional and economic pain than not buying at all. This frenzied behavior is a distinctive feature in their consumer model. They also find that inaction regret can lead firms to create frenzies by conducting advanced selling at high prices. In addition, they introduce a fraction denoting the percentage of the market segment in which consumers anticipate regret. That is, they classify the market into consumers who anticipate regret and customers who do not anticipate regret.

In Diecidue et al. [11] study, they segmented the consumers in terms of how regret affects their decisions and what triggers the regret. Specifically, according to the former criteria, consumers are divided into pragmatic and regret-reflecting consumers; according to the latter criteria, consumers are divided into buy-type and always-type. Özer and Zheng [28] assume that regret arises when a consumer initially chooses to wait but later encounters a stock-out or when the consumer buys the product at a high price but realizes that the product is still available at a discounted price. They find that when consumers are more influenced by the negative sentiment due to a stock-out than that due to paying a premium, markdown outperforms everyday low prices more often to become the seller’s optimal policy. However, they consider that the high-price regret had less of an impact on consumers’ purchase decision than did stock-out regret.

The findings in the previous studies show that regret is context dependent [17], [27], [36], and [41]. In situations when a different feedback information or feedback structure is provided, consumers’ anticipated regret will be quite different. Therefore, according to Cooke et al. [10], we consider two types of products evoking consumers’ different degrees of anticipated high-price and stock-out regrets and explore the pricing and marketing implications for each type of the product. Additionally, we consider parametering the anticipated regret of consumers to help the seller better understand the behavioral regularities of consumers in online purchase decisions.

SECTION III. Markdown Under Consumers’ Anticipated Regret

A. Problem Description

We consider a monopolistic seller selling a single product to a group of consumers during two sales periods. Under a markdown policy, the product is sold at a full price $p$ in Period 1 and at a discounted price $\delta p$ in Period 2. Here, $\delta$ is known as the price discount factor. We assume that the lead time of inventory replenishment is very long and the seller cannot replenish the inventory during the whole sales season.

We use $q~(0< q< 1)$ to denote the inventory fill rate in Period 2, which represents consumers’ actual probability that the product will be available in Period 2. Aided by data mining and data analysis techniques, online sellers are able to estimate or predict their potential market demand during a certain period. To increase the probability of a sell-out, they place a limited number of commodities in the market, creating an atmosphere of scarcity. For example, on Single’s Day in China, many online sellers offer discounts on only a limited number of commodities. After that, some items will be withdrawn from the sale or placed on sale in other markets. That is, the online sellers always have a rough estimate of the percentage of the market demand to be met in Period 2 (i.e., $q$ ).

We consider that the market is composed of two types of consumers, i.e., the pragmatic consumers and the regret-reflecting consumers. Suppose $Q_{i}^{p}$ and $Q_{i}^{r}$ are the product demands of the pragmatic and regret-reflecting consumers in Period $i (i=1, 2)$ , respectively; $U_{i}^{p}$ and $U_{i}^{r}$ are the utilities of the pragmatic and regret-reflecting consumers, respectively; $N$ is the potential market demand; $\mu$ is the percentage of regret-reflecting consumers in market; and 1-$\mu$ is the percentage of pragmatic consumers. In fact, $\mu$ is not related to consumers’ personality traits; instead, $\mu$ varies across products and situations. For a certain product in a certain situation, $\mu$ is exogenous. The retailer can determine the pricing and inventory strategies based on the market segmentation information to achieve its optimal revenue.

We adopt the regret parameters as in Özer and Zheng (2016), i.e., the parameter $\alpha \in$ [0, 1] measures the marginal value of the high-price regret and the parameter $\beta \in$ [0, 1] measures the marginal value of the stock-out regret.

In addition, we use $v$ to denote consumers’ reservation price, satisfying a uniform distribution U[0, $V$ ]. Suppose that each consumer buys at most one unit. The pragmatic consumers will buy the product immediately if their reservation price $v\ge p$ in Period 1 and $\delta p\le v< p$ in Period 2. They do not let regret affect their decisions on whether or not to purchase the product. The regret-reflecting consumers will weigh the utility of buying the product in Period 1 and the utility of buying the product in Period 2. If the utility in Period 1 is not less than that in Period 2, they will immediately buy the product; otherwise, they will consider buying the product in Period 2.

