Resale or agency: pricing strategy for advance selling in a supply chain considering consumers’ loss aversion

The position of this study

	Advance selling	Consumers’ loss-aversion	Two-period	Supply chain	Contracts
Zhao & Stecke (2010)	✓	✓	✓	—	—
Cho & Tang (2013)	✓	—	✓	✓	—
Khouja & Zhou (2015)	✓	—	✓	✓	✓
Baron et al. (2015)	—	✓	✓	—	—
Abhishek et al. (2015)	—	—	—	✓	✓
Zhao et al. (2016)	✓	—	✓	✓	—
Ma et al. (2016)	—	✓	—	✓	✓
Li et al. (2016)	✓	✓	✓	—	—
Cachon & Feldman (2017)	✓	—	✓	✓	✓
Tang & Ang (2017)	✓	—	✓	—	—
Karle & Möller (2018)	✓	✓	✓	—	—
Tian et al. (2018)	—	—	—	✓	✓
Shi et al. (2018)	✓	—	✓	✓	✓
Ma et al. (2019)	✓	—	✓	✓	—
Guo et al. (2019)	—	—	✓	✓	✓
Zennyo (2020)	—	—	✓	✓	✓
This paper	✓	✓	✓	✓	✓

	Advance selling	Consumers’ loss-aversion	Two-period	Supply chain	Contracts
Zhao & Stecke (2010)	✓	✓	✓	—	—
Cho & Tang (2013)	✓	—	✓	✓	—
Khouja & Zhou (2015)	✓	—	✓	✓	✓
Baron et al. (2015)	—	✓	✓	—	—
Abhishek et al. (2015)	—	—	—	✓	✓
Zhao et al. (2016)	✓	—	✓	✓	—
Ma et al. (2016)	—	✓	—	✓	✓
Li et al. (2016)	✓	✓	✓	—	—
Cachon & Feldman (2017)	✓	—	✓	✓	✓
Tang & Ang (2017)	✓	—	✓	—	—
Karle & Möller (2018)	✓	✓	✓	—	—
Tian et al. (2018)	—	—	—	✓	✓
Shi et al. (2018)	✓	—	✓	✓	✓
Ma et al. (2019)	✓	—	✓	✓	—
Guo et al. (2019)	—	—	✓	✓	✓
Zennyo (2020)	—	—	✓	✓	✓
This paper	✓	✓	✓	✓	✓

Table 1

The position of this study

	Advance selling	Consumers’ loss-aversion	Two-period	Supply chain	Contracts
Zhao & Stecke (2010)	✓	✓	✓	—	—
Cho & Tang (2013)	✓	—	✓	✓	—
Khouja & Zhou (2015)	✓	—	✓	✓	✓
Baron et al. (2015)	—	✓	✓	—	—
Abhishek et al. (2015)	—	—	—	✓	✓
Zhao et al. (2016)	✓	—	✓	✓	—
Ma et al. (2016)	—	✓	—	✓	✓
Li et al. (2016)	✓	✓	✓	—	—
Cachon & Feldman (2017)	✓	—	✓	✓	✓
Tang & Ang (2017)	✓	—	✓	—	—
Karle & Möller (2018)	✓	✓	✓	—	—
Tian et al. (2018)	—	—	—	✓	✓
Shi et al. (2018)	✓	—	✓	✓	✓
Ma et al. (2019)	✓	—	✓	✓	—
Guo et al. (2019)	—	—	✓	✓	✓
Zennyo (2020)	—	—	✓	✓	✓
This paper	✓	✓	✓	✓	✓

	Advance selling	Consumers’ loss-aversion	Two-period	Supply chain	Contracts
Zhao & Stecke (2010)	✓	✓	✓	—	—
Cho & Tang (2013)	✓	—	✓	✓	—
Khouja & Zhou (2015)	✓	—	✓	✓	✓
Baron et al. (2015)	—	✓	✓	—	—
Abhishek et al. (2015)	—	—	—	✓	✓
Zhao et al. (2016)	✓	—	✓	✓	—
Ma et al. (2016)	—	✓	—	✓	✓
Li et al. (2016)	✓	✓	✓	—	—
Cachon & Feldman (2017)	✓	—	✓	✓	✓
Tang & Ang (2017)	✓	—	✓	—	—
Karle & Möller (2018)	✓	✓	✓	—	—
Tian et al. (2018)	—	—	—	✓	✓
Shi et al. (2018)	✓	—	✓	✓	✓
Ma et al. (2019)	✓	—	✓	✓	—
Guo et al. (2019)	—	—	✓	✓	✓
Zennyo (2020)	—	—	✓	✓	✓
This paper	✓	✓	✓	✓	✓

