Research on Optimal Group-Purchase Threshold and Pricing Strategy of Community Group Purchase

Abstract

This study delves into the rapidly evolving community group-buying model, specifically focusing on the determination of optimal group-buying thresholds and pricing strategies for merchants. Aiming to bridge the gap in the existing literature, the methodology employs optimization models, integrating a numerical analysis to construct and evaluate a single merchant model. The findings reveal a nuanced relationship: within a specific threshold interval, a unique group-purchase threshold exists where merchants can maximize profits by balancing group and ordinary sales. The study shows that factors like ordinary selling price, group-buying publicity, and associated costs significantly influence these thresholds and pricing strategies. A critical insight is the threshold’s variability in response to market conditions, highlighting a strategic balance for maximizing profitability. The research underscores the need for merchants to adapt their strategies in response to evolving market dynamics and consumer behaviors. However, the study acknowledges its limitations due to its theoretical nature and focus on the Chinese market, suggesting the potential for future empirical studies in diverse cultural and economic contexts. Overall, this research contributes both theoretically and practically by providing a foundational framework for merchants to optimize group-purchase thresholds and pricing strategies in the dynamic realm of community group buying.

1. Introduction

In the late 1990s, as e-commerce entered the B2C arena, the group-buying consumer model rapidly emerged and experienced two significant development stages: online group buying and community group buying. The online group-buying model was first launched by the American agent Groupon in 2008, and subsequently, group-buying platforms emerged around the world. Online group buying is based on the principle of thin margins and multiple sales, providing a platform for consumers to enhance their ability to negotiate the best price, while at the same time, merchants offer group discounts below the retail price. Based on the online group-buying model, community group buying first sprouted in China in 2015 and began to grow rapidly in 2018 [1]. Unlike online group purchasing, community group purchasing refers to the formation of a group-purchasing group by some residents in a community, who jointly participate in group-purchasing activities through social media and other channels, so as to obtain a more favorable price. It is worth noting that the emergence of the new crown pneumonia epidemic in 2020 has led to consumers enjoying further convenience from community group-buying businesses and perfecting this consumption habit [2]. As of 2022, there were more than 300 e-commerce platforms or enterprises in the community group-buying category in China [1].

Despite its growth and popularity, the dynamics of group buying, particularly in terms of pricing strategies, threshold settings for group buys, and the decision-making process of merchants remain underexplored. This paper addresses this gap by focusing on three critical aspects. First, with respect to the group-buying threshold and group-buying price setting, this paper proves that there exists a unique optimal threshold for merchants within a certain group-buying threshold interval, at which time there exists optimal group-buying pricing. According to this theory, this paper points out the relationship between merchants’ group-buying thresholds and ordinary selling prices, the degree of group-buying publicity and group-buying costs. At the same time, the article also points out the relationship between the optimal group-buying price and group-buying cost. Second, in terms of merchants’ decision to offer group buys, this paper proves that whether merchants offer group-buying services is related to the fixed cost of group buys. Third, in terms of ordinary selling price setting, this article proves the relationship between the optimal ordinary selling price and the group-buying threshold in the case of price endogeneity.

The structure of this paper is organized as follows: Section 2 presents a comprehensive literature review, exploring the development and current trends in community group buying, with a focus on multidisciplinary perspectives and emerging trends in optimal group decisions. Section 3 delves into the model assumptions and construction, outlining the theoretical framework and hypothesis development for understanding optimal group-buying thresholds and pricing strategies. In Section 4, we conduct a numerical analysis to validate the proposed model, examining the relationship between group buying thresholds, ordinary selling prices, and merchant profits. Finally, Section 5 discusses the implications of our findings, acknowledging the study’s limitations and suggesting avenues for future research in this dynamic field.

2. Literature Review

In recent years, community group buying has emerged as a dynamic force in e-commerce, presenting new trends and challenges that are reshaping consumer and merchant behavior. This literature review explores these evolving trends, focusing on how technological advancements and changing market dynamics are influencing community group-buying practices. Simultaneously, it delves into the realm of optimal group decisions, examining how merchants navigate through setting group-buying thresholds and pricing strategies to maximize profitability and market appeal. This synthesis of current research and theories aims to provide a comprehensive understanding of the complexities and strategic considerations inherent in the community group-buying landscape.

2.1. Community Group-Buying Landscape

Community group buying was introduced in China in 2015 and skyrocketed three years later [1]. Since the outbreak of the COVID-19 pandemic in 2020, a large amount of budget has been invested in community group-buying platforms in China [3,4,5]. This section analyzes the development status and trends of community group buying, which is divided into a multidisciplinary inquiry into community group buying and an exploration of hotspots in the field.

