Impact of Consumer Strategic Behavior on the Supplier Channel Selection in a Retailing Platform

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Introduction
Te world's e-commerce market keeps on expanding. Statista [1] assesses the worldwide retail e-commerce sales in 2022 surpassed 5.7 trillion dollars and will continue to grow. To capture a larger market share, e-commerce platforms constantly innovate and incorporate the agency selling service in an efort, like Platform Open Plan of JD.com. Suppliers can therefore ofer products directly to consumers by paying commissions to platforms (agency selling channel), selling products to platforms (reselling channel), as well as combining both of the two channels (hybrid channel). Taking the fast fashion brands on JD.com as examples, MLB adopts the pure reselling channel strategy, GAP chooses the pure agency selling channel, and MUJI chooses the hybrid channel strategy.
One of the key challenges for businesses to increase their proftability is deciding which of the three channel strategies to use, as each channel strategy has its characteristics that must be taken into consideration. Existing literature [2,3] discusses the three channel strategies deeply. It is demonstrated that the traditional reselling channel results in a double marginalization efect, as each company seeks to maximize its own profts. In the pure agency selling channel, suppliers may face challenges in ensuring market coverage and gathering information, which are functions that retailers typically excel at. Te hybrid channel can ofer greater market penetration, as it combines the strengths of both reselling and agency selling channel. However, it can also lead to issues such as price undercutting, channel confict, and reduced trust between suppliers and platforms. Terefore, suppliers are faced with choosing among diferent channel strategies to get the optimal profts. Tere has been a lot of literature on channel selection and whether new channels should be introduced. Tsay and Agrawal [3], and Shi et al. [4] consider the trade-ofs between the advantages of increased sales and the disadvantages of channel cannibalism. Moreover, recent studies have extensively discussed channel strategies with diferent emphasis, such as diferentiated goods [5], information sharing [6], and operating cost [7].
Meanwhile, online retailing has witnessed the prevalence of strategic consumers. Consumers may openly access previous pricing information through platforms, which encourages waiting for promotions before making a purchase. Tis behavior can create fuctuations in demand and lead to losses for retailers, which are proved in early research Besanko and Winston [8]. Nowadays, a growing number of studies [9,10] investigate how to resist the efect of strategic consumers. Recent studies have begun to examine the efect of strategic consumers in various scenarios, such as sharing economy [11], product returns [12], and channel selection [13]. To the best of our knowledge, the impact of strategic consumers on channel selection in the background of multiperiods in a retailing platform is not fully understood by existing research. On the one hand, strategic consumers intensify the channel competition, which may harm the supplier's proft, but on the other hand, it may mitigate the double marginalization efect at the same time, which may make the supplier better of. Tus, understanding the strategic consumer behaviors is essential for suppliers to make informed channel selection.