3. Basic model

3.1 Model setting

This paper sets a two-period supply chain system consisting of a manufacturer (he) and an e-retailer (she), in which the manufacturer produces a new product and plans to cooperate with the e-retailer to release it through advance selling in the first period and normally sell it in the second period. We assume that the total market size is 1 and consumers are divided into two groups, the informed and the uninformed, according to their degrees of information perception (Huang et al., 2017; Zhao et al., 2016). That is, only the informed consumers know of the e-retailer’s advance selling and this proportion of informed consumers is set as |$\lambda $|⁠. Thus, the proportion of the uninformed consumers is |$1-\lambda $|⁠.

In this paper, we design two scenarios regarding the contracts of the two members in the supply chain: the resale contract and the agency contract. Under the resale contract, the e-retailer as a reseller has the pricing power for the consumers and is responsible for the inventory, transportation and after-sales costs of the product. After observing the wholesale price |$w$| charged by the manufacturer, the e-retailer decides whether to advance sell or not. When advance selling is conducted, then the advance selling price |$p_{1}^{W}$| is released and the informed consumers arrive and decide whether to purchase the product during the advance selling period. When the advance selling period ends, the e-retailer releases the spot selling price |$p_{2}^{W}$| in the second period. The consumers who were aware of the advance selling but did not purchase the product and uninformed consumers arrive and decide whether to buy the product. When the e-retailer does not sell the product in advance, she releases only the spot selling price |$p_{2}^{W}$| and all consumers decide whether to purchase the product during the spot selling period.

Under an agency contract, the e-retailer serves only as a selling agent and the pricing and related costs of the product are taken on by the manufacturer. First, the e-retailer sets the proportional fee rate |$a$| per unit of the product. After observing the proportional fee rate, the manufacturer decides whether to sell the product to consumers in advance. When advance selling is conducted, then the advance selling price |$p_{1}^{A}$| is released in the first period. The informed consumer observes |$p_{1}^{A}$| and decides whether to buy the product in the advance selling period. When the advance selling period ends, the manufacturer releases the spot selling price |$p_{2}^{A}$| in the second period. The consumers who knew of the advance selling but did not purchase the product and the uninformed consumers arrive and decide whether to buy the product. When the advance selling is not performed, the manufacturer releases only the spot selling price |$p_{2}^{A}$| and all consumers decide whether to purchase the product during the spot selling period.

Because the selling activities of the product are performed through the e-retailer’s online platform, some order fulfilment costs are generated. Order fulfilment costs refer to the costs that occur from the time that a product is launched to the time that the consumer receives it, and they include inventory costs, storage costs, packaging costs and transportation costs (Tian et al., 2018). Kapner (2014) studied actual sales data and found that the costs of fulfilment operations could run as high as 25% of sales revenue; therefore, we assume that the order fulfilment costs can reach up to 25% of the unit price. When an e-retailer adopts the resale contract, the order fulfilment costs are charged by the e-retailer and each unit of the product generates an order fulfilment cost |$c_W$|⁠. When an e-retailer adopts the agency contract, the order fulfilment costs are charged by the manufacturer and each unit of the product generates an order fulfilment cost |$c_A$|⁠. To facilitate the subsequent calculations and analysis, this paper assumes |$c_W=c_A=c$| (Tian et al., 2018).

The notations and parameters used to develop the models in this paper are as follows.

|$t$|

|$t=1,2$| present the first period and the second period of product sales, respectively

|$v$|

Consumers’ valuation of the product and |$v\sim U[0,1]$|

|$f$|

Probability density function of consumers’ valuation

|$F$|

Cumulative density function of consumers’ valuation

|$U_t$|

Consumer’s utility in period |$t, t=1,2$|

|$w$|

Wholesale price charged by the manufacturer to the e-retailer

|$p_{t}^{j}$|

Price charged by the e-retailer/manufacturer in period |$t$| under the resale/agency contract, |$t=1,2, j=W,A$|

|$a$|

The proportional fee rate charged by the e-retailer to the manufacturer

|$\beta $|

Consumer’s loss aversion coefficient, |$\beta \leq 0$|

|$c$|

Order fulfilment cost per unit

|$\lambda $|

Proportion of the informed consumers in the market, |$\lambda \in [0,1]$|

|$\theta $|

Proportion of the informed consumers who buy in advance

|$D_{t}^{j}$|

Demand in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$Q_{t}^{j}$|

Ordering quantity in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$\pi _{R,t}^{j}$|