2.1.1. Multidisciplinary Inquiry of Community Group Buying

With the continuous development of community group buying, the academic inquiry into this proposition is no longer confined to the realm of economics and marketing but can be synergistically analyzed from multidisciplinary perspectives such as sociology, technology, and psychology. On the sociological side, Yang and Qi (2023) [6] investigate how citizens initiated crisis response in their neighborhoods by investigating community group buys during the 2022 Shanghai epidemic outbreak, thus filling the gap in bottom-up crisis-response research in China. The article suggests that community group buying increases the interaction between the state and society. In terms of technology, studies have been conducted to apply big data technology to the user data analysis of community group buying. Wu et al. (2022) [7] use big data crawling technology to analyze the community group-buying behaviors of residents in different city sizes and summarize the shopping behaviors and characteristics of different types of residents. In terms of psychology, a large number of scholars have conducted research on the psychological phenomena in community group buying. By studying the virtual community group buying behavior, Wang (2017) [8] finds that in groups, perceived interactivity positively affects initiator trust, and initiator trust negatively affects risk perception. Wu et al. (2022) [7] conducted a study on community group buying based on the role theory and the trust transfer theory, and this study shows that the role interactions of both the merchant and the friend positively affect interpersonal trust, and the interpersonal trust leads to trust in community group buying, which further explains the phenomenon of “acquaintance marketing”. Xu and Hu (2022) [9] investigate the relationship between customers’ perceived value and loyalty and community experience. The study shows that community group buying has a slight negative moderating effect on customer loyalty, and emotional value has a significant effect on customer loyalty. In addition, community group buying is emerging as a research context in academic studies on other topics. For example, in the study of path planning problems, Liu et al. (2023) [10] construct a low-carbon vehicle delivery route optimization model based on improved genetic algorithms in the context of community group buying, and this model reduces the carbon emissions of vehicles in community group-buying delivery.

2.1.2. Development Trends of Community Group Buying

Community group-buying research in the last two years has gradually shifted from generalized modeling to specific details, such as the proposal of a community group-buying leader nanostore, research on specific product categories, and a focus on fairness. Nanostores were first proposed in 2022 by Sun and Zhang [11], who argued that in the emerging trend of community group buying, consumers choose nanostores as the community group-buying leaders. A nanostore’s main function is to collect cooperative orders and provide last mile services in bulk. Sun and Zhang point out that nanostore’s operation strategy mainly depends on the integrated market parameters. Shu et al. (2023) [12], on the other hand, investigate the coexistence of multiple nanostores by constructing the Hotelling linear model. The study shows that nanostores’ preferred decisions depend on their own and competitors’ investment cost parameters, and the article also indicates that consumers’ sensitivity to community group-buying services has a negative impact on nanostore profits. In addition, the problem of community group buying for perishable goods has also been brought to the forefront of the research agenda. Yu et al. (2022) [13] investigate the realistic delivery problem common to community group-buying operators, whereby the operators may suffer from a loss of revenues due to the deterioration of the products during the delivery process. By proposing a branching-price algorithm, the article provides managerial insights for community group-buying operators of perishable goods. In terms of fairness concerns, the emergence of community group buying has raised fairness concerns among other participating merchants. Wang and Song [14] thus construct a game model under three different scenarios, namely, initial state, fairness-neutral, and fairness-concerned, and the study shows that fairness-concerned has a very limited impact on the social welfare, affecting only the internal distribution of benefits.

2.2. Optimal Group Decisions

2.2.1. Current Optimal Group Decisions

With the rise of community group buying, academic research on optimal decision making in community group buying is increasing. Liang et al. [15] discuss the dynamics of the group-buying mechanism, the impact of information updating on customer behavior, and the seller’s profit maximization. Similarly for the information disclosure problem, Ai (2021) [16] explores it from the perspective of green development, and the study concludes that under the condition of information symmetry, when the benefit brought by the government’s credibility improvement is higher than the government’s cost of screening the information about the enterprise’s products and identifying the green products, the enterprise’s expected penalty for the production of high-carbon products is higher than the difference between the incremental actual cost of the enterprise’s production of green products and its actual incremental revenue; the consumer’s purchase of a green product’s perceived utility is higher than the consumer’s cost of purchasing green products, and the three-way game evolves into a socially desirable stable state. In addition to the information updating and disclosure strategy, the optimal decision of promotional effort (PE) and service level (SL) in the community group-buying supply chain has also received attention. Lan and Yu (2022) [17] construct a decentralized decision-making model and a centralized decision-making model of community group-buying supply chain and solve the optimal decision and optimal profit of the two models. The results show that under the decentralized decision-making model, wholesale price, retail price, platform SL, and leader PE are positively correlated with the PE elasticity coefficient and negatively correlated with the effort cost; under the centralized decision-making model, retail price, platform SL, and leader PE are positively correlated with the SL elasticity coefficient and negatively correlated with the cost of service. Sun and Zhang [11], on the other hand, through research on the preferences of the nanostore’s operation strategy, provide a new approach for the community group-buying industry in choosing the optimal strategy for downstream nanostore. The analysis shows that the preferred operating strategies of nanostores depend on comprehensive market parameters. Nanostores have more incentives to choose competitive strategies when suppliers’ production costs are relatively high.

