Abstract
Purchasing new experience products or services often involves significant quality uncertainty for both consumers and firms. Social learning through online reviews helps reduce this uncertainty but exacerbates strategic waiting, as consumers delay purchases to gain more information. This paper examines the impact of social learning on firms’ pricing policies in the presence of strategic consumers under two widely adopted schemes: Contingent pricing and price guarantee. We find that while social learning always benefits the firm, it enables the price guarantee scheme to outperform contingent pricing in terms of profitability for highly patient consumers, which would not be possible without social learning. Notably, social learning drives a range of pricing patterns, even making price skimming optimal under price guarantee for highly patient consumers, as high initial prices combined with markdowns effectively alleviate strategic waiting, enhancing review outcomes and the firm’s profitability. Additionally, social learning always enables the firm to extract greater consumer surplus for impatient consumers under price guarantee. In contrast, social learning under contingent pricing consistently benefits consumers and can achieve win-win outcomes when consumers are moderately patient. Our extensions validate the robustness of these findings under different assumptions, including fully rational consumers and partially forward-looking firms. In particular, a partially forward-looking firm can achieve win-win outcomes with social learning under price guarantee, expanding its practical applicability. This study provides novel insights into the role of social learning in shaping pricing strategies, highlighting its implications for firm profitability and consumer welfare in markets influenced by review dynamics and strategic consumers.
Introduction
Consumers often face quality uncertainty, particularly when purchasing new experience products. This uncertainty deters demand, as consumers may be reluctant to make purchases without sufficient information about the product’s attributes, such as reliability, durability, and ease of use. Firms selling new experience products also grapple with quality uncertainty, which complicates the pricing and marketing strategies. The rise of online shopping since the early 2000s has provided consumers and firms with unprecedented access to online reviews, offering valuable insights into the experience of other buyers. Today, over 90% of consumers consult online reviews before making a purchase (Statista, 2023). A behavior known as social learning, where purchase decisions are shaped by peer feedback through reviews or word of mouth. Social learning benefits not only consumers by reducing quality uncertainty but also helps firms adjust pricing and marketing strategies to better meet consumer expectations (Jing, 2011b; Papanastasiou and Savva, 2017; Yu et al., 2016).
However, social learning is a double-edged sword for both firms and consumers. While it helps reduce quality uncertainty, social learning also incentivizes strategic waiting, as forward-looking consumers delay purchase decisions to gather more information from early buyers’ reviews. This delay can significantly disrupt firms’ revenue generation (Gallego and Şahin, 2010; Swinney, 2011; Yu et al., 2015). To mitigate strategic waiting, firms employ pricing schemes such as
The interplay among pricing schemes, social learning, and consumers’ strategic waiting behavior is intricate and warrants rigorous analyses. Specifically, contingent pricing may lead consumers to delay purchases due to price uncertainty, while price guarantee alleviates strategic waiting by offering refunds for price markdowns but incurs additional costs for the firm. Moreover, social learning further complicates the dynamic by prompting strategic consumers to postpone purchases, anticipating both price reductions and more reliable quality information. This delay reduces the number of reviews, thereby undermining the effectiveness of social learning. On the other hand, although low introductory prices can incentivize immediate purchase, which may enhance review quality, they also reduces the number of consumers who benefit from better-informed decisions later. These interdependencies highlight the multifaceted and challenging nature of the problem.
This paper explores these interactions, focusing on two central research questions: First, how should a firm price its product in the presence of social learning and consumer strategic waiting under each pricing scheme? Second, what are the implications of social learning on the firm’s profitability and consumer surplus?
To answer these questions, we consider a monopolistic firm selling a new experience product over a two-period selling season. Both the firm and consumers initially lack complete knowledge of the product’s quality, knowing only its distribution (Papanastasiou and Savva, 2017; Sun, 2012; Yu et al., 2016). In the first period, consumers decide whether to purchase immediately or wait, influenced by the product’s current price, consumers’ idiosyncratic product preferences, patience levels, expected second-period prices, and their beliefs about product quality. When social learning is present, early buyers post reviews based on their experiences, affecting the purchase decisions of remaining consumers and the firm’s second-period pricing. This process creates a two-sided learning process, where both the firm and consumers update their beliefs of the product’s quality based on the posted reviews (Papanastasiou, 2020; Papanastasiou and Savva, 2017; Sun, 2012; Yu et al., 2016). To capture realistic consumer behavior, we assume that consumers exhibit bounded rationality, forming their quality beliefs based on the aggregate numbers of positive and negative reviews rather than analyzing the detailed review sequence.