Motivated by the above discussions, this paper examines the optimal channel selection in the presence of consumer strategic behavior, weighing the added benefts in agency selling channel and channel competition between agency selling and reselling channel. In specifc, the study of this paper addresses the following questions: What are the equilibrium solutions of the supply chain members in reselling, agency selling and hybrid channel strategies? Which channel strategy would be optimal for suppliers? What efects do strategic behaviors have on the optimal channel strategy? In order to better understand how strategic consumers impact channel selection, we model supplier and retail platform interactions as a fve-stage Stackelberg game. We examine the equilibrium prices and corresponding profts under each channel. Specifcally, the supplier as the frstmover decides the channel strategy and sets the initial wholesale or retail prices, and the platform follows to establish the retail price. Ten, they successively establish the fnal prices in the second selling period. On this basis, we further investigate how changes in strategic consumer patience level afect pricing, proft, and channel selection.
Our major fndings are summarized as follows. Firstly, we explain the role of strategic consumer behaviors in optimal prices by solving and analyzing the equilibrium solutions. When the patience level of strategic consumers is limited, suppliers and platforms induce consumers to purchase by reducing prices in the frst period and increasing them in the second period. Moreover, in response to consumers with high patience level, pure-channel merchants sell more products at lower margins, while hybrid-channel merchants react by raising prices in order to attract high-value consumers due to the coexistence of competition and collaboration. In addition, in line with Cachon and Swinney [10], we discover that intertemporal price diference reduces so that intertemporal competition rises as customers' strategic level grows under normal conditions. Te presence of channel competition also results in a special case where intertemporal competition initially rises and then falls within a given parameter range in Strategy H, demonstrating that channel competition diminishes the impact of strategic consumers.
Second, this study examines the optimal strategy for suppliers and the role of strategic consumers in selection. For suppliers, the hybrid channel always dominates the pure agency selling channel. Additionally, the optimal channel strategy is a threshold strategy of the commission rate, below which is the hybrid channel and otherwise the reselling channel. Te results are consistent with Xie et al. [14]. Furthermore, we incorporate strategic consumers to investigate the selection threshold. With varied levels of patience, we discover that the threshold strategy is nonmonotonic. Tis provides a supplement to the literature on channel selection by studying strategic behaviors.
Tird, we analyze how the supplier's optimal strategy interacts with optimal strategies of platforms and consumers. Te selection of the hybrid channel strategy can beneft both suppliers and platforms when the commission rate is reasonable. Additionally, when moderate commission rate and low strategic level are satisfed, consumers in the hybrid channel obtain the optimal surplus. Earlier literature [15,16], points out that adding suppliers' direct selling channels reduces retailers' profts. In contrast, we come to the conclusion that hybrid channel is benefcial to both sides, since we take into account the competition and cooperation game in the background of retailing platform. It also shows that the hybrid channel can regulate supply chain participants' profts to resolve their conficts and create a win-win-win scenario.
Te rest of this paper is structured as follows. We provide a brief review of the pertinent literature in Section 2. Section 3 has a description of our model. Section 4 analyzes the equilibrium results for three channel strategies. Te optimal supplier strategy is presented in Section 5. Te efects of strategic consumers on channel selection are revealed in Section 6. Additionally, Section 7 further discusses the role of optimal strategy on the platform and consumers. Te paper is wrapped up in Section 8 with a summary.