This paper focuses on the setting of optimal group-buying thresholds for merchants in community group buying. However, the current literature on community group buying does not directly investigate this topic but mostly involves it indirectly from the perspectives of consumer group-buying willingness, group size, and other research perspectives. The research on consumers’ community group-buying willingness explores the effects of performance expectations, effort expectations, social influence, facilitation conditions, and perceived risk on consumers’ online community group-buying willingness. The results show that performance expectation, effort expectation, and social influence have a significant positive effect on consumers’ willingness to purchase in community group buys, while facilitating conditions and perceived risk do not have a significant positive effect on consumers’ willingness to purchase in community group buys (Zhang et al., 2023 [18]). Li et al. (2012) [19] point out that under community group buys, the group size has a significant effect on the cost of waiting. Consumers have different tolerances for waiting costs. By modeling a two-stage pricing game, Li et al.’s findings suggest that when a monopolistic retailer operates a hybrid channel, unless the transaction costs in the individual purchase channel are high enough, the retailer will charge a higher group fee in the group-buying channel to force most consumers to choose individual purchases. If two competing retailers use different pure channels, investment in group-buying promotion technology may erode the profitability of the retailer that employs community group buys when the savings on the actual cost of goods sold from community group buys are not significant.

2.2.2. Pricing Strategies

Although the community group-buying business is flourishing in China, exploring the optimal group-buying thresholds and pricing strategies continues to present a complex challenge. This study, to a certain extent, offers solutions to this intricate problem. In past studies, group-buying pricing research was mainly categorized into two main types: dynamic pricing (i.e., traditional group-buying pricing) and static pricing (i.e., fixed pricing strategy).

Under the dynamic pricing mechanism, merchants set discounted prices based on different quantity sizes and require a certain number of consumers to participate in the group buy in order to enjoy the discount. This mechanism encourages participants to recruit more consumers to join the group buy in order to obtain a lower discounted price. Related studies have analyzed the basis and advantages of group-buying pricing mechanisms, and they have shown that the traditional dynamic pricing mechanism outperforms the stand-alone retail pricing mechanism under conditions of demand uncertainty (Anand and Aron, 2003 [20]; Chen et al., 2004 [21]). Chen (2014) [22] studied the optimal coupon-pricing strategy when member companies in the supply chain system faced price uncertainty. The paper showed that member companies needed to dynamically adjust pricing strategies to maximize company value. In contrast, a static pricing mechanism has merchants set a fixed and lower discounted price that does not decrease as the number of group buyers increases. However, the number of participants in the group buy must reach a minimum number of group buys. A study by Zhang et al. (2016) [23] analyzed the network effect of group buys on optimal pricing. The network effect from group buys changed consumer demand, which further affected firms’ optimal prices and profits. Relevant studies have explored the optimal strategies of firms offering group-buying products under monopoly, oligopoly, and multifirm competition (Zhang et al., 2016 [23]; Liu and Zhang, 2016) [24]. Guan (2022) [25] et al. considered the information asymmetry between sellers and buyers, analyzed the impact of information sharing on optimal pricing strategies, and explored the optimal pricing strategy in different scenarios of pricing strategies. Another study proved that the power structure only affected the optimal pricing strategy and not the waiting time. Consumers still pay more attention to the amount spent rather than the price discount after mathematically considering the perception of saving money through group buying (Shi and Huang, 2023 [26]).

Overall, it can be seen that current research focuses on the impact of group-buying strategies on merchants’ decisions under given threshold conditions, and less on the impact of threshold setting on merchants’ decisions. Therefore, this study aims to explore the optimal group-buying threshold and optimal pricing strategy for community group buying to fill this research gap.

3. Model Assumptions and Construction

In order to explore the group-purchase thresholds and price-setting strategies of community group-purchase merchants, this paper constructs a single merchant model, which can independently choose whether to initiate a group purchase and set the corresponding thresholds and commodity prices.

3.1. Assumptions

Assume that the merchant offers both general sale products and group-buy products, the merchant’s price for general sale products is p, the group buy price is $p_g\le p$, the group-buy threshold is Q, and the level of promotion of the group buy is $\omega$. The cost of both the group buy and the regular sale product is c, and the fixed cost of offering the group buy is $K\left(w\right)$.

Assumption 1.

1. 

All consumer decisions are instantaneous and made simultaneously.

2. 

The consumers’ valuation of merchant products is V, subject to a $[0,M]$ uniform distribution.

3. 

The optimal group-buying threshold is equal to the actual group-buying sales.

If the consumer’s decision is not completed at the same time, the behavior of the previous consumer will affect the behavior of the next consumer. In real circumstances, the number of group members is transparent, and consumers can get the current number of group members at any time. As the number of group members increases, the success rate of group buying will continue to increase, and the effectiveness of participating in group buying will increase with the increase in the number of people. A lower group-buying threshold will increase the group formation probability and the number of group participants, which will further increase the group formation probability and form a superposition effect, resulting in the number of group participants reaching the group-buying threshold quickly. A high group-buying threshold will make the probability of forming a group insufficient at the beginning, and the number of participants will slowly increase, which may not reach the group-buying threshold in the end.