We outline the main findings as follows. First, we examine contingent pricing under social learning, revealing that social learning enables the firm to adopt more flexible pricing strategies—skim, consistent, or penetration—that vary based on consumer patience and review outcomes. While social learning compels the firm to lower first-period prices to encourage early purchases, it also allows higher second-period prices when reviews are positive, enhancing profitability. Ultimately, social learning creates a win-win situation under contingent pricing, benefiting both the firm and consumers.
Second, we uncover new pricing dynamics introduced by social learning under price guarantee. Traditional price discrimination theory posits that skim pricing under price guarantee requires the presence of non-price-sensitive consumers. However, our findings reveal that with social learning, skim pricing can be optimal even when all consumers are price-sensitive. This is particularly true for highly patient consumers, where a combination of high first-period prices and markdowns under price guarantee encourages early purchases, enhancing both review outcomes and firm profitability. In this case, social learning leads to higher first-period prices under price guarantee than under contingent pricing. Moreover, social learning consistently improves the firm’s profitability but only benefits consumers who are sufficiently patient under price guarantee.
Moreover, our comparative analysis underscores the trade-offs between the two pricing schemes. In the absence of social learning, contingent pricing proves more profitable for the firm due to its greater pricing flexibility. However, with social learning, price guarantee becomes more advantageous when consumers exhibit high levels of patience, indicating that price guarantee is more effective in mitigating strategic waiting. Notably, we show that contingent pricing with social learning results in mutually better outcomes for both the firm and consumers compared to price guarantee.
Lastly, our extensions validate the robustness of our findings. When consumers are fully rational, the primary insights regarding social learning’s impact on pricing strategies and outcomes remain consistent. Moreover, we consider a partially forward-looking firm setup and reveal new scenarios where price guarantee leads to win-win outcomes, broadening the practical relevance of our results.
The rest of this paper is structured as follows. Section 2 reviews the related literature. Section 3 introduces the model and its preliminaries. Section 4 presents the equilibrium results under the contingent pricing scheme, while Section 5 analyzes the equilibrium results under the price guarantee scheme. Section 6 compares the results across the two pricing schemes, emphasizing the impacts of social learning. Section 7 discusses model extensions, including the effects of consumer rationality and the firm’s discounting of future profits. Finally, Section 8 concludes the paper and outlines directions for future research. The Electronic Companion contains all the proofs, accompanied by both the technical reasoning and the underlying logic to improve comprehension. Notably, we include the
Literature Review
Our work draws upon and contributes to three streams of research, including pricing with strategic consumers, contingent pricing with social learning, and research related to the price guarantee scheme.
Pricing with Strategic Consumers
Pricing in the presence of strategic waiting consumers has been extensively documented in the literature since the seminal work of Coase (1972), highlighting how monopoly retailers suffer from consumers delaying purchases in anticipation of price reductions. Subsequent research has consistently shown that strategic consumers prefer to wait for discounts, affecting firms’ pricing and inventory decisions (Aviv et al., 2019; Cachon and Swinney, 2009; Su, 2007). For example, Cachon and Swinney (2009) demonstrate that strategic consumer behavior drives firms to stock less, reduce price discounts, and ultimately earn lower profits. Additionally, committing to a predetermined price path, regardless of whether it includes markdowns, performs poorly compared to contingent pricing strategies.
Several studies employ two-period stylized models to examine how pricing schemes can mitigate strategic waiting behavior. Su and Zhang (2008) show that firms can reduce strategic waiting by making future purchase opportunities less attractive, such as through upward price trajectories or limited product availability. Similarly, Liu and Van Ryzin (2008) find that restricted stock availability discourages consumers from delaying purchases, thereby enhancing firm profitability. Aviv and Pazgal (2008) argue that an announced fixed-discount pricing strategy can outperform contingent pricing, while Cachon and Feldman (2015) propose frequent discounting as a superior approach compared to static or contingent pricing.
Although dynamic pricing may encourage consumers to delay purchases, research indicates that firms can still maintain profitability. Ovchinnikov and Milner (2012) show that offering end-of-period discounts can benefit firms in the long run, even if consumers adjust their behavior to wait for these opportunities. Wu et al. (2015) analyze a firm selling product versions at full price in the first period and at markdowns in the second, demonstrating that strategic markdowns can stabilize profitability. Additional research has examined related topics such as consumer credit (Papouskova and Hajek, 2019) and return policies (Kim et al., 2022; Liu et al., 2022).