B. Consumers’ Utility Formulation

For pragmatic consumers, their utilities in Periods 1 and 2 are $U_{1}^{p} =v-p$ and $U_{2}^{p} =q(v-\delta p)$ , respectively. For regret-reflecting consumers, given the seller’s pricing and inventory decision, they will determine whether and when to buy the product. The formulas for the regret-reflecting consumers’ utility are given in (1) and (2), respectively (Özer and Zheng, 2016).

$$\begin{align*} U_{1}^{r}=&(v-p)-q\alpha (p-\delta p) \tag{1}\\ U_{2}^{r}=&q(v-\delta p)-\beta (1-q)(v-p)\tag{2}\end{align*}$$

Regarding the utilities of regret-reflecting consumers, each type of regret is the forgone surplus multiplied by the probability that this forgone surplus is incurred [27]. Equation (1) represents the utility of regret-reflecting consumers who experience high-price regret in Period 1. Here, v-p is the consumption surplus in Period 1, $q(p-\delta p)$ is the cost saving of buying the product in Period 2 with the probability $q$ , and $- q\alpha (p_{1}-\delta p)$ is the negative utility caused by their anticipated high-price regret. Equation (2) represents the utility of regret-reflecting consumers who experience stock-out regret in Period 2. Here, $q(v$ -$\delta p$ ) is the consumption surplus in Period 2, (1-$q$ )($v$ -$p$ ) is the consumption surplus of buying the product in period 1 with the probability 1-$q$ and $- \beta$ (1-$q$ ) ($v$ -$p$ ) is the negative utility caused by their anticipated stock-out regret. As we have discussed earlier, the regret-reflecting consumers will buy the product in Period 1 if and only if $U_{1}^{s} \ge \max \left \{{{U_{2}^{s},0} }\right \}$ . According to (1)–(2), we obtain the consumers’ indifferent purchasing decision point $v_{s}$ in Proposition 1.

Proposition 1:

Under the seller’s markdown policy, the regret-reflecting consumers’ indifferent purchasing decision point $v_{s}$ is $v_{s} \equiv \left [{ {(1+\alpha)(1-\delta)q \mathord {\left /{ {\vphantom {(1+\alpha)(1-\delta)q {(1+\beta)(1-q)}}} }\right. } {(1+\beta)(1-q)}+1} }\right]p$ .

In this study, the indifferent purchasing decision point $v_{s}$ is the threshold of the reservation price for the regret-reflecting consumers who are indifferent between buying the product in Periods 1 or 2. Under the seller’s markdown policy, if the regret-reflecting consumer’s reservation price satisfies $v_{s}\le v\le V$ , she will buy the product in Period 1; and if her reservation price satisfies $\delta p\le v\le v_{s}$ , she will buy the product in Period 2.

C. Seller’s Optimal Pricing Strategy

In this section, we use a backward induction method to characterize the seller’s optimal pricing strategy. According to Proposition 1, the demands of the pragmatic consumers in Periods 1 and 2 are $Q_{1}^{p} ={(1-\mu)(V-p)N} \mathord {\left /{ {\vphantom {(1-\mu)(V-p)N V}} }\right. } V$ and $Q_{_{2}}^{p} ={(1-\mu)(p-\delta p)N} \mathord {\left /{ {\vphantom {(1-\mu)(p-\delta p)N V}} }\right. } V$ , respectively; the demands of the regret-reflecting consumers in Periods 1 and 2 are $Q_{1}^{r} ={\mu (V-v_{s})N} \mathord {\left /{ {\vphantom {{\mu (V-v_{s})N} V}} }\right. } V$ and $Q_{_{2}}^{r} ={\mu (v_{s} -\delta p)N} \mathord {\left /{ {\vphantom {{\mu (v_{s} -\delta p)N} V}} }\right. } V$ , respectively. Therefore, the demands of all consumers in Periods 1 and 2 are $Q_{1}=(V$ -$p+\mu p$ -$\mu v_{s}$ )$N/V$ and $Q_{2}$ = ($p$ -$\mu p+\mu v_{s}$ -$\delta p$ )$N/V$ , respectively. The seller’s revenue is $R(p)=pQ_{1}+\delta ~pqQ_{2}$ . Then, the seller’s optimal initial price is given in Proposition 2.

Proposition 2:

Given the seller’s price discount $\delta$ and inventory fill rate $q$ , the seller’s optimal initial price is $p^{\ast }=V \mathord {\left /{ {\vphantom {V {2\left [{ {(1+\mu M)(1-\delta q)+q\delta ^{2}} }\right]}}} }\right. } {2\left [{ {(1+\mu M)(1-\delta q)+q\delta ^{2}} }\right]}$ , where $M={(1+\alpha)(1-\delta)q} \mathord {\left /{ {\vphantom {(1+\alpha)(1-\delta)q {(1+\beta)(1-q)}}} }\right. } {(1+\beta)(1-q)}$ .

According to Proposition 2, we can form the following corollaries.

Corollary 1:

The seller’s optimal price $p^{\ast }$ decreases as the high-price regret $\alpha$ increases.

Corollary 2:

The seller’s optimal price $p^{\mathrm {\ast {}}}$ increases as the stock-out regret $\beta$ increases.

Corollary 3:

The seller’s optimal price $p^{\mathrm {\ast {}}}$ decreases as the percentage of regret-reflecting consumers in the market $\mu$ increases.