Literature Review
Our paper is related to three streams of literature, including channel selection and competition, consumer strategic behavior, and retailing platform.
Te frst stream concentrates on the selection and competition generated by multiple channel formats. Multichannel manufacturers not only sell to consumers through the conventional reselling channel but also engage directly in the downstream market. Early research [15,16] discussed whether suppliers should add direct selling channels, pointing out that such channels can decrease retailer profts and supply chain efciency. Nonetheless, subsequent literature [2,3,17,18] analyzes channel confict impacted by consumer preference, supply chain control right, and ofers insights into strategies to address it, such as dynamic pricing strategies and commission payments. Tese articles establish a theoretical foundation of coordinating dual channels, and thus, recent studies further consider detailed factors and scenarios that impact channel selection. Some research focuses on factors related to supply chain members, such as decision-making power [19,20], information sharing [6,21], and the operating objectives [22,23] Other research focuses emerging business scenarios, such as diferentiated goods Tan and Carrillo [5]; Tao et al. [24]; 2 Complexity blockchain [25], omni-channel retailing [23], and live streaming [26], where new attributes afect supply chain structure and decisions. Te authors of [7] investigate the channel selection among reselling, agency selling, and hybrid selling formats based on channel preference and operating cost. In contrast, this paper takes into account strategic consumers behaviors, which is prevalent in retailing platforms but has not received much attention in channel selection research. Strategic consumer behavior is manifested in the expectation of future price reduction and the delay of consumption willingness, thus afecting merchant proftability and pricing. Hence, this paper explores the optimal channel selection based on strategic consumer behaviors and channel preference.
Another crucial stream is the study of strategic consumers. Tis research can be traced back to Coase [27] who demonstrated that customers who strategically delay their purchases can force a monopolist to set prices at marginal cost. In addition, Besanko and Winston [8] pointed out that such behavior can result in signifcant losses for retailers. In follow-up research, pricing strategies were studied to resist strategic consumer behavior, including intertemporal pricing [28], pricing commitment [9], and quick response [10]. Besides, information asymmetry and disclosure are considered [29,30]. Lin et al. [31] found that manufacturers and retailers earn higher profts in the presence of strategic consumers in the view of holistic supply chain. In terms of recent pricing research considering strategic consumers, it has begun to capture the characteristics of supply chains under complex consumption scenarios, for instance, segmented market such as sharing economy [11] and low-carbon products [32], two-echelon newsvendor [33], purchase behaviors including repeat purchasing [34], defective product returns [12], and so forth. Tere are related articles exploring strategic consumers' impact in channel selection. Yu et al. [13] focus on how strategic consumers impact ofine and online reselling and agency selling formats; Huang et al. [35] introduce store brand and explore its competition with suppliers. In contrast, this article explores the interaction of strategic consumer and channel selection among reselling, agency selling, and hybrid selling in the retailing platform while taking into account competitive cooperative relationship in the hybrid channel.
Lastly, the retailing platform is the foundation for our research. Te interplay between retailing platform and consumers gives transformative impact on the retailing environment. Te emerging research issues of retailing platforms include pricing strategies, consumer behavior, channel integration, and strategies. Pricing strategies involve pricing policy such as online coupon [36,37], bundling pricing [38], contract design [39,40], and pricing policies in emerging new retailing, such as omni-channel Huang and Guo [41]; shipfrom-store [42]. Additionally, consumer behaviors are afected by purchase intentions [43], customer satisfaction [44,45], and perceived value [38,46]. More importantly, channel strategies, as the focus of this paper, involve channel introduction [47][48][49][50] and channel competition and selection [35,51,52]. Shi et al. [50] explore the interaction between the selection of agency selling or reselling formats and downstream retailers for suppliers, with introduction of third-party retailers as the emphasis. Tis paper examines the selling formats on platform by considering competition and cooperation between platforms and suppliers as well as the impact of strategic consumer behaviors in platforms. We add contribution to channel selection research by applying a two-period game-theoretic model to examine the pricing decisions of supply chain members under diferent channel strategies in the presence of strategic consumers.