Contingent Pricing with Social Learning
Consumer reviews and social learning have drawn considerable scholarly attention, spanning diverse research streams, such as social networks (Qiu et al., 2021), information disclosure and sharing (Li, 2017; Ma et al., 2024; Shin and Zeevi, 2024), product line design and new product launches (Feldman et al., 2019; Kwark et al., 2018), and inventory decisions (Hu et al., 2016; Papanastasiou, 2020). A notable body of literature explores optimal contingent pricing (i.e., dynamic pricing) strategies in the presence of social learning. For instance, Feng et al. (2019) combine analytical modeling and empirical analysis to demonstrate how merchants adjust prices dynamically in response to consumer reviews to influence future feedback. Ma et al. (2021) develop a social learning model dependent on user participation and examine the influence of this learning process on the dynamic pricing strategies employed by service providers. Other studies investigate contingent pricing strategies that account for both social learning and consumers’ strategic waiting behavior, typically employing two-period models. Jing (2011b) employs a linear model of social learning to explore its effects on consumer purchasing decisions. Results show that it is the learning externality that drives postpone purchases. Jing (2011a) further investigates the interaction between social learning and dynamic pricing for durable goods, revealing that high learning intensity may lead firms to release products earlier and charge higher prices to uninformed consumers.
Few studies have examined the combined effects of consumers’ strategic waiting behavior and the Bayesian social learning process. Using a signaling model, Yu et al. (2016) establish that a monopolist reduces first-period sales volume and prices to counter strategic waiting and social learning effects. Papanastasiou and Savva (2017) compare preannounced pricing and responsive pricing under Bayesian learning, finding that preannounced pricing typically follows an increasing price trajectory, while responsive pricing allows for price adjustments in either direction.
The above-mentioned literature, with the exception of (Feng et al., 2019), assumes that consumers can accurately infer true product quality from reviews. However, in practice, reviews are inherently subjective and may be biased (Li and Hitt, 2008). Addressing this limitation, Crapis et al. (2017) and Ifrach et al. (2019) explore monopoly pricing when consumer reviews consist of binary feedback (“like” or “dislike”) derived from their net utility. Crapis et al. (2017) analyze static and dynamic pricing schemes within a non-Bayesian framework, while Ifrach et al. (2019) demonstrate that a stationary optimal pricing strategy can attract a larger consumer base. Moreover, Shin et al. (2023) consider two review models—quality-based and value-based—and show that retailers may adopt distinct pricing strategies, such as skim pricing or penetration pricing, depending on the prevailing review model.
In contrast, we adopt a rational expectation equilibrium framework to capture the dynamics between price and demand in the review generation and social learning processes. Specifically, we assume that consumers exhibit bounded rationality, focusing on the aggregate numbers of positive and negative reviews when forming their quality beliefs. Such a framework allows us to integrate the bounded rationality assumption and strategic waiting behavior (Huang et al., 2017; Li and Jiang, 2022; Song et al., 2019). Based on the review generation and social learning processes, we analyze and compare the firm’s optimal pricing strategies under two schemes: Contingent pricing and price guarantee, when consumers exhibit strategic waiting behavior.
Price Guarantee Scheme
The price guarantee scheme consists of two distinct dimensions: time and structure. The time dimension involves firms offering consumers a low-price guarantee for a specific product within a set period, while the structure dimension refers to firms committing to match competitors’ prices across various sales channels. This paper focuses on the time dimension of the price guarantee scheme. For an in-depth review of the structure dimension, see Jiang and He (2021).
In a monopoly context, Levin et al. (2007) develop a discrete-time optimal control model to simultaneously determine the offered price, strike price, and fee for the price guarantee scheme. Lai et al. (2010) explore posterior price matching, finding that a firm can increase profit when the fraction of strategic consumers is moderate and consumers’ valuations decline moderately over time. This occurs because price matching eliminates consumers’ strategic waiting incentives, enabling firms to charge higher prices during the regular selling season. Furthermore, Cohen-Vernik and Pazgal (2017) endogenize the refund amount in their model, allowing firms to determine the optimal reimbursement percentage for price differences. From a behavioral perspective, Huang et al. (2017) introduce bounded rationality to explain the widespread adoption of price guarantee schemes. Wu et al. (2025) examine the effectiveness of price guarantees in a Markovian pricing context and find that such guarantees can effectively retain consumers by encouraging high-valuation customers to purchase early and enabling firms to engage in price discrimination based on customers’ willingness to pay.