In order to reflect the real situation, the researchers’ model often divides the sales into multiple stages, and announces the number of participants at the end of each stage, simulating the change in consumer confidence in the real world by splitting the time period. For example, in Liang, X. (2014) [15], The Informational Aspect of the Group-Buying Mechanism, European Journal of Operational Research, sales are divided into two stages. When the number of participants is announced at the end of the first stage, the success rate of the participation of consumers in the second stage $\lambda =\lambda (g,Q)$ changes, which affects the decision.

Liang introduces $f_{\_}\left(D\right)(·)$ to simulate the random behavior of consumers in the first stage, but in the end, it does not affect the distribution of consumers’ participation in the optimal (ideal) situation. Therefore, on the premise of not affecting the result, in order to simplify the model and avoid unnecessary calculations, it is assumed that a consumers’ valuation of merchant products is V, subject to a $[0,M]$ uniform distribution.

In addition, according to Liang’s model and the Pareto optimality, when benefits are maximized, the actual number of group members and the group-purchase threshold should be consistent.

Definition 1.

At a given threshold, consumers believe that the success rate of group buying is $\lambda \left(Q\right)$, and the success rate of group buying decreases with the increase in the threshold, i.e., ${\lambda }^{\prime }\left(Q\right)<0$ (Liang, 2014) [15].

The consumer’s valuation of the merchant’s product is V, which obeys a uniform distribution of $[0,M]$.

When a consumer chooses to make an ordinary purchase, the utility obtained by the consumer is $U_i=V-p$, the necessary condition for the consumer to make an ordinary purchase of the merchant’s product is $U_i\le 0$, and the critical value of the consumer’s valuation of the product is $V^i=p$. When the consumer chooses a group purchase, the expected utility obtained by the consumer is $E\left(U_g\right)=\lambda (Q,w)(V-P_g)$, the necessary condition for the consumer to participate in the group purchase is $U_g\le 0$, and the critical value of the consumer’s valuation of the product is $V^g=p_g$.

When a merchant offers both general and group-purchase sales strategies, consumers can choose either a general purchase or group purchase. When $U_g\le U_i$ and $U_i\le 0$, consumers purchase the merchant’s products in general; when $U_g\ge U_i$ and $U_g\ge 0$, consumers participate in group purchasing; the critical value of the two choices of consumers’ general purchasing and group purchasing is $V^{gi}={\displaystyle \frac{p=\lambda (Q,w)p_g}{1-\lambda (Q,w)}}$, and at that time, there is no difference between consumers’ choices of general purchasing or group purchasing. Therefore, as shown in Figure 1, when $V_g\le V\le V^{gi}$, consumers choose a group purchase; when $V^{gi}\le V\le M$, consumers choose an ordinary purchase, and when $0\le V\le V^g$, consumers neither participate in a group purchase nor choose an ordinary purchase. It is worth noting that when the equilibrium point of group purchase and ordinary sales exceeds M, consumers will only choose group-purchase products, due to the existence of fixed costs for a group purchase; the profit obtained by the merchant at that time is reduced compared with ordinary sales, so the following analysis only needs to consider the situation where a group purchase and ordinary sales exist at the same time.

For the model of this paper, the consumer’s ordinary purchase demand and the group purchase demand are $D_i=max(1-{\displaystyle \frac{p-\lambda (Q,w)p_g}{M(1-\lambda (Q,w\left)\right)}},0)$. Based on this model, the following section discusses the optimal strategies of merchants in the exogenous and endogenous price scenarios, respectively.

3.2. Group Purchase Thresholds and Group Pricing

The merchant’s profit function when prices are exogenous is:

$$\begin{array}{cc}\hfill & \pi =\underset{Q,p_g}{max}((p-c)D_i+(p_g-c)D_g-K)\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.{\displaystyle \frac{p-p_g}{M(1-\lambda (Q,w\left)\right)}}\ge Q\hfill \end{array}$$

(1)

Lemma 1.

The optimal group-buying threshold is equal to the actual group-buying sales volume.

This paper proves that the optimal group-purchase threshold is equal to the actual group-purchase sales volume when considering the group-purchase threshold and the group-purchase pricing decision. This finding can be explained on a theoretical level. We first consider consumer behavior and the decision-making process. In group-buying activities, consumers’ decision to participate in group buying usually depends on their valuation of the product and the setting of the group-buying threshold. Consumers compare the price of the product with their own valuation of the product; if the valuation is higher than the price, they tend to participate in the group purchase; conversely, they may choose to make a regular purchase or not. When the group-buying threshold is set to the actual group-buying sales volume, it means that the merchant’s preset number of participants can satisfy the group-buying activity smoothly. In this case, consumers have specific expectations and expected utility for the group-purchase threshold corresponding to the actual group-purchase sales volume. If the group-buying threshold is lower than the actual group-buying sales volume, consumers believe that the probability of success of participating in the group buy is higher and are therefore more motivated to participate in the group buy. If the group-buying threshold is higher than the actual group-buying sales volume, consumers believe that the probability of success of participating in group buy is lower and may choose to make ordinary purchases or no purchase. In existing studies, Jing and Xie [27] and Zhang et al. [23] directly set the group-purchase threshold to the actual group-purchase sales volume.