E-retailer’s profit in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$\pi _{M,t}^{j}$|

Manufacturer’s profit in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$\pi ^{j}$|

The profit of the whole supply chain under contract, |$j=W,A$|

|$AS/NAS$|

Superscripts respectively indicate whether advance selling action is made or not

|$W/A$|

Superscripts respectively indicate that the resale contract or the agency contract is chosen

|$t$|

|$t=1,2$| present the first period and the second period of product sales, respectively

|$v$|

Consumers’ valuation of the product and |$v\sim U[0,1]$|

|$f$|

Probability density function of consumers’ valuation

|$F$|

Cumulative density function of consumers’ valuation

|$U_t$|

Consumer’s utility in period |$t, t=1,2$|

|$w$|

Wholesale price charged by the manufacturer to the e-retailer

|$p_{t}^{j}$|

Price charged by the e-retailer/manufacturer in period |$t$| under the resale/agency contract, |$t=1,2, j=W,A$|

|$a$|

The proportional fee rate charged by the e-retailer to the manufacturer

|$\beta $|

Consumer’s loss aversion coefficient, |$\beta \leq 0$|

|$c$|

Order fulfilment cost per unit

|$\lambda $|

Proportion of the informed consumers in the market, |$\lambda \in [0,1]$|

|$\theta $|

Proportion of the informed consumers who buy in advance

|$D_{t}^{j}$|

Demand in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$Q_{t}^{j}$|

Ordering quantity in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$\pi _{R,t}^{j}$|

E-retailer’s profit in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$\pi _{M,t}^{j}$|

Manufacturer’s profit in period |$t$| under contract |$j$|⁠, |$t=1,2, j=W,A$|

|$\pi ^{j}$|

The profit of the whole supply chain under contract, |$j=W,A$|

|$AS/NAS$|

Superscripts respectively indicate whether advance selling action is made or not

|$W/A$|

Superscripts respectively indicate that the resale contract or the agency contract is chosen

In addition, to facilitate the subsequent analysis, this paper adopts the following assumptions.

(1) The manufacturer and the e-retailer are risk neutral, aim to maximize their own profits, and cannot set a price that causes them to incur a loss. In addition, the manufacturer’s production follows the make-to-order strategy and production costs are not considered since this paper focuses on the comparisons of two different contracts in the supply chain.

(2) With the resale contract, the e-retailer conducts advance selling using her own platform. With the agency contract, the manufacturer conducts advance selling through the e-retailer’s platform. Because the selling activities occur on the e-retailer’s platform, the two parties can freely switch between the advance selling mode and no advance selling mode according to the game results; therefore, we assume that the conversion costs are 0.

(3) All consumers are strategic consumers. In the advance selling period, due to the lack of detailed product evaluations on the new product, all consumers are homogeneous at this time (Cachon & Feldman, 2017; Lim & Tang, 2013; Zhao & Stecke, 2010; Zhao et al., 2016). When the consumers who buy in advance receive the product, they experience it before realizing their own evaluations about the product. We assume the product cannot be refunded after being used (Huang et al., 2017; Wei & Zhang, 2018; Zhao & Stecke, 2010). In reality, for example, fresh products and digital products are not allowed to be returned (He et al., 2019). This is also the case for electronic products that are not allowed to be returned after being activated (Safari et al., 2015).

(4) According to prospect theory (Kahneman, 1979), consumers will be loss averse if the product does not meet their expectations. When the advance selling period ends, the evaluation information appears in the market and consumers can also search for information on the product. At this time, consumers may realize the valuation of the product and can decide to purchase it if the product meets their requirements. Therefore, consumers are not loss averse in the spot selling period. Following Zhao & Stecke (2010), we assume that informed consumers have the same degree of loss aversion.

3.2 Consumer utility

Because all consumers are strategic consumers, informed consumers in the market may compare their utilities in the advance selling period with those in the spot selling period. When their utility in the advance selling period is higher than that in the spot selling period, they choose to buy in advance. Uninformed consumers decide only whether to purchase the product in the spot selling period because they do not know of the advance selling. Then, we separately analyse the relationship between consumers’ purchasing behaviours and their utilities.