The existing literature on price guarantee is limited, and the role of social learning—a key feature in this paper—has not been explored within this context. This research fills that gap by examining contingent pricing and price guarantee in the presence of strategic consumers and social learning. We demonstrate that in the presence of social learning, a firm may adopt different pricing strategies—skim, consistent, or penetration—depending on consumers’ strategic waiting incentives, product quality, and review outcomes under each pricing scheme. Our study provides a novel rationale for why major e-tailers implement price matching during key promotional events in the presence of social learning, offering valuable managerial and practical insights for firms and consumers.
Model Setup and Preliminaries
We consider a monopolistic firm selling a new experience product over two consecutive periods. Let
In this section, we first detail the model of consumer behavior and quality belief, followed by a description of the firm’s decisions and profit functions.
Consumers’ Purchase Decisions
Consumer Utility
We assume the market consists of risk-neutral consumers with heterogeneous idiosyncratic preferences for the product. Consumer heterogeneity is modeled using a Hotelling framework (Hotelling, 1929). Specifically, the product is positioned at 0, and a consumer’s preference, modeled by
Consumers form their quality beliefs for each period, denoted by
We assume that the utility of no purchase is zero. At the beginning of the first period, consumers evaluate their expected net utility in each period to decide whether to purchase in the first period or postpone. Specifically, consumer
Without loss of generality, we normalize the number of consumers to one and assume that each consumer purchases at most one product. Consumers are aware of the product at the beginning of the selling season and make purchase decisions based on their expected net utilities. If a consumer’s expected net utility in the first period is nonnegative and exceeds that of the second period, the consumer purchases the product in the first period; otherwise, the consumer postpones the purchase decision until the second period. Let
Without social learning, consumers’ quality beliefs in both periods align with their prior beliefs; that is,
Review Generation
After purchasing and experiencing the product in the first period, consumers post reviews about its quality based on their net ex-post utility
(thumbs up), when the ex-post utility is nonnegative, or a negative review, denoted by
(thumbs down), otherwise. This binary review modeling approach simplifies conventional star rating scales and aligns with the settings in Crapis et al. (2017) and Ifrach et al. (2019).
Recall that
; for
. Finally, for
and
based on the sign of their ex-post utility

Review generation and social learning.
At the beginning of the second period, consumers who have not yet purchased the product can observe posted reviews and update their beliefs about the product’s quality. While review aggregators provide access to individual review sequences, processing such detailed information can be cumbersome and presents significant computational challenges. To address this, we adopt a behavioral assumption of bounded rationality, where consumers focus on the aggregated numbers of
and
to form their quality belief, rather than analyzing the detailed review sequences. Notably, the bounded rationality and forward-looking behavioral assumptions can complement each other and can both be integrated into a rational expectations equilibrium framework (Huang et al., 2017; Li and Jiang, 2022; Song et al., 2019). In Electronic Companion EC.1, we describe a within-subject experiment conducted to validate this assumption. Moreover, we discuss the implications of fully rational consumers in Section 7, where we demonstrate that our main results are robust under this setting.
Based on these aggregated reviews, we assume that second-period consumers form one of three beliefs, denoted by
We further assume that consumers use a quasi-Bayesian decision rule to estimate product quality from aggregated reviews, as they find detailed review sequences difficult to process. This leads them to form posterior beliefs by calculating a probability-weighted average over the reviews in the corresponding range in equation (5), rather than making precise inferences. Let
Equation (6) illustrates that, alongside actual product quality and consumer heterogeneity, the first-period price (
In the presence of social learning, consumers lack direct knowledge of the actual product quality in the first period and instead form quality beliefs based on price and preferences. Anticipating quality information from future reviews, social learning may prompt consumers to delay their purchase decision. However, for any consumer
Under either pricing scheme, the firm sequentially announces the price
We assume
Finally, we describe the sequence of events as follows:
At the beginning of the first period, the firm sets price Consumers decide whether to purchase immediately or delay strategically, based on the first-period price, Consumers who purchase in the first period post reviews based on their perceived utility at the end of the first period. At the beginning of the second period, both the firm and consumers update their beliefs about product quality after reviewing the posted reviews. The firm sets the second-period price, Remaining consumers who have not yet purchased make their decisions in the second period.
The event sequence is summarized in Figure 2. Note that the only variation in the sequence of events between the two pricing schemes is that the firm must reimburse the price difference in the second period if markdowns occur under the price guarantee scheme.

Sequence of events.