Corollary 4:

When $\mu \le$ ($1+\beta$ )/($1+\alpha$ ), the seller’s optimal price $p^{\ast }$ first increases and then decreases as the price discount factor $\delta$ increases; when $\mu >$ ($1+\beta$ )/($1+\alpha$ ), the seller’s optimal price $p^{\ast }$ increases as the price discount factor $\delta$ increases.

D. Numerical Analysis

In this section, we examine the effects of anticipated regret, market segmentation and the price discount factor on the seller’s pricing and marketing strategy using some numerical examples.

Figs. 1(a)–​1(b) show the sensitivity analysis of high-price regret $\alpha$ and stock-out regret $\beta$ on the optimal initial price $p^{\ast }$ . That is, if consumers are increasingly worried about purchasing products at a higher price (i.e., $\alpha$ increases), the optimal price $p^{\ast }$ gradually decreases. This proves Corollary 1. However, if consumers are increasingly worried about not being able to obtain the product (i.e., $\beta$ increases), the optimal price $p^{\ast }$ gradually increases. This proves Corollary 2. The results indicate that the seller should lower the initial price to ease consumers’ concerns about the high price and promote their purchase during the first sales period; conversely, the seller should raise the initial price to obtain more revenue from consumers worried about running out of stock. These findings are consistent with real-life practices, and they also justify that sellers should consider the types and characteristics of products when they establish markdown policies.

FIGURE 1.

Effects of regret on the optimal initial price (V=400, N=600, q={0.3, 0.7}, $\mu =0.6$ , $\delta =0.6$ ).

Figs. 2(a)–​2(b) show the sensitivity analysis of high-price regret $\alpha$ and stock-out regret $\beta$ on the optimal initial inventory $K^{\ast }$ . That is, if consumers are increasingly worried about purchasing products at a higher price, the seller’s optimal initial inventory $K^{\ast }$ slightly increases as $\alpha$ increases. However, if consumers are increasingly worried about not being able to obtain the product, the seller’s optimal initial inventory $K^{\ast }$ slightly decreases as $\beta$ increases. These interesting findings are of practical values for sellers. For Type-A products (lower $\alpha$ and higher $\beta$ ), the seller should not hold too much inventory; however, for Type-B products (higher $\alpha$ and lower $\beta$ ), the seller should hold more inventory.

FIGURE 2.

Effects of regrets on the optimal initial inventory (V=400, N=600, q={0.3, 0.7}, $\mu =0.6$ , $\delta =0.6$ ).

Fig. 3 shows the effect of the percentage of regret-reflecting consumers in the market $\mu$ on the optimal price $p^{\mathrm {\ast }}$ . That is, if increasingly more consumers anticipate that they may regret their decisions when they purchase products in the face of the seller’s markdown strategy (i.e., $\mu$ increases), the optimal price $p^{\ast }$ gradually decreases. This proves Corollary 3. The results indicate that if more consumers in the market are pragmatic consumers, the seller can gain more revenue by raising the selling price. However, if more consumers in the market are regret-reflecting consumers, the seller needs to lower the initial price to mitigate the impact of their regret on purchase decisions. Of course, this result is relative and comparative, which is not inconsistent with the results of Fig. 1. The pricing for each specific type of product needs to be determined in a specific context.

FIGURE 3.

Effect of the percentage of regret-reflecting consumers in the market on the optimal initial price (V=400, N=600, q=0.6, $\mu =$ (0: 0.1: 1), $\delta =$ {0.3, 0.7}, $\alpha =$ {0.2, 0.8}, and $\beta =$ {0.2, 0.8}).

Figs. 4(a)–​4(b) show the effects of the price discount factor $\delta$ on the optimal price $p^{\ast }$ and the optimal revenue $R^{\ast }$ . That is, if the seller offers smaller price discount in Period 2 (i.e., $\delta$ increases), the optimal price $p^{\ast }$ first gradually increases and then slightly decreases. This proves Corollary 4. In addition, the seller’s optimal revenue $R^{\ast }$ first increases and then decreases as $\delta$ increases. This means that the seller can choose a suitable price discount factor $\delta$ to maximize its revenue. For example, in the scenario where $\alpha =0.2$ , $\beta =0.8$ , $\mu =0.3$ and $q=0.6$ , the seller can determine the optimal $\delta =0.68(\approx 0.7)$ to achieve its maximum revenue.

FIGURE 4.

Effects of the price discount factor on the optimal initial price and revenue (V=400, N=600, q=0.6, $\mu =$ {0.3, 0.7}, $\delta =$ (0: 0.1: 1), $\alpha =$ {0.2, 0.8}, and $\beta =$ {0.2, 0.8}).

Moreover, based on the above results, we can see that the optimal price of the Type-A product is higher than that of the Type-B product because the Type-A product is endowed with unique value by consumers, and it is not easily replaced by other products. In addition, the optimal price of a product with a low inventory fill rate in Period 2 is higher than that of a product with a high inventory fill rate because the former product is scarcer.