(1) Purchasing in the spot selling period

According to the utility function of Cachon & Swinney (2009), the utility of one consumer when he decides to make a purchase in the spot selling period can be expressed as follows:

$$\begin{align} U_2 = v-p_2. \end{align}$$

(3.1)

We assume that consumers’ individual valuation of the product is uniformly distributed in |$[0,1]$| (Chiang et al., 2003). If |$U_2\geq 0$| is satisfied, consumers who arrive in the spot selling period will buy the product.

(2) Purchasing in the advance selling period

During the advance selling period, due to the lack of detailed product information about the new product, all consumers at this time have homogeneous valuations. However, consumers who purchase the product during the advance selling period may experience loss aversion if the product does not meet their expectations (Kahneman, 1979). This paper uses the piecewise linear loss-averse utility function in Zhao & Stecke (2010) to represent the loss averse behaviour of a consumer, that is,

$$\begin{align*} &utility = \left\{ \begin{array}{ll} surplus-\beta & \textrm{if surplus is negative and thus loss occurs}\\ surplus & \textrm{otherwise},\\ \end{array} \right. \end{align*}$$

where the parameter |$\beta $| represents the intensity of the consumers’ loss aversion (⁠|$\beta \geq 0$|⁠). A higher |$\beta $| represents consumers’ higher loss aversion. If a consumer buys the product in advance but his/her realized individual valuation of the product satisfies |$v\le{p_1}$|⁠, he/she will experience loss aversion. In the advance selling period, due to the lack of information and experience about the product, the consumers’ valuation of the product is homogeneous. Thus, the consumer has a certain probability for perceiving the loss (Zhao & Stecke, 2010). The probability of loss is |$F(p_1)$|⁠, and then we obtain the consumers’ utility function during the advance selling period as

$$\begin{align} & U_1 = E[v-p_1-\beta{F(p_1)}]. \end{align}$$

(3.2)

According to the informed consumers’ strategic behaviour, they choose whether to buy the product through comparing the utility functions in the two periods. Then, we can conclude that the informed consumers will buy the new product in the advance selling period if |$U_1\geq \max \{U_2,0\}$| ; otherwise, they will wait until the spot selling period.

4. Advance selling strategy under resale contract

Under a resale contract, the manufacturer first sets the wholesale price |$w$|⁠. After observing the wholesale price, the e-retailer decides whether to conduct advance selling or not and makes pricing decisions. The time sequence is shown in Fig. 1, and we use the backward method to solve the equilibrium.

Fig. 1.

Game sequence under the resale contract.

4.1 E-retailer’s strategy

First, we analyse the demand and profit in the spot selling period. To ensure that the consumers who arrive in the spot selling period purchase the products, the condition |$v-p_{2}^{W}\geq 0$| needs to be met. Then, the proportion of consumers who purchase the products in the spot selling period is |$1-p_{2}^{W}$| and the demand in the spot selling period is

$$\begin{align} D_{2}^{W}=((1-\theta) \lambda+(1-\lambda))\left(1-p_{2}^{W}\right), \end{align}$$

(4.1)

where |$\theta $| represents the proportion of informed consumers who purchase the products in the advance selling period, |$(1-\theta ) \lambda $| indicates the number of informed consumers who did not purchase the product during the advance selling period and |$1-\lambda $| indicates the number of uninformed consumers.

Thus, the profit function of the spot selling period is

$$\begin{align} & \pi_{R,2}^{W, AS}=\left(p_{2}^{W}-w-c\right)((1-\theta) \lambda+(1-\lambda))\left(1-p_{2}^{W}\right). \end{align}$$

(4.2)

Since |$\partial ^{2} \pi _{R,2}^{W, AS} / \partial p_{2}^{W 2}<0$|⁠, after setting |${{\partial \pi _{R,2}^{W, AS}}/ {\partial p_{2}^{W}}}=0$|⁠, we have the optimal spot selling price as

$$\begin{align} & p_{2}^{W^{*}}=\frac{1+w+c}{2}. \end{align}$$

(4.3)

Combining this equation with Formula (4.2), we have

$$\begin{align} \pi_{R, 2}^{W, A S}=\frac{(1-c-w)^{2}((1-\theta) \lambda+(1-\lambda))}{4}. \end{align}$$

(4.4)

Then, we analyse the demand and profit in the advance selling period. Since only informed consumers know of the advance selling, the demand in the advance selling period is relevant only to informed consumers. The informed consumers