It is straightforward to verify that, for the same prices
In this section, we examine the firm’s optimal decisions under the contingent pricing scheme, where the firm can dynamically adjust its prices across both periods. We consider two cases:
Contingent Pricing Without Social Learning
In the absence of social learning, consumers cannot gain information from product reviews and must rely solely on their prior belief about product quality for purchase decisions, such that
(Equilibrium Prices Under
)
The firm’s unique equilibrium prices are
Proposition 1 establishes that, in the absence of social learning, the firm adopts a skim pricing strategy over the two periods. This strategy emerges because consumers only choose to delay their purchases till the second period if the firm significantly reduces prices. Note that in this case, the firm prefers consumers to purchase in the first period because of the higher price. Consequently, as consumers exhibit greater patience (i.e., as
In the presence of social learning, consumers face a trade-off between the immediacy of purchasing and the potential benefits of delaying to acquire additional information. Specifically, consumers with lower patience levels (i.e., smaller
Specifically, with social learning, the firm and consumers form the posterior quality belief
(First-Period Demand w.r.t. Price Under
)
Given the first-period price
Lemma 1 demonstrates that the first-period price influences not only consumers’ immediate decision to purchase or delay but also how different types of reviews impact their purchasing decisions in the second period. Specifically, as the first-period price increases, more consumers choose to postpone their purchase decisions to the second period. Moreover, consider consumer
Based on Lemma 1, we derive the firm’s optimal pricing strategy
The firm’s expected profit and first-period demand strictly decrease with The close-form expressions of
Proposition 2(i) reveals that, under
Proposition 2(ii) illustrates how consumers’ strategic waiting behavior affects the optimal prices. While the first-period price strictly decreases with

Firm’s optimal prices in the presence of social learning under contingent pricing. The symbols
Proposition 2(iii) shows that while
In this section, we assess the impact of social learning under the contingent pricing scheme. Recall that social learning allows both the firm and the second-period consumers to update their beliefs based on reviews posted by first-period consumers. The following proposition details the properties of the consumers’ posterior quality belief
(Second-Period Quality Beliefs Under
)
At the optimal prices
Proposition 3(i) demonstrates that completely positive reviews lead to a posterior quality belief that exceeds the prior belief. In contrast, mixed or completely negative reviews cause the posterior beliefs to fall below the prior. This finding highlights the influence of review polarity on consumers’ perception of quality.
Proposition 3(ii) further reveals that as consumers grow more patient, the posterior quality beliefs decrease. This is because when consumers have a greater tendency to delay purchases, Proposition 2 implies that the firm lowers the first-period price to stimulate early purchases, but nevertheless, the first-period demand decreases. As indicated by equation (6), both a lower first-period price and reduced demand signal lower perceived product quality to second-period consumers, resulting in diminished posterior quality beliefs irrespective of the review outcome.
While a higher patience level (

Posterior beliefs (left) and corresponding probabilities (right) with respect
By comparing the equilibrium prices under
Proposition 4 shows that, in the presence of social learning, the firm typically sets lower prices in both periods compared to the no-social-learning, except when the review outcome is completely positive. Social learning, therefore, acts as a double-edged sword for the firm. On one hand, it strengthens consumers’ incentive to delay purchases in anticipation of additional information and potential price reductions. In response, the firm has to lower its first-period price to encourage early purchases. On the other hand, in the second period, consumers update their quality perceptions based on the reviews, which increase their willingness to pay if the reviews are positive but decrease if the reviews are mixed or negative. This allows the firm to charge a higher second-period price when reviews are positive but forces it to lower the price when reviews are mixed or negative.
Proposition 4 might suggest that social learning benefits consumers while disadvantaging the firm due to the typically lower prices it induces. Yet, Proposition 5 reveals that under the contingent pricing scheme, the positive impact of social learning—specifically, the higher prices the firm can set when reviews are positive, capitalizing on increased consumer willingness to pay—outweighs the negative effect of lower prices in other scenarios. As a result, social learning ultimately benefits both consumers and the firm, creating a win-win situation.
Both the firm’s optimal profit and consumer surplus are higher with social learning than without it under contingent pricing.