The theoretical results of this study are consistent with the general conclusions from economic theory and practice; however, it should be noted that our study provides managerial insights into the pricing of different types of commodities from the perspective of analyzing consumers’ anticipated regret, which is a new perspective on sellers’ commodity pricing and marketing strategies in reality.

SECTION IV. Experimental Estimation of Consumers’ Anticipated Regret Parameters

A. Objective Participants

The goal of the experiment is to justify the existence of consumers’ anticipated regret in the markdown context and estimate the values of consumers’ high-price regret $\alpha$ and stock-out regret $\beta$ in the analytical model proposed in Section 3. The parameterization method can help sellers better understand consumers’ behavioral regularities and the market and protect them from the potential negative consequences of miscalibrating the behavioral parameters in practice.

We conduct the experiment in a behavioral decision lab at a comprehensive university in northeastern China. There are 24 computers in the lab, and we can have up to 24 subjects participate in the experiment simultaneously. There were 86 undergraduate students recruited for the experiment with payoffs contingent on their performances. One subject was not allowed to participate due to being late. A total of 85 subjects, which includes 33 males (39%) and 52 females (61%), participated in the experiment. They were randomly divided into four separate but homogeneous experiments.

B. B Design and Procedure

To estimate these parameters, consumers’ wait-or-buy choice data at different price discount $\delta$ and product fill rate $q$ need to be collected. We use the choice-list method to collect the data [3] and [15] by presenting subjects with blocks of questions each containing a binary wait-or-buy question for different values of $q$ . To be noted that $\delta$ is held constant in each block, and varied across blocks.

In this experiment, we assume that consumers’ reservation price satisfies uniform distribution U[0, 250], and the product’s tag price is 200. The wait-or-buy option varied for different product fill rates $q=10$ %, 20%$\ldots$ 90% and price discount factors $\delta =5$ %, 15%, 25%, 50%, and 75%. Each subject was provided with forty-five $(9\times 5)$ questions. The experiment was designed and conducted using Z-tree [13], which enables economic experiments to be conducted without much prior experience. Upon arrival, each subject picked up a sealed envelope and read the experimental instructions, which are given in the Appendix.

Based on commodity theory [5] and [37] suggests that consumers view limited-supply products as scarce only when the products are attractive to them. In our study, we used a “limited-edition-hardcover novel” as the item to be sold. To ensure that the chosen book was attractive to the subjects, we listed nine novels with different styles and themes and asked the subjects to choose their favorite one.

Regret is largely conditional on the knowledge of the outcomes of the chosen and the foregone alternatives [29], and the feedback and its structure can also influence people’s decisions [40]. In this experiment, subjects were given feedback on both the chosen and the foregone options in order to elicit feelings of anticipated regret. Specifically, after the subjects completed nine questions under a certain price discount factor, the computer presented the subjects with individually, showing whether the subject can or cannot buy the product (based on a random number) and the utility loss of the better (foregone) choice. The feedback and the consumers’ potential utility loss of the better (foregone) choice are given in Table 2.

TABLE 2 Feedback and Consumers’ Potential Utility Loss of a Better (Foregone) Choice

For example, if the product fill rate in Period 2 is $q=70$ %, then you have a 30% chance of missing the book in Period 2. In a decision, ① if you choose to ‘buy’ the book, you will see the potential utility loss of buying the book at a high price before the reading festival, i.e., $p\times (1-\delta)$ (with a 70% probability) or no utility loss from avoiding missing the book during the festival (with a 30% probability); otherwise, ② if you choose to ‘wait’, you will see no utility loss from avoiding buying the book at a high price (with a 70% probability) or the potential utility loss of missing the book, i.e., $v$ -$p$ (with a 30% probability).

At the end of the experiment, the subjects were asked two additional questions. First, did you anticipate that you would miss a less expensive deal to obtain the book if you bought it in Period 1? Second, did you anticipate that you would not obtain the book at the discounted price if you bought it in Period 2? These questions are utilized to test the experimental reliability that whether the participants anticipated high-price regret and stock-out regret during the experiment.

The sealed envelopes contained two numbers: the price discount factor $\delta$ and the book fill rate $q$ . The subjects learned that they would be paid according to a certain wait-or-buy decision with ($q$ , $\delta$ ). In this scenario, if a subject chose to “buy now”, then he will receive the payment $v$ -$p$ ; if he chose to “wait”, then he will receive the payment $v$ -$p\times (1-\delta)$ , which is determined by whether a U[1, 100] random integer is less than or equal to $q$ (Baucells et al., 2017). At the end of the experiment, all subjects were asked to provide their Alipay account as the payment method for participating in this experiment.