Model
We consider a supply chain which contains a supplier and a retail platform, facing strategic consumers. Te supplier is motivated to select three channel strategies, which are reselling channel strategy (R), agency selling channel strategy (A), or hybrid channel strategy (H). Every channel strategy has its traits. In the reselling channel, retailing platforms can exert their advantages to improve consumer satisfaction and willingness to pay; the agency selling channel enables suppliers to sell directly to consumers, cutting out middlemen, and increasing their profts; the hybrid channel strategy can incorporate the benefts of the two channels, while pit platforms and suppliers in competition with each other, cannibalizing sales and profts. Tus, suppliers can choose suitable channel strategy in line with their operation and sales to improve profts. For example, MUJI, a fast fashion brand, sells products on JD.com through both self-owned stores and fagship stores. In the self-owned store, MUJI sells its products to JD.com for reselling; in contrast, MUJI sells directly to consumers in the fagship store, while JD.com provides the platform as an agent. Te channel structures are depicted in Figure 1.
In the reselling channel strategy, the supplier sets the wholesale price, while the retail platform orders the product and decides the selling price to the consumers. In the agency selling channel strategy, the supplier sets the selling price and delivers its product directly to consumers via the platform, while the platform charges a commission rate ϕ for each unit of sales. We assume 0 < ϕ < 0.5, which is consistent with Geng et al. [53] and Xie et al. [14]. In practice, JD.com sets commission rate at 3%-20% for most product kinds, and Amazon sets the rate up to 45% for equipment accessories category. In the hybrid channel strategy, the supplier could use both the reselling and agency selling channel to deliver its product. In practice, self-run stores of platform tend to bring a better user experience due to thorough storage, logistics, and after-sales quality. Tus, this model introduces β to describe the acceptance level of agency selling channel, where β in [0, 1].
Strategic consumers take into account the future opportunities and making their purchasing decisions within two selling period based on expected utility, where i � 1, 2 { } denotes the selling period. Assume that consumers' valuation v follows the uniform distribution of [0, 1], which is consistent with existing literature [2,54]. In practice, purchasing products immediately help consumers enjoy the maximum value. While as time goes on, the perceived value of a product decreases, which afects the consumer's willingness to pay for it. Tus, we use α(0 < α < 1) to measure this decline in value, which also refects the patience level of strategic consumers. As Liu et al. [55] analyzed, a higher value of α implies that the consumer is more patient and is willing to wait longer for the product. In Complexity contrast, when α � 0, consumers' perceived value of the product αv can decrease to zero over time. As a result, they may be willing to pay a higher price for the product than if they had waited for its price to decrease. Besides, we assume β > α, which means the consumers have limited strategic behaviors; otherwise, all consumers are waiting to purchase in the second period. And it is consistent with Liu and Zhang [56]. Specifcally, in the frst period, consumers choose whether or not to purchase and choose the channel from reselling or agency selling channels. When purchasing from the reselling channel in the frst period, the consumer's utility is u R 1 � v − p r1 ; in the agency selling channel, consumer's utility is u A 1 � βv − p a1 . If consumers are patient enough to wait and buy in the second period, consumers' utilities in the reselling channel are u R 2 � αv − p r2 , while utilities in agency selling channel are u A 2 � αβv − p a2 . Taking Strategy H as example, when u R is calculated as the indiferent valuation of consumers buying between reselling and agency selling channel in period 1.
and v 4 � (p a2 /αβ). Te purchasing demand in Strategy H in each period and channel can be depicted in Figure 2. Note that Strategy R and A are special cases of Strategy H. Te strategy R only has the demands in the frst and second periods of the reselling channel, namely, r 1 and r 2 as shown in the fgure while the strategy A only shows a 1 and a 2 . Te detailed notation of decision variables, model parameters, and other symbols is shown in Table 1.
We model a fve-stage Stackelberg game to illustrate the interactions of the supplier and the retailing platform. Figure 3 shows the sequence of events. In stage 1, the supplier decides the channel strategy from reselling, agency selling, and hybrid channels, given exogenous commission rate ϕ. In stage 2, when selecting hybrid channel, the supplier decides the wholesale price w 1 in the reselling channel strategy and the retail price p a1 in the agency selling. In stage 3, the platform decides the retail price p r1 for reselling. In stage 4, the supplier sets the wholesale price w 2 and retail price p a2 . In stage 5, the platform sets the retail price p r2 .
Te proft of both supplier and retail platform contains four parts. For suppliers, the proft comes from the wholesale proft and direct selling proft through platform in the frst and second periods. For platforms, the proft comes from sales commission of supplier and sales proft in the frst and second periods. Combining the demand mentioned above, the proft of supplier and platform are written as follows. Supplier's proft in the hybrid channel: Platform's proft in the hybrid channel:

Complexity
Similar to hybrid channel strategy, the proft functions in the reselling and agency selling channel are stated as follows. In the reselling channel, the proft of supplier is

Equilibrium Analysis
In this section, we characterize and analyze the equilibrium outcomes of reselling, agency selling, and hybrid channel strategies.

Reselling Channel Strategy.
For suppliers, the proft comes from the wholesale proft; for platforms, the proft comes from sales profts. Combining the demand mentioned above, the proft of supplier and platform is written as follows. For the supplier, the objective function and constraints can be expressed as follows: Te proft of the platform is as follows: We frstly prove that the objective function is convex, then use the KKT condition to write the optimization problem with inequality constraints into an unconstrained optimization problem, and use backward induction to characterize the equilibrium prices. Please refer to the Appendix, which contains all proofs of the paper.
Te equilibrium outcomes of the pure reselling channel strategy are stated in Teorem 1. Theorem 1. Te equilibrium outcomes in the reselling channel strategy are as follows: Teorem 1 shows that the optimal prices and profts of both the supplier and the platform only depend on the patience level of strategic consumers. Furthermore, we investigate how prices change as the patience level of strategic consumers changes.

Lemma 2.
Optimal prices in the reselling channel strategy fuctuate with the patience level of consumers are in ways as follows: Lemma 2 describes the impact of strategic consumers on pricing, which is also depicted in Figure 4. We fnd that the responses of the supplier and platform to strategic behaviors are moderated by the patience level. In specifc, wholesale price and retail price in the frst period are monotonous, and 6 Complexity they decrease with the increment of the patience level; while wholesale price and retail price in the second period are nonmonotonic, they frst increase and then decrease as patience level grows. It can be explained as follows. When patience level is limited, reducing the price diferences between the two periods can mitigate strategic consumer efect. When patience level is large, merchants comply with consumers instead and lower the prices in the second period.
Tey have to move their focus to the second period to achieve optimal result that is small profts but quick return. Moreover, intertemporal competition increases as patience level increases, which refer to the gap between prices in the frst period and the second period decreases continuously, consistent with Cachon and Swinney [10]. It can be explained by reducing the price gap between two periods lessens the strategic consumer efect, efectively inducing more consumers to purchase in the frst period to obtain higher proft.

Agency Selling Channel
Strategy. Moreover, we examine the equilibrium outcomes of the agency selling channel strategy. For the supplier, the objective function and constraints can be expressed as follows: Te proft of the platform is as follows. And it shares the same constraints as the supplier.
Trough backward induction as above, we obtain the following theorem. Theorem 3. Te equilibrium outcomes in the agency selling channel strategy are as follows: Teorem 3 shows that the optimal prices and profts of both the supplier and the platform only depend on acceptance of agency selling channel by consumers and patience level of consumers. Terefore, we analyze how two factors afect the prices.

Lemma 4.
Optimal prices in the agency selling channel strategy fuctuate with the patience level of consumers, and acceptance of agency selling channel is in ways as follows: As lemma proved, strategic consumer behavior reinforces intertemporal competition. Specifcally, the price diference between the frst and second periods decreases with the Complexity 7 increment of patience level. In addition, the impact of patience level on optimal pricing is depicted in Figure 5. Let the point of indiference between the frst and second periods be θ 2 , and θ 2 � (p a1 − p r2 )/(β − α). For the supplier, the objective function and constraints can be expressed as follows:   8 Complexity max π s w 1 , w 2 , p a1 , p a2 � max w 1 Te proft of the platform is as follows.
max π p p r1 , p r2 � max p r1 − w 1 In the hybrid channel strategy, we decide p a , w simultaneously, so we examine convexity of the objective function through Hessian matrix frstly. Ten, the constrained optimization problem is written as Lagrange function by KKT condition. Finally, through backward induction, we obtain the following theorem.

Complexity 9
Theorem 5. Te equilibrium outcomes in the hybrid channel strategy are as follows: Teorem 5 shows that the optimal prices and profts of both the supplier and the platform depend on patience level of consumers and acceptance of agency selling channel by consumers. We then analyze how prices change as patience level and acceptance of agency selling channel change.

Lemma 6.
Optimal prices in the hybrid channel strategy fuctuate with the patience level of consumers, and acceptance of agency selling channel is in ways as follows: Various distinct outcomes have been obtained due to the coopetition in the hybrid channel. Te optimal prices decrease and then increase in the frst period, while keep increasing in the second period as consumers become more strategic. Te underlying reason for the distinctions in pricing strategies between hybrid and pure channels is the competitive-cooperative relationship between suppliers and platforms in the hybrid channel. Particularly, when patience level continues to climb, the optimal reaction of price reductions in the pure channels is unable to deliver small profts and big returns due to channel competition in Strategy H. Instead, platforms and suppliers cooperate to raise prices throughout each phase to capture value from high-value consumers.
Moreover, consistent with pure channel strategies, strategic consumer behaviors strengthen intertemporal competition in the hybrid channel strategy under general conditions. Interestingly, we also discover that channel competition mitigates intertemporal competition to some extent, which refers to channel competition predominates while intertemporal competition efect declines as the strategic level grows. We can intuitively observe the phenomenon in the special case in Ω 3 , (small β, large ϕ and α), where channel competition and platform commission consume the majority of earnings in agency selling, and thus, the intertemporal competition efect brought by strategic consumers is diminished. Figure 6 displays optimal pricing in hybrid channel strategy under typical conditions.