Analysis of Price Guarantee
In this section, we analyze the firm’s optimal decisions under the price guarantee scheme, where the firm offers consumers a full refund of the price difference if the second-period price is lower than the first. We consider two scenarios:
Price Guarantee Without Social Learning
Similar to Section 4.1, in the absence of social learning, consumers base their purchase decisions solely on the prior belief about product quality; that is,
The firm’s equilibrium prices are
Unlike the optimal strategy under
As in the case of
(First-Period Demand w.r.t. Price Under
)
Given the first-period price
Lemma 2 shows that when the review outcome is completely positive, the firm may employ a skim, consistent, or penetration pricing strategy across the two periods. Doing so still ensures that some consumers always purchase in the second period. In contrast, when the review is mixed or negative, the optimal strategy is to either adopt consistent pricing, resulting in zero demand, or mark it down sufficiently to generate additional demand from remaining consumers in the market. Therefore, compared to the exclusive use of consistent pricing in the absence of social learning (Proposition 6), the presence of social learning introduces much richer and more varied pricing strategies under
Based on Lemma 2, we derive the firm’s optimal pricing strategy
There exists thresholds The firm’s expected profit and first-period demand are piecewise functions that strictly decrease with
The close-form expressions of
Proposition 7 demonstrates that under

Firm’s optimal prices in the presence of social learning under price guarantee. The symbols
When consumers are sufficiently patient (
Lastly, our findings offer an alternative explanation of when and why a firm should adopt a skim pricing strategy. The conventional Price Discrimination Theory (Moorthy and Winter, 2006; Png and Hirshleifer, 1987; Shaffer and Zhang, 2000) suggests that under a price guarantee, a firm should adopt a skim pricing strategy only when it can offset margins lost to price-sensitive consumers (who claim refunds) by setting a high first-period price for non-price-sensitive consumers (who do not claim refunds). We demonstrate that, in the presence of social learning, a skim pricing strategy remains viable even when all consumers are price-sensitive. Specifically, when consumers are highly patient, the combination of social learning and a markdown policy with a high first-period price not only incentivizes early purchases but also enhances the review outcome, ultimately benefiting the firm. Overall, our study uncovers new dynamics introduced by social learning under the price guarantee scheme.
The next section explores the implications of social learning on the firm’s pricing strategy and profitability under the price guarantee scheme.
In this section, we examine the impact of social learning under the price guarantee scheme. The following proposition details the properties of the consumers’ posterior quality belief

Posterior beliefs (left) and corresponding probabilities (right) with respect
At the optimal prices
Proposition 8(i) reveals that under
A notable distinction from Proposition 3 arises when consumers are highly patient (i.e.,
Proposition 9 evaluates the impact of social learning on prices by comparing the equilibrium prices under
Proposition 9(i) reveals that under the price guarantee scheme, the firm sets a higher first-period price when social learning is present. This is because, unlike the case without social learning, where the firm lowers the first-period price to encourage early purchases and boost initial demand, social learning prompts the firm to raise the first-period price to improve the posterior beliefs of consumers who anticipate a second-period markdown and leverage the price guarantee. Proposition 9(ii) further shows that when the firm adopts consistent pricing for mixed or negative reviews to minimize refunds under the price guarantee, the second-period prices may be higher than those without social learning. These findings stand in stark contrast to Proposition 3, which demonstrates that under contingent pricing, the firm sets a lower first-period price and reduces the second-period price for mixed or negative reviews in the presence of social learning.
The following proposition compares the firm’s profit and consumer welfare.
The firm’s optimal profit is higher with social learning than without it; consumer surplus is lower with social learning when
Proposition 10 shows that the firm benefits from social learning. However, unlike the contingent pricing scheme where consumer surplus is always higher with social learning, the price guarantee scheme leads to lower consumer surplus for relatively impatient consumers. This is because impatient consumers prefer early purchases, which allows the firm to extract more surplus by maintaining consistent prices. In contrast, patient consumers benefit from frequent markdowns, refunds, and additional product quality information from reviews, all of which increase consumer surplus in the presence of social learning.
Comparison of Pricing Schemes
In this section, we compare the firm’s performance and consumer welfare under the contingent pricing and price guarantee schemes. We begin by examining the scenario without social learning.
(Pricing Scheme Comparison Without Social Learning)
The firm’s optimal profit is strictly higher under contingent pricing than under price guarantee. The consumer surplus is strictly higher under price guarantee for
Proposition 11 shows that without social learning, contingent pricing is more profitable for the firm than price guarantee. This is because, although price guarantee effectively mitigates consumer strategic waiting, the associated refund costs limit the firm’s overall profitability. In contrast, the pricing flexibility under contingent pricing allows the firm to manage demand more effectively. However, the effect on consumer surplus is more nuanced. Specifically, the consumer surplus under price guarantee is strictly higher for impatient consumers but lower for patient consumers. This outcome arises from the pricing dynamics described in Propositions 1 and 6. Under price guarantee, the firm adopts a consistent pricing that induces consumers to purchase only in the first period. This price is lower than the first-period price but higher than the second-period price under contingent pricing. Consequently, impatient consumers who tend to purchase early face a higher first-period price under contingent pricing, reducing their surplus. In contrast, patient consumers who are willing to wait benefit from the lower second-period price under contingent pricing. Thus, consumer surplus is lower for impatient consumers but higher for patient consumers under contingent pricing than under price guarantee.