C. Data and Initial Checks

The experiment data includes series of wait-or-buy decisions that subjects made for different ($q$ , $\delta$ ) combinations. We adopt Holt and Laury [15] and Baucells et al. [3] method to identify subjects’ indifferent purchasing decision points, which imply that as each $q$ increases, the subjects switch from selecting “buy” at low $q$ ’s to selecting “wait” at high $q$ ’s, and they do not switch back to “buy” at even higher $q$ ’s. In this study, we define the indifferent purchasing decision point as the mid value of the highest “buy” $q$ and the lowest “wait” $q$ at which, for a specific price discount factor $\delta$ , the subject is indifferent between buying and waiting. For example, if the price discount factor $\delta$ equals 0.75 and a subject chooses to buy when $q=60$ % and to wait when $q=70$ %, then we can determine that the indifferent purchasing decision point for this subject is ($q=65$ %, $\delta =0.75$ ). If a subject chooses to buy for all choices with the same $\delta$ , his indifferent decision point is ($q=95$ %, $\delta$ ). If a subject chooses to wait for all choices regarding the same $\delta$ , his indifferent decision point is ($q=5$ %, $\delta$ ).

In this experiment, our data show strong support for the existence of indifferent purchasing decision points 71/85 (83.5%) subjects exhibited such a switching pattern in all choices, and only 14/85 (16.5%) subjects switched more than once regarding the same price discount factor $\delta$ . We removed the data from 14 subjects and used the remaining data to define the indifferent purchasing decision points. This led to $355\,\,(71\times 5)$ values, and we used them to estimate the realistic values of the anticipated regret parameters in the consumers’ utility functions.

D. Parameter Estimation and Results

Given the structure of our data, we can estimate the values of consumers’ anticipated regret parameters in our experiment. First, we examined the correlation between the price discount factor $\delta$ and the inventory fill rate $q$ . The results show that all pairs of ($\delta$ , $q$ ) are significantly related to each other (all Pearson’s correlation coefficients > 0.8 and all significance values < 0.05). Then, we used the indifferent purchasing decision point equation given in Proposition 1 to estimate the values of the anticipated regret parameters. We rewrote the above function as follows.

$$\begin{equation*} q(\delta)=\frac {(1+\beta)(v_{s} -p)}{\alpha (1-\delta)p+v_{s} -\delta p+\beta (v_{s} -p)}\tag{3}\end{equation*}$$

We use $k$ (integer $k\in$ [1, 71]) to denote each subject; thus, we have five pairs of indifferent purchasing decision points $(\delta _{i}$ , $q_{j})_{k}$ for each subject, where integer $i$ ($\in$ [1, 5]) is the sequence number of the price discount factor $\delta$ , and integer $j$ ($\in$ [1, 9]) is the sequence number of the inventory fill rate $q$ . Then, we substituted the five observed $(\delta _{i}$ , $q_{j})_{k}$ into (3) to obtain the estimated ($\alpha _{k}$ , $\beta _{k}$ ) via a nonlinear regression using SPSS. Thus, we obtained 71 pairs of consumers’ anticipated regret values, as shown in Fig. 5.

FIGURE 5.

Results of the regret parameter estimation.

In Fig. 5, each small circle represents a pair of anticipated regret values ($\alpha _{k}$ , $\beta _{k}$ ), which was estimated based on subject $k$ ’s five indifferent purchasing decision points. We used the mid value of all the anticipated regret values as the estimated value of the anticipated high-regret $\alpha$ and the anticipated stock-out regret $\beta$ , that is, $\alpha =0.312$ and $\beta =0.792$ . The result implies that the product used in this experiment is a Type-A product, which makes it much easier to evoke consumers’ stock-out regret than high-price regret. This result is generally in line with the notion that one’s favorite book is a product that a consumer is worried about being unable to acquire rather than buying it at a high price. The result justifies the effectiveness of the regret elicitation and parameterization method proposed in this study.

E. Model Comparisons

To justify the superiority of the proposed markdown model under consumers’ anticipated regret, in this section, we compare the proposed model with a general markdown model that does not incorporate consumers’ anticipated regret. In the general model, consumers’ utility in Period 1 is $U_{1}=v$ -$p$ and that in Period 2 is $U_{2}=q(v$ -$\delta p)$ . The optimal initial price is $p^{\ast }=V/2[(1-\mu +\mu M)(1-q\delta)+q\delta ^{2}]$ , where $M=$ (1-$q\delta$ )/ (1-$q$ ). We compare the effects of $\delta$ and $\mu$ on the seller’s optimal revenue $R^{\ast }$ , as shown in Fig. 6.

FIGURE 6.

Comparison of two models (case a: N=600, V=400, $\alpha =0.312$ , $\beta =0.792$ , $\delta =0.6$ , and $\mu =$ (0: 0.1: 1); case b: N=600, V=400, $\alpha =0.312$ , $\beta =0.792$ , $\delta =$ (0: 0.1: 1), and $\mu =0.6$ ).

Fig. 6 shows that the proposed model performs better than the general model in revenue. Obviously, if the seller neglects the effect of consumers’ anticipated regret on their utilities and demand forecasting bias, he cannot determine a profitable markdown strategy.