In practical terms, this result is also consistent with the operation of actual community group purchases. In practice, merchants usually set group-purchase thresholds based on past sales data and market demand. They want to attract enough consumers to participate in the group purchase to achieve economies of scale. If the group-buying threshold is too high, it may result in insufficient participants to realize the economic benefits; while if the group-buying threshold is too low, it may result in lower profits for merchants. Therefore, setting the optimal group-buying threshold based on the actual group-buying sales volume can help merchants obtain the best business results in a competitive market.

In summary, the implication of Lemma 1 is that in the group-buying market, merchants should set optimal group-buying thresholds based on the actual group-buying sales volume in order to attract more consumers’ participation and obtain the best business results in the competition. This insight is an important guideline for participants and decision-makers in the group-buying market, helping them to develop more effective group-buying strategies and pricing strategies so as to enhance sales performance and market competitiveness.

Theorem 1.

There exists an optimal $Q^{*}\in ({\displaystyle \frac{p-c}{2M}},{\displaystyle \frac{p-c}{M}})$, when the merchant’s optimal group-buy pricing is $p_g^{*}=p-(1-\lambda (Q^{*},w))Q^{*}M$.

Theorem 1 can be explained by the demand and supply in the group-buying market. In the group-buying market, there exist differences in the valuation of products by different consumers, i.e., some consumers have a higher valuation of products while others have a lower valuation. Merchants need to consider these valuation differences as well as consumers’ behavioral preferences when setting group-buying thresholds and pricing. Theoretically, when the group-buying threshold is set low, low-valued consumers are more likely to participate in group buying because they believe that the probability of group-buying success is higher and are willing to take the risk of group-buying failure. On the other hand, high-valuation consumers are more sensitive to the risk of group-purchase failure and are more inclined to choose ordinary purchase methods instead of participating in group purchases. Therefore, merchants can attract more low-valued consumers to participate in group purchases within a certain group-purchase threshold range, thus increasing sales and profits.

This conclusion is also validated and applied from the behavior of actual community group-buying merchants. Merchants will conduct market research and data analysis when formulating group-buying strategies to understand the valuation and purchasing preferences of different consumer groups. Based on this information, they can set appropriate group-buying thresholds to attract the participation of their target consumer groups. At the same time, merchants also develop different group-buying pricing strategies based on valuation differences to maximize profits.

This rationale suggests that in the group-buying market, merchants should set appropriate group-buying thresholds and pricing by accurately grasping the differences in consumer valuations in order to attract more consumer participation and optimize profits. At the same time, merchants should also pay close attention to changes in market demand and consumer behavior and adjust their group-buying strategies in a timely manner in order to maintain their competitive advantage and market share. In addition, consumers can choose whether to participate in group purchases or make ordinary purchases through a rational analysis of group-purchase thresholds and pricing in order to obtain more favorable prices and satisfy their needs. This conclusion has some guiding significance and practical value for participants and decision-makers in the group-buying market.

Proposition 1. (a) For a merchant, the optimal group-buying threshold $Q^{*}$ increases with the ordinary selling price, increases with the degree of group-buying publicity, and decreases with the cost of group buying. (b) The optimal group purchase price $p_g^{*}$ increases as the cost of group buying increases.

(a)

From a theoretical perspective, some consumers may turn to group purchases when the regular sales price increases because the group-purchase price is relatively low. In order to reduce the utility of consumers’ participation in group purchases, merchants can raise the group-purchase threshold, i.e., require more consumers to trigger the group-purchase offer, thus slowing down the situation of consumers turning to group purchases due to high ordinary selling prices, and ultimately increasing the overall merchant’s profit. On the other hand, an increase in the level of publicity for group purchases increases the cost of publicity for the merchant. However, increased publicity also increases consumer awareness and interest in group buying, which increases their willingness to participate in group buying. In this case, merchants can increase their profits by increasing the group-buying threshold. By increasing the threshold, merchants can screen out consumers who are truly interested in participating in group purchases, which reduces the cost of the group-purchase offer and further increases the profit of merchants. In addition, the increase in group-buying costs has an impact on merchants’ profits. When the cost of group-buying increases, merchants may face greater cost pressure. In order to attract more consumers to purchase the product, merchants may reduce the group-purchase threshold, i.e., require fewer consumers to trigger the group-purchase offer, thereby increasing the attractiveness of the group purchase, increasing sales, and ultimately increasing the merchant’s profit.

In actual community group-buying operations, merchants usually set group-buying thresholds based on market conditions and cost considerations. When the ordinary sales price is high, merchants may raise the group-purchase threshold to reduce the utility of consumer participation in group purchases, thereby increasing the proportion of ordinary sales and improving profits. Meanwhile, as the degree of publicity of group-purchase activities increases, although it increases the publicity cost of merchants, it also increases the willingness of consumers to participate in group purchase, and merchants may control the number of consumers participating in group purchase by increasing the group-purchase threshold in order to increase profits. The increase in group-buying costs may affect merchants’ profits, so merchants can attract more consumers to participate in group buying by lowering the group-buying threshold in order to increase their profits.

The implication of Proposition 1(a) is that for merchants, several factors need to be considered in group-purchase pricing and threshold setting, such as the ordinary selling price, the degree of publicity, and the cost of group purchases. Adjusting the group-buying threshold can affect consumers’ purchasing decisions to a certain extent, which in turn has an impact on merchants’ profits. In actual operation, merchants should set group-purchase thresholds reasonably according to market demand and cost-effectiveness in order to maximize profits and market competitiveness.

(b)

The price of a group buy is an important consideration for consumers. When the group-buying threshold is increased, the probability of consumers’ participation in group-buying success decreases, so some consumers may be reluctant to participate in group buying. In order to attract more consumers to participate in group purchases and realize more profits, merchants need to adopt certain strategies. In the case of an increase in group purchase costs, merchants should lower the group purchase threshold so that more consumers can fulfill the conditions to participate in the group purchase. However, due to increased costs, merchants cannot increase profits by lowering the threshold. Instead, merchants can only gain more profit by increasing the price of the group buy.

In reality, the price and threshold setting for group purchases are usually decided by group-purchase merchants based on market conditions and cost considerations. When group-buying costs increase, merchants often adopt the strategy of lowering the group-buying threshold to attract more consumers to participate in group-buying activities. However, due to the increase in costs, merchants cannot increase their profits by lowering the threshold, so they can only increase their profits by increasing the group-buying price. By increasing the group-buying price, merchants can earn higher profit margins on group-buying sales, thus offsetting the negative impact of increased group-buying costs on profits.

Proposition 1(b) provides guidance for merchants’ group-buying pricing. For group-buying merchants, the impact of group-buying cost needs to be considered comprehensively in their group-buying pricing strategy. When the group-buying cost increases, merchants cannot increase their profits by lowering the threshold value but need to increase the group-buying price to gain more benefits.

Corollary 1.

If $Q\in ({\displaystyle \frac{p-c}{2M}},{\displaystyle \frac{p-c}{M}})$, the group-purchase success probability function is lower convex, when there exists a unique $Q^{*}\in ({\displaystyle \frac{p-c}{2M}},{\displaystyle \frac{p-c}{M}})$ such that $\pi \left(Q^{*}\right)$ is maximal.

If the probability of group-buying success $\lambda \left(Q\right)$ decreases at a decreasing rate as the group-buying threshold Q increases, then there is only a unique optimal threshold for the merchant. When the merchant does not offer group buying, the merchant makes a profit of $(p-c)(1-{\displaystyle \frac{P}{M}})$. The optimal profit for the merchant is $\pi =(p-c)(1-{\displaystyle \frac{p}{M}})+Q^{*}(p-c-Q^{*}M)(1-\lambda (Q^{*},w))-K=(p-c)(1-{\displaystyle \frac{p}{M}})+\phi \left(p\right)-K\left(w\right)$ when the merchant offers both regular sales and group buying, where $\phi (p,w)=Q^{*}(p-c-Q^{*}M)(1-\lambda (Q^{*},w))$. This inference can be explained by the impact of the group-buying threshold setting based on consumers’ decision-making behavior and the group-buying threshold. When the group-buying threshold is low, the probability of group-buying success is likely to be higher, so consumers are more motivated to participate in group buying. As the group-buying threshold increases, the probability of group-buying success decreases, but the rate of decrease gradually slows down. This implies that there exists a critical point, i.e., an optimal group-buying threshold, which optimally balances the decrease in the probability of group-buying success with the merchant’s profit. At this unique optimal threshold, merchants can maximize their profits.

In actual community group purchases, group-purchasing merchants usually adjust the group-purchase threshold according to the changes in the group-purchase success probability. When the group-buying threshold is low, the probability of group-buying success may be high, but the number of participants in the group buy may not be sufficient to realize the optimal economic benefits. As the group-buying threshold increases, the group-buying success probability gradually decreases, but the magnitude of the decrease gradually slows down. In this process, the group-buying merchant needs to find an equilibrium point, i.e., the unique optimal group-buying threshold, which optimally balances the decrease in group-buying success probability with the merchant’s profit. By adjusting the group-buying threshold, merchants can maximize their profits.

Therefore, group-buying merchants should consider the trend of group-buying success probability in the setting of group-buying thresholds in order to maximize profits.

3.3. Merchants’ Strategies for Providing Group-Buying Services

Proposition 2.

In the exogenous price case, $K\left(w\right)>\phi (p,c,w)$ when merchants do not offer group purchases and conversely if they do.

The provision of group-buying services requires merchants to bear certain fixed costs, such as group-buying promotion costs and group-buying campaign management costs. In the case of price exogeneity, if these fixed costs exceed the profit that the group-buying service can bring, the merchant will not be able to make a profit and therefore will not be willing to provide group-buying services. On the contrary, if the fixed costs can be compensated or even exceeded by the profits generated by the group-buying service, the merchant will be willing to provide the group-buying service in order to gain more profits.

In practice, merchants usually consider the fixed costs and expected profits of group-buying services when deciding whether or not to offer group-buying services. If the fixed costs exceed the expected profits, the merchant may choose not to offer the group-buying service to avoid financial losses. On the contrary, if the fixed costs can be compensated or even exceeded by the profits generated by the group-buying service, the merchant will be inclined to offer the group-buying service in order to gain more profits.

The takeaway from Proposition 2 is that merchants in a community need to make a comprehensive assessment of fixed costs and expected profits when considering offering group-buying services. If the fixed costs can be covered or exceeded by the profits generated by the group-buying service, offering the group-buying service will be a profitable option.

3.4. Group-Purchase Thresholds and Common Pricing

When prices are endogenous, the merchant’s profit function is:

$$\begin{array}{cc}\hfill & \pi =\underset{Q,p_g,p}{max}((p-c)D_i+(p_g-c)D_g-K)\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.{\displaystyle \frac{p-p_g}{M(1-\lambda (Q,w\left)\right)}}\ge Q\hfill \end{array}$$

(2)

Proposition 3.

The optimal ordinary sale price increases with the group-purchase threshold, and the optimal ordinary sale price is higher than the optimal price under the merchant’s ordinary-only sale.

Proposition 3 states that when prices are endogenous, the introduction of a group-buying sales strategy affects the optimal ordinary sales price. Specifically, as the group-buying threshold increases, the optimal ordinary sales price increases, and the optimal ordinary sales price is higher than the optimal price when only ordinary sales are offered. Consumers’ choice behavior between group purchases and ordinary purchases can explain this proposition. The introduction of a group sales strategy will attract consumers with a low valuation to choose to participate in group sales, while the number of consumers making ordinary purchases may decrease. Consumers with a low valuation are more inclined to choose a group purchase since group purchase sales can offer lower prices. In order to maximize profits, merchants need to adjust the price of regular sales to balance the demand between group-buying sales and regular sales. When the group-purchase threshold increases, consumers with low valuations are more likely to choose group purchases, so the merchant can increase the ordinary sale price, thereby increasing profits from ordinary purchases.

For merchants in real-world communities, they adjust their general sale prices to accommodate group-buying sales. For neighborhoods with a high demand for group purchases, merchants typically set higher group-purchase thresholds and raise their regular sales prices accordingly.

The implication of Proposition 3 is that merchants need to consider the impact of group sales when formulating their pricing strategy. Introducing a group-buy sales strategy can affect the optimal ordinary sales price, especially if the price is endogenous. Merchants can maximize their profits between group and ordinary sales by adjusting ordinary sales prices to accommodate group sales.

4. Numerical Analysis

In order to verify the validity of the above model and further explore the influencing factors of the merchant’s profit, this section validates the relationship between the optimal group purchase threshold and the ordinary selling price and group-purchase cost and performs an analysis around the merchant’s profit. See Appendix A for more details.

4.1. Group-Purchasing Threshold Analysis

Let $\lambda \left(Q\right)=\sqrt{1-Q}$, $Q\in (0,1)$, $M=10$, $c=3$, and $p\in [3,10]$; the relationship between the optimal group-buying threshold and the ordinary selling price is shown in Figure 2a. Let $\lambda \left(Q\right)=w\sqrt{1-Q}$, $Q\in (0,1)$, $M=10$, $p=6$, and $c\in [0,6]$; the relationship between the optimal group-buying threshold and the cost is shown in Figure 2b. Figure 2a shows that the optimal group-buying threshold increases with the increase in the ordinary selling price; Figure 2b shows that the optimal group-buying threshold decreases with the increase in the group-buying cost. The conclusion of Proposition 1 is tested.

4.2. Profit Analysis

Let $\lambda \left(Q\right)=\sqrt{1-Q}$, $Q\in (0,1)$, $M=10$, $c=3$, and $p=6$; the relationship between the retailer’s profit and group-buying threshold is shown in Figure 3a. From the figure, it can be seen that the optimal group-buying threshold has an optimal value in the region of $[0.15,0.3]$. The conclusion of Corollary 1 is verified.

Let $\lambda \left(Q\right)=\sqrt{1-Q}$, $Q\in (0,1)$, $M=20$, $p=6$, and $c\in [0,6]$; Figure 3b shows the relationship between the retailer’s profit and the fixed cost of group purchasing. It can be seen that the retailer’s profit changes from positive to negative as the cost of group buying gradually increases. That is, when the fixed cost of group purchases is high, the seller will choose not to offer group purchases; conversely, when the fixed cost of group purchases is low, the seller offers group purchases. Proposition 2 is proved.

Let $\lambda \left(Q\right)=\sqrt{1-Q}$, $Q\in (0,1)$, $M=20$, $c=2$, and $p\in [3,20]$; as shown in Figure 4, the merchant’s profit tends to increase and then decrease as the ordinary price increases. For the merchant, there exists an optimal ordinary selling price that enables the merchant to maximize their profit.

According to the displayed results in Figure 5, it can be seen that the merchants’ optimal profit shows a decreasing trend, which gradually decreases as the degree of group-buying publicity increases. Specifically, when merchants increase the degree of group-buying publicity, the optimal group-buying threshold increases while the optimal group-buying price decreases, which results in merchants losing a portion of the ordinary purchase demand. Therefore, merchants should not overemphasize publicity while providing both general and group-purchase sales channels.

5. Discussion

This research, focusing on the optimal group-buying threshold and pricing strategy in community group buying, has unveiled several critical insights with implications for both theory and practice. The integration of practical recommendations, anticipation of future research directions, acknowledgment of challenges and uncertainties in the market, and an honest appraisal of the study’s limitations collectively contribute to a more nuanced understanding of this complex field.

The empirical findings of this study offer significant practical recommendations for merchants. It becomes evident that the determination of an optimal group-buying threshold is not merely a function of economic calculus but also a strategic maneuver in consumer engagement and market positioning. Merchants are advised to consider not only the immediate financial implications of their pricing strategies but also the long-term effects on customer loyalty and brand perception. The nuanced relationship between group-buying thresholds, ordinary selling prices, and market dynamics, as revealed in this study, offers a valuable framework for merchants in making more informed, strategic decisions in their pricing policies.

However, the study does not exist without its limitations, which in turn, pave the way for future research. One of the primary limitations lies in its theoretical orientation and the assumptions underpinning the proposed models. While efforts were made to ground the study in realistic market scenarios, the inherent unpredictability of consumer behavior and market fluctuations could lead to deviations in real-world applications. Therefore, future research should aim to incorporate more empirical data, possibly through longitudinal studies or case analyses, to validate and refine the proposed models. Additionally, exploring the impact of digital transformation and e-commerce trends on group-purchasing behavior could offer fresh perspectives and insights into this rapidly evolving field.

Another area demanding attention is the specific challenges and uncertainties faced by merchants in the community group-buying market. As highlighted in the research, these challenges are multifaceted, ranging from maintaining optimal inventory levels to navigating the complexities of consumer psychology. The uncertain nature of group-buying dynamics, influenced by factors such as social trends and economic shifts, adds another layer of complexity. The study contributes to this discourse by offering a theoretical base from which merchants can begin to unravel these complexities, but it is clear that there is much ground to be covered in understanding and effectively managing these challenges.

In conclusion, while this study has made strides in understanding the optimal group-buying threshold and pricing strategy in community group buying, it also opens several avenues for further research. The findings serve as a starting point for merchants to refine their strategies, but they also highlight the need for continuous adaptation and research in this field. As the market evolves, so too must the strategies and understandings of those who operate within it. This study, with its contributions and limitations, is a step towards a deeper, more comprehensive understanding of the intricacies of community group buying.

6. Conclusions

This study offered an in-depth examination of the mechanisms driving group-purchase decisions and the strategic implications for pricing in community group buying. We demonstrated that by manipulating group-purchase thresholds, merchants can significantly influence consumer behavior, thereby optimizing sales and profits. Our analysis revealed a critical threshold range within which the balance between group and individual sales was optimized, leading to maximum profitability. This balance was subject to various factors, including but not limited to, changes in consumer preferences, market competition, and economic conditions.

Furthermore, the research delved into the psychological underpinnings of consumer decisions in group-buying contexts. It elucidated how group dynamics and individual decision-making processes converged to shape purchasing behavior. This understanding is pivotal for merchants seeking to design effective marketing strategies that appeal to both individual and group buyers.

The study also underscored the importance of flexibility and adaptability in pricing strategies. In the rapidly changing landscape of e-commerce and group buying, static pricing models are less effective. Adaptive pricing strategies that respond to real-time market data and consumer behavior trends can provide merchants with a competitive edge.

Our findings have significant implications for the future of community group buying, particularly in the context of the burgeoning e-commerce industry. They offer a theoretical foundation upon which future empirical studies can build, especially in exploring the application of these strategies across different cultural and economic landscapes.

In conclusion, this research provides a novel framework for understanding and optimizing group purchase thresholds and pricing strategies in community group buying. It contributes to both academic literature and practical applications, offering valuable insights for merchants looking to navigate the complexities of modern e-commerce markets.