Next, we compare the firm’s performance and consumer surplus under contingent pricing and price guarantee when social learning is present.
(Pricing Scheme Comparison with Social Learning)
There exists
Proposition 12 demonstrates that in the presence of social learning, the firm achieves higher profitability under price guarantee when consumers are sufficiently patient. This occurs because price guarantee mitigates consumers’ strategic waiting behavior and reduces their sensitivity to the first-period price. As a result, the firm can set a high first-period price that enhances consumers’ posterior quality beliefs and encourages second-period purchases. In contrast, under contingent pricing, the firm must significantly lower the first-period price to induce early purchase, reducing overall profitability. Consequently, price guarantee coupled with social learning allows the firm to extract greater consumer surplus and achieve superior profitability with patient consumers. When consumers are relatively impatient, the advantages of price guarantee diminish. Its impact on early purchases becomes less significant, and the need to provide refunds under the scheme restricts pricing flexibility, diminishing the firm’s ability to extract consumer surplus and, consequently, overall profitability.
Combining the results with Propositions 5 and 10, Proposition 12 highlights that social learning enhances the firm’s profitability under both contingent pricing and price guarantee schemes. However, its effectiveness depends on consumer patience: Social learning is more impactful under contingent pricing for impatient consumers and under price guarantee for patient consumers. In terms of consumer welfare, one can show that less patient consumers (

Comparison of profits (left) and consumer surplus (right) at the optimal prices under contingent pricing and price guarantee (
Social learning under contingent pricing results in a win-win situation for both the firm and consumers across both pricing schemes for
We consider two extensions of the base model: Fully rational consumers in Section 7.1 and the scenario where the firm discounts the second-period profit (i.e.,
Fully Rational Consumers
In the base model, consumers are assumed to have bounded rationality and can only infer a range of product quality when observing mixed reviews. This assumption reflects the challenges consumers face in accessing complex review information. In this extension, we explore the case of fully rational consumers who can infer the exact product quality from mixed reviews. Specifically, fully rational consumers use the count of positive and negative reviews to precisely identify the product quality, i.e.,
Since there is no difference between bounded and full rationality in the absence of social learning, we focus solely on the

Equilibrium prices under
We further examine the robustness of the main results on the impact of social learning in different pricing schemes. The findings, detailed in Figure EC.1 in Electronic Companion EC.3, are consistent with Propositions 4, 5, 9 and 10, and Corollary 1: with fully rational consumers, social learning leads the firm to lower the first-period price under contingent pricing but increases it under price guarantee. Furthermore, both the firm and consumers benefit from social learning under contingent pricing, while under price guarantee, the firm consistently benefits, and consumers benefit only when they exhibit high patience. Lastly, social learning under contingent pricing creates a win-win situation for both the firm and consumers when consumers are moderately patient. These findings highlight the consistency between the results under full and bounded rationality, validating the robustness of the bounded rationality assumption in the base model.
In the base model, we assume
(Impact of
)
Under Under
Observation 1 is intuitive. Under
Figure EC.5 illustrates the impact of social learning on the firm’s profit and consumer surplus across different pricing schemes as
Figure EC.6 further compares the firm’s profit and consumer surplus under contingent pricing and price guarantee. We find that without social learning, the firm tends to perform better under contingent pricing due to its pricing flexibility, while consumers are generally better off under price guarantee when the firm is more forward-looking than consumers. These results are consistent with Proposition 11. However, when consumers are more patient than the firm, the firm benefits more from price guarantee due to its effectiveness in inducing early purchases. Similarly, the results in the presence of social learning are largely consistent with Proposition 12, although the comparison of consumer surplus becomes more nuanced, depending on the firm’s emphasis on long-term profits and the consumers’ patience level.