SECTION V. Discussions and Conclusion

A. Theoretical and Managerial Implications

Real-life online sellers realize that consumers will anticipate regret when they face markdown prices and inventory shortage. They also know that if they could utilize such behavioral regularities, they can improve their revenue to some extent. Many practitioners and academics provide evidence that sellers are good at evoking consumers’ anticipated regret by setting appropriate future price discounts and providing limited inventories. Our study belongs to this field and contributes to the extant literature both in theory and in practice.

One innovation of this study is that we consider the impacts of product categories on the markdown policies of online sellers. Two categories of products are studied according to their degree of anticipated regret evoked by consumers. This classification assumes that some products are much easier to evoke consumers’ stock-out regret than high-price regret. This does not mean that the product triggers only one type of anticipated regret. In fact, in the context of markdowns, each product triggers two forms of anticipated regret, but the degree to which different product trigger each type of regret differs. We attribute the difference in the degree to the unique characteristic of products. Regret offers sellers an important lever to optimize their prices across different product types. The difficulty in this regard lies in offering managerial insights for sellers to determine different pricing and inventory strategies for the two types of products. In this study, we conducted sensitivity analysis and found that Type-A products perform better than Type-B products in revenue, Type-B products perform better than Type-A product in sales volume. These results also allow sellers to select the proper product type to achieve their market goals.

Another innovation of this study is that we bridge the theoretical modeling with empirical justification in the field of online sellers’ markdown strategies considering consumers’ anticipated regret. There are two difficulties, which are how to elicit consumers’ different types of anticipated regret and how to estimate the values of the anticipated regret parameters. In this study, we enhance and complement the existing literature by using a behavioral experiment to overcome the difficulties and generate new and important insights that allow the optimal markdown policy to work better in reality. The experiment has justified the existence of consumers’ anticipated high-price regret and stock-out regret by identifying their indifferent purchase decisions in the markdown context. The collected behavioral data are further processed to estimate the values of the anticipated regret parameters. Therefore, we can help sellers better understand consumers’ behavioral regularities in their purchase decisions and protect them from the negative consequences of miscalibrating the behavioral parameters in practice.

B. Limitations and Future Research

This study still has limitations that provide avenues for future studies. First, this study neglects the possibility of product returns by consumers who bought products at the regular price in Period 1. If consumers are worried about missing the desired product in the markdown phase, they may purchase the product in the early stage and observe whether they have the opportunity to rebuy it at a cheaper price and return the original product to seller. This speculation behavior can alleviate consumers’ anticipated regrets, but will impact the seller’s daily operations and long-term revenue. Therefore, how consumers’ product return behavior impacts the seller’s markdown policy, and how the seller can react to it need to be further investigated. Second, we used three weeks as the markdown lead time in the experiment; however, in reality, consumers may react differently to the same price discount in different time frames, which is the so-called consumers’ time preference behavior. Implications of anticipated regret in the face of price markdowns should be further examined under different time frames in the future.

Appendix A

SECTION A. Proof of Proposition 1

The strategic consumers will buy the product in Period 1 if and only if $U_{1}^{s} \ge \max \left \{{{U_{2}^{s},0} }\right \}$ , that is, $U_{1}^{s} \ge U_{2}^{s}$ and $U_{1}^{s} \ge 0$ ; we analyze the two conditions as follows.

1. If $U_{1}^{s} \ge U_{2}^{s}$ , according to (3) and (4), we have $(v-p)-q\alpha (p-\delta p)\ge q(v-\delta p)-\beta (1-q)(v-p)$ , thus we have $v\ge \frac {1+q\alpha -q\alpha \delta -\delta p+\beta -\beta q}{(1-q)(1+\beta)} p=\left [{ {\frac {(1+\alpha)(1-\delta)q}{(1-q)(1+\beta)}+1} }\right]p\equiv v_{s}$ .

2. If $U_{1}^{s} \ge 0$ , according to (3), we have $v\ge \left [{ {1+\alpha q(1-\delta)} }\right]p_{1}$ .

As $\alpha \in [{0,1}]$ and $\beta \in [{0,1}]$ , according to (1) and (2), we can verify that $p_{1} -v_{s} =\frac {q(1-\delta)p}{(1+\beta)(1-q)}\left ({{\alpha \beta -1-\alpha q-\alpha \beta q} }\right) \le \left [{ {1+\alpha q(1-\delta)} }\right]\dfrac {q(1-\delta)p}{(1+\beta)(1-q)}(1-1-\alpha q-\alpha \beta q)=-\dfrac {\alpha q^{2}(1-\delta)p}{1-q}\le 0$ . Thus we have $v_{s} \ge \left [{ {1+\alpha q(1-\delta)} }\right]p_{1} \ge p_{1}$ . The proposition is proved.

SECTION B. Proof of Proposition 2

The seller’s objective function for revenue maximization is given as $\max R(p)=PQ_{1} +\delta pqQ_{2} =p\frac {N}{V}(V-p+\mu p-\mu v_{s})+ \delta p\frac {N}{V}(p-\mu p+\mu v_{s} -\delta p)$ .

Since $N/V$ is constant, thus we can convert the above objective function as $\max I(p)=p(V-p+\mu p-\mu v_{s})+\delta p(p-\mu p+\mu v_{s} -\delta p)$ . We define $M=\frac {(1+\alpha)(1-\delta)q}{(1+\beta)(1-q)}$ , thus we have $v_{s}=$ ($1+M)p$ ; then $I(p)$ can be rewritten as $\max I(p)=-\left [{ {(1+\mu M)(1-\delta q)+q\delta ^{2}} }\right]p^{2}+Vp$ .

We take the first-order and second-order derivatives of $I(p)$ with respect to $p$ , as $\delta \in [{0,1}]$ , $q\in [{0,1}]$ , $\mu \in [{0,1}]$ and $M\ge 0$ , we have $\frac {dI(p)}{dp}=-2\left [{ {(1+\mu M)(1-\delta q)+q\delta ^{2}} }\right]p+V$ and $\frac {d^{2}I(p)}{dp^{2}}=-2\left [{ {(1+\mu M)(1-\delta q)+q\delta ^{2}} }\right]\le 0$ . Thus, we can obtain the optimal $p^{\ast }=V \mathord {\left /{ {\vphantom {V {2[(1+\mu M)(1-\delta q)+q\delta ^{2}]}}} }\right. } {2[(1+\mu M)(1-\delta q)+q\delta ^{2}]}$ when $\frac {dI(p)}{dp}=0$ . Here, the proposition is proved.

SECTION C. Proof of Corollary 1

We define $X=\left ({{1+\mu \frac {(1+\alpha)(1-\delta)q}{(1+\beta)(1-q)}} }\right)(1-\delta q)+q\delta ^{2}$ , thus $p^{\mathrm {\ast }}=V/2X$ . We take the first-order derivative of $X$ with respect to $\alpha$ , as $\delta \in [{0,1}]$ , $\beta \in [{0,1}]$ and $q\in [{0,1}]$ , we can obtain $\frac {dX(\alpha)}{d\alpha }=\mu \frac {(1-\delta)(1-\delta q)q}{(1+\beta)(1-q)}>0$ . Thus, $X$ increases in the high-price regret factor $\alpha$ , implying that $p^{\ast }$ decreases in the high-price regret factor $\alpha$ . Here, the corollary is proved.

SECTION D. Proof of Corollary 2

We define $X=\left ({{1+\mu \frac {(1+\alpha)(1-\delta)q}{(1+\beta)(1-q)}} }\right)(1-\delta q)+q\delta ^{2}$ , thus $p^{\mathrm {\ast }}=V/2X$ . We take the first-order derivative of $X$ with respect to $\beta$ , as $\delta \in [{0,1}]$ , $\alpha \in [{0,1}]$ , $\beta \in [{0,1}]$ and $q\in [{0,1}]$ , we can obtain $\frac {dX(\beta)}{d\beta }=-\mu \frac {(1+\alpha)(1-\delta)(1-\delta q)q}{(1+\beta)^{2}(1-q)}< 0$ . Thus, $X$ decreases in the stock-out regret factor $\beta$ , implying that $p^{\ast }$ increases in the stock-out regret factor $\beta$ . Here, the corollary is proved.

SECTION E. Proof of Corollary 3

We define $X=\left ({{1+\mu \frac {(1+\alpha)(1-\delta)q}{(1+\beta)(1-q)}} }\right)(1-\delta q)+q\delta ^{2}$ , thus $p^{\mathrm {\ast }}=V/2X$ . We take the first-order derivative of $X$ with respect to $\mu$ , as $\delta \in [{0,1}]$ , $\alpha \in [{0,1}]$ , $\beta \in [{0,1}]$ and $q\in [{0,1}]$ , we can obtain $\frac {dX(\mu)}{d\mu }=\frac {(1+\alpha)(1-\delta)(1-\delta q)q}{(1+\beta)(1-q)}>0$ . Thus, $X$ increases in the ratio of strategic consumers $\mu$ , implying that $p^{\ast }$ decreases in the ratio of strategic consumers $\mu$ . Here, the corollary is proved.

SECTION F. Proof of Corollary 4

We define $X=\left ({{1+\mu \frac {(1+\alpha)(1-\delta)q}{(1+\beta)(1-q)}} }\right)(1-\delta q)+q\delta ^{2}$ , thus $p^{\mathrm {\ast }}=V/2X$ . We take the first-order and second-order derivatives of $X$ with respect to $\delta$ , as $\mu \in [{0,1}]$ , $\alpha \in [{0,1}]$ , $\beta \in [{0,1}]$ and $q\in [{0,1}]$ , we can obtain $\frac {dX(\delta)}{d\delta }=-\frac {\mu (1+\alpha)q(1-\delta q)}{(1+\beta)(1-q)}-\left ({{\frac {1+\mu (1+\alpha)q(1-\delta)}{(1+\beta)(1-q)}} }\right)q+2\delta q,\frac {d^{2}X(\delta)}{d\delta ^{2}}=\frac {2\mu (1+\alpha)q^{2}}{(1+\beta)(1-q)}+2q>0$ ; Thus, we know that $X(\delta)$ is concave in $\delta$ . Further when $\frac {dX(\delta)}{d\delta }=0$ , we can have $\delta _{0} =\frac {\mu (1+\alpha)(1+q)+(1-q)(1+\beta)}{2\left ({{(1-q)(1+\beta)+\mu q(1+\alpha)} }\right)}\ge \frac {\mu (1+\alpha)(1+q)+(1-q)(1+\beta)}{2\left ({{(1-q)(1+\beta)+\mu (1+q)(1+\alpha)} }\right)}=\frac {1}{2}$ . When $\mu (1+\alpha)\le (1+\beta)$ , we have $\delta _{0} =\frac {\mu (1+\alpha)(1+q)+(1-q)(1+\beta)}{2\left ({{(1-q)(1+\beta)+\mu q(1+\alpha)} }\right)}\le 1$ ; when $\mu (1+\alpha)>(1+\beta)$ , we have $\delta _{0} >1$ . Thus, when $\mu (1+\alpha)\le (1+\beta)$ , we have $\frac {1}{2}\le \delta _{0} \le 1$ , thus $X$ decreases in $\delta$ if $0\le \delta \le \delta _{0}$ , and $X$ increases in $\delta$ if $\delta _{0} \le \delta \le 1$ ; when $\mu (1+\alpha)>(1+\beta)$ , we have all $\delta \le 1< \delta _{0}$ , thus $X$ decreases in $\delta$ . It implies that when $\mu (1+\alpha)\le (1+\beta)$ , $p^{\ast }$ first increases in $\delta$ and then decreases in $\delta$ ; when $\mu (1+\alpha)>(1+\beta)$ , $p^{\ast }$ increases in $\delta$ . Here, the corollary is proved.

Appendix B: Experimental Instructions

You are about to participate in five sets of experiments, each of which requires nine “wait-or-buy” decisions. You will make forty-five decisions during the experiment, and each decision corresponds to an independent experimental scenario. After each set of experiments, you will see the feedback on your decision results in this set on the computer screen. There are no right or wrong answers; just express your preferences. By doing so you can earn a substantial amount of money that will be paid to you as is explained below. Remember, the information on your screen is personal, do not talk with one another during the experiment. If you have any questions, you can raise your hand during the experiment.

1. The context of the experiment is as the following:

   1. Please open the browser. You will see a page of online book store, which shows different kinds of novels. When you click your interested novel, the page will automatically jump to the introduction of the book. After browsing the pages, you can choose to add your favorite novel to your shopping cart.

   2. Please open the z-leaf file on your computer. In each decision, you will see that the novel is sold at different price discounts and different inventory fill rates. You need to make your purchase decision based on the specific situational prompts on the page.

“Suppose that you visited an online book store, and saw one of your favorite novel is sold at 200 RMB. You know you can resell it for 250 RMB at any time. So you added the novel into your shopping cart and were about to purchase. However, then you saw one advertisement on the website that this online book store will hold a reading festival in three weeks and all books will be marked down at that time. But the customers were also noticed that since the amount of the book is limited, you might not be able to get this book during the festival, and the book will be out-of-stock for a long time afterward, and you cannot buy it from other online or offline channels either. Under this circumstance, should you buy the book now or wait for a markdown price later?”

After completing each set of experiments, you will see the feedback information as follows: if the product fill rate in Period 2 is $q=70$ %, then you have a 30% chance of not getting the book in Period 2. Thus, in a decision, ① if you choose to ‘buy’, you will see the potential utility loss of buying the book at a high price before the reading festival, i.e., $p\times (1-\delta)$ (with 70% probability) or no utility loss of avoiding not getting the book during the festival (with 30% probability); otherwise, ② if you choose to ‘wait’, you will see no utility loss of avoiding buying the book at a high price (with 70% probability) or the potential utility loss of not getting the book, i.e., $v$ -$p$ (with 30% probability).

2. The method that you will be paid is given as below:

As you entered the room you can see an envelope placed on your desk. You are required not to open the envelope before the end of the experiment. The envelope marked two numbers: the price discount factor $\delta$ and the book fill rate $q$ . You will be paid according to the certain wait-or-buy decision with ($q$ , $\delta$ ). In addition, you will be paid 5 RMB as the show-up fee for participating the experiment. You are suggested to provide your Alipay account, and the experiment assistant will release the experimental reward to your account within 3–5 working days afterwards.