Optimal Distribution Channel Strategy
In this section, we compare equilibrium profts of the supplier among reselling, agency selling, and the hybrid channel strategies to investigate the optimal channel selection.
Comparing optimal profts of the supplier in the agency selling strategy and hybrid channel strategy, we obtain the following result and proposition: Proposition . Te hybrid channel strategy always dominates the agency selling channel strategy for the supplier.
According to Proposition 7, the supplier will always be more lucrative using the hybrid channel strategy than the agency selling channel strategy regardless of the channel competition level and commission rate. Te result is consistent with existing literature, such as Xie et al. [14]. It can be explained that the extra proft from the reselling channel in the hybrid channel strategy dominates proft loss brought by the competition in the hybrid channel strategy. In practice, suppliers seldom utilize JD.com as a pure agency selling channel. It gives practical insights for GAP, who implements pure agency selling strategy in JD.com instead. In the face of declining sales share, GAP should adjust its online channel according to its own strength and competitive advantage. Based on our proposition, GAP is supposed to decide whether to introduce reselling channel or terminate the agency selling channels by comprehensively weighing the cost, manpower, and other factors.
Comparing optimal profts of the supplier in the hybrid channel and reselling channel strategies, there exists ϕ 0 satisfying Terefore, we get Proposition 8.

Proposition 8.
Te optimal channel strategy for the supplier is a threshold strategy of commission rate, below which is the hybrid channel strategy and the reselling channel strategy otherwise.
Proposition 8 shows that when the commission rate is low, the hybrid channel is optimal, while when the commission is high, pure reselling channel is more proftable.
When the commission rate is low, the extra proft from the agency selling channel in the hybrid channel strategy dominates proft loss brought by the competition in the hybrid channel strategy for the supplier. When the commission rate is high, the extra proft that the supplier obtains from the agency selling channel becomes small and is dominated by proft loss in channel competition.

The Strategic Role of Consumer Behavior
In this section, we analyze the strategic role of consumer behaviors.

Proposition 9. Te impact of consumer strategic behaviors on the threshold of optimal channel strategy is nonmonotonic.
Proposition 9 shows that the threshold commission rate of the optimal channel strategy changes with the change of patience. Figure 7 depicts how threshold commission rate changes with patience level. In specifc, the threshold commission rate to select pure reselling channel strategy decreases frst and then increases with the increment of patience level.
In order to explain the underlying reasons, we analyze the impact of strategic consumers on profts. Proft in the Strategy H predominates over that in the Strategy R when the strategic consumer is not taken into account due to the additional proft in the added agency selling channel. Considering strategic behaviors, there are two main efects on profts as Figure 8 shows. Strategic consumer behaviors enhance channel competition, which lowers proftability in Strategy H, and at the same time, they mitigate the double marginalization efect, which would beneft suppliers in reselling channel. As a result, when the strategic level is modest, proft in Strategy H declines, and that in Strategy R increases, which lowers the range of phi to select Strategy H. As the patience level continues to rise, earnings in the Strategy H rise, whereas profts in the Strategy R decline, due to the diferent pricing policies stated in the aforementioned sections playing major roles. Tus, the threshold ϕ for selecting the Strategy H rises.
Interestingly, Strategy H becomes the optimal approach and is unafected by the commission rate when consumers are sufciently strategic. It also gives a partial explanation of the practice. For example, the mentioned fast-fashion brands, MLB and MUJI, they have similar commission rates because of the same product category but diferent channel selections. It is explained that consumers have diferent patience levels with brands. Due to the branding efect, consumers are willing to wait patiently for a particular brand until the price drops to the expected level in the second period and are less loyal to other brands in contrast. Terefore, MUJI is willing to choose hybrid channel because its target consumers have higher loyalty towards it. For MLB, it appeals to fashion-conscious young people, who tend to prefer variety and thus have more substitute brands.

Discussion
In this section, we further consider platform profts and consumer surplus under the optimal channel selection strategy of the supplier.