Combining the observations in Figures EC.5 and EC.6, we observe that social learning under both contingent pricing and price guarantee can result in a win-win situation for both the firm and consumers across both contingent pricing and price guarantee schemes. Figure EC.7 depicts the win-win situation for both pricing schemes. Specifically, the win-win situation arises under price guarantee with social learning when the firm and consumers are both moderately forward-looking. In this scenario, the effectiveness of price guarantee in inducing early purchases is particularly beneficial to both the firm and consumers. Specifically, the firm sets a low first-period price to incentivize early purchases while raising the second-period price only for completely positive reviews. For mixed or negative reviews, the absence of second-period demand under this pricing strategy minimizes the need for markdowns and refunds, ultimately enhancing profitability. At the same time, consumer surplus improves due to better alignment between pricing policies and quality perceptions. In contrast, under contingent pricing, the firm needs to significantly reduce the second-period price for mixed or negative reviews to attract demand, reducing the firm’s profitability compared to price guarantee. This result is distinct from Corollary 1, which states that social learning can only result in a win-win situation under contingent pricing when
This paper investigates the interplay between pricing strategies, social learning, and consumers’ strategic waiting behavior, focusing on two widely adopted pricing schemes: Contingent pricing and price guarantee. We find that social learning enables the firm to adopt more flexible strategies tailored to consumer strategic waiting and review outcomes. Notably, social learning makes price skimming policies optimal under price guarantee for highly strategic consumers, as high first-period prices combined with markdowns enhance review outcomes and firm profitability. This finding unveils that it can be optimal for a firm to adopt price skimming even when all the consumers are price sensitive, contrasting with the conventional price discrimination theory. Importantly, social learning benefits firms under both pricing schemes but impacts consumer surplus differently: Contingent pricing consistently increases consumer surplus, whereas price guarantee benefits patient consumers but lowers surplus for impatient ones.
Our comparative analysis reveals that without social learning, contingent pricing is more profitable due to its pricing flexibility. However, in the presence of social learning, price guarantee becomes more advantageous when consumers are sufficiently patient. Moreover, social learning under contingent pricing creates win-win outcomes for both firms and consumers when consumers are moderately patient and the firm is forward-looking. In contrast, price guarantee is more effective in mitigating consumer strategic waiting, enabling the firm to extract greater surplus from patient consumers in the presence of social learning.
The model extensions validate the robustness of our findings. When consumers are fully rational, the primary insights regarding social learning’s impact on pricing strategies and outcomes remain consistent. Moreover, the partially forward-looking firm scenario highlights additional contexts in which price guarantee can lead to win-win outcomes, expanding the practical applicability of our results.
This study offers novel insights into pricing dynamics, consumer surplus, and firm profitability, enriching the understanding of pricing strategies in the context of social learning and strategic consumer behavior. Future research could extend these findings in several ways. First, integrating more complex consumer review dynamics, such as biased or heterogeneous reviews, may yield deeper insights into social learning. Second, exploring the interplay between pricing strategies, promotional activities, and brand reputation such as discounts or loyalty programs could provide valuable managerial implications. Finally, analyzing these dynamics in competitive markets could further illuminate optimal pricing strategies in the presence of rival firms.
Supplemental Material
sj-pdf-1-pao-10.1177_10591478251329858 - Supplemental material for Pricing in the Presence of Strategic Consumers and Social Learning Under Contingent Pricing and Price Guarantee
Supplemental material, sj-pdf-1-pao-10.1177_10591478251329858 for Pricing in the Presence of Strategic Consumers and Social Learning Under Contingent Pricing and Price Guarantee by Zhong-Zhong Jiang, Jinlong Zhao, Zelong Yi, Ying-Ju Chen and Guang Li in Production and Operations Management
Footnotes
Acknowledgment
We are grateful to the departmental editor (Professor Asoo Vakharia), an anonymous senior editor, and two anonymous referees for very helpful comments and suggestions.
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The authors received the following financial support for the research, authorship and/or publication of this article: Zhong-Zhong Jiang was partially supported by the National Social Science Fund of China (23&ZD050), the National Natural Science Foundation of China (NSFC) (71971052, 72192830, and 72192831), and the Fundamental Research Funds for the Central Universities (N2306008 and N2406005). Zelong Yi was partially supported by the NSFC (72171154 and 72222019). Ying-Ju Chen was partially supported by the Research Grants Council of Hong Kong (C6020-21GF).
Notes
How to cite this article
Jiang Z-Z, Zhao J, Yi Z, Chen Y-J and Li G (2025) Pricing in the Presence of Strategic Consumers and Social Learning Under Contingent Pricing and Price Guarantee. Production and Operations Management 34(10): 3063–3081.
References
Supplementary Material
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