Optimal Channel Strategy of the Supplier and the Platform.
Firstly, we analyze the equilibrium strategies of supplier and retailing platform as depicted in Figure 9, where "Win-Win," "Win-Lose," "Lose-Lose" are equilibrium results for both parties. Te former refers to the supplier, while the latter refers to the platform. For example, "Win-Lose" represents the supplier owns the optimal profts but the platform not.
For platform, it earns in direct proportion to consumer demands and takes an extra commission from the supplier. As a result, the optimal channel strategy for the platform is opposite to the supplier. In specifc, the optimal strategy for platform is a commission rate threshold strategy, and below the threshold, the reselling channel is selected; otherwise, the hybrid channel is selected. Moreover, the threshold commission rate to select pure reselling channel strategy increases frst and then decreases, which is caused by strategic consumer' efect to channel competition and double marginalization efect as discussed previously.
Combining the optimal channel strategy of the supplier, the supplier and platform can achieve equilibrium results through the hybrid channel strategy under the moderate commission rate level. Meanwhile, the range of commission rates to achieve win-win situations frst drops and then increases as consumer patience levels rise. It demonstrates the proft confict between the supplier and the platform. When consumers are strategic, the unpredictable behaviors of consumers lead to the difculty of dynamic pricing in the upstream supply chain. In contrast, the upstream supply chain participants will have more efective pricing countermeasures if consumers are myopic or overly strategic.
As the agency selling channel is accepted more widely, the scope of win-win strategy grows. When consumers have more favorable sentiments toward the agency selling channel, the supplier has a better status and more negotiating power, which compels the platform to embrace the supplier's optimal channel strategy to a greater extent.
Additionally, we discover that win-win strategies are always under hybrid channel, regardless of the patience level and acceptance levels of the agency selling channel. It demonstrates the hybrid channel strategy can regulate the proft of supply chain members to alleviate their relationship. Comparing with earlier literature [15,16], they prove that adding direct selling channels for supplier reduces retailers' profts. Te diference derives from the competition and cooperation game in the background of retailing platform.

Hybrid Channel
Reselling Channel Patience level α Commission rate ϕ

Optimal Channel Strategy of Upstream Supply Chain and
Consumer Surplus. Moreover, we further consider the consumer surplus. Te consumer surplus in three channel strategies is calculated as follows: (14) Figure 10 shows the win-win-win strategy for consumers and supply chain members. Captions are respectively: the former refers to the supplier, the middle refers to the platform, and the latter refers to consumers.
For optimal channel selection of consumers, the reselling channel strategy is dominated by the hybrid channel strategy, which is in contrast to the fndings of suppliers. Tis is due to the double marginalization efect in the reselling channel, which greatly harms consumers' utility while maximizing the proft of suppliers. Moreover, the hybrid channel is optimal when consumers' patience level is low, whereas the agency selling channel is selected when the patience level is high. It can be explained through the pricing strategies in diferent channel structures discussed in Part 4. Consumers favor the hybrid channels when consumer strategic level is low because the channel competition in hybrid channel strategy results in a low overall price level. However, with the strategic enhancement, the hybrid channel turns to targeting higher-valued consumers and raising prices, while agency selling channel enables consumers to achieve maximum utility.
In combination with supplier and platform's optimal channel selection, it reveals two conditions under which the hybrid channel strategy is win-win-win: the commission rate at a moderate level and the patience level of consumers cannot be too large. Te range of win-win-win scenarios decreases as consumers become more discerning or agency selling's popularity increases, where consumers are encouraged to choose agency selling channel. Tis shows the managerial implication for the platform, which is that the upstream supply chain should alleviate positively the detrimental impact of strategic consumers' patience level on the overall proft through various business ways, such as dynamic pricing strategy. Meanwhile, continuously strengthening on store construction makes consumers prefer to shop through the platform, so as to promote a win-win-win situation of three parties.
In addition, the hybrid channel strategy is the only way to implement the win-win-win situation, further demonstrating the efectiveness of hybrid channels to resolve interest conficts.

Te Impact of Strategic Consumer on Supply Chain and Social
Welfare. Finally, we analyze the efect of strategic consumers on supply chain members and overall social welfare. We further examine how the proft of each stakeholder in the hybrid channel is impacted by strategic consumers, as Strategy H is proved to produce a win-win outcome in the previous section. Figure 11 depicts the profts of strategic consumers at diferent patience levels under the hybrid channel. Te revenues of platforms and suppliers decline initially and then increase when the level of patience rises; this is consistent with Section 6's analysis. For both suppliers and platforms, complete strategic and shortsighted support their pricing decisions and maximum proftability. However, consumer surplus has the exact opposite pattern. Consumer surplus and social welfare are both maximized when consumers are moderately strategic, while they exhibit a declining tendency as strategic levels rise or fall. Tis result highlights both the conficting interests between consumers and merchants as well as the general consistency of interests upstream in the supply chain.

Conclusion
Tis paper studied channel selection of supplier in the background of online retailing in the presence of strategic consumers. We frst propose a game-theoretic model to investigate the equilibrium decisions of the interactions of the supplier and the retail platform when facing the strategic consumers and address the optimal channel strategy. Moreover, we identify the impact of strategic consumers on optimal strategy. Finally, we further discuss whether or when the platform and consumer is better of in supplier's optimal strategy and the strategic consumers' role in social welfare.  14 Complexity Tis paper frst solves the equilibrium price solutions. Te results indicate the upstream supply chain would lessen the gap between the two periods of price when patience is limited in order to fend of the detrimental efects of strategic consumers. Meanwhile, channel competition is intensifying with the increasing of strategic level, which mitigates the intertemporal competition. Additionally, when consumers are sufciently savvy, the bulk-cheap technique leads to maximum profts in the pure channel strategies. In the hybrid channel, platforms and merchants collaborate to extract value from high-value consumers due to their cooperative-competitive connection. Te distinction between pure channels and the hybrid channel gives practical implications for frms that they should pay attention to the heterogeneity of consumers and implement corresponding pricing strategies under diferent channel strategies.
Te supplier's optimal channel strategy is then revealed. It is a nonmonotonic threshold strategy of commission rate; below which, Strategy H is selected, and otherwise, Strategy R. Compared with Strategy A, the hybrid channel strategy is more proftable. Additionally, the optimal channel strategy is unafected by commission rates when consumers are patient enough. Tese research results emphasize the management decisions on channel selection considering strategic consumer. In detail, brands with more patient target consumers, namely high consumer loyalty, are supposed to give priority to the hybrid channel, whereas brands with low levels of patience prioritize the pure reselling channel, which explains why MLB and MUJI choose different channels.
Finally, we demonstrate that a moderate commission rate can be advantageous for both supplier and platform when the hybrid channel strategy is selected. Additionally, taking consumer surplus into consideration, low patience level and a reasonable commission rate can result in a winwin-win situation. It gives implications for how suppliers and platforms should collaborate through hybrid channels. Furthermore, the upstream supply chain should also take the patience of consumers into account to maximize proft.
Our study has several limitations, which can be extended in future studies. Firstly, this paper examines optimal pricing and channel strategies considering competitive partnership between the supplier and a single platform. For further research direction, scholars can study how suppliers make channel selection in the multi-platform competition environment, such as live streaming platform. Secondly, the focus of this article is on the demand side of consumers, and more factors can be integrated on the supply side in the future, such as limited capacity, product line competitions, and so forth.

A. Proof of Theorem 1
For the supplier, the objective function and constraints can be expressed as follows: max π s w 1 , w 2 � max w 1 Te proft of the platform is as follows: Firstly, the supplier selects pure reselling channel and announces wholesale prices. Ten, the platform formulates the pricing strategy according to wholesale prices. In the second period, the supplier adjusts wholesale price due to strategic behaviors, and then, platform adjusts prices subsequently.
Te constrained optimization problem is transformed into an unconstrained optimization problem by using the KKT condition and Lagrange multiplier method.

Data Availability
Te data supporting the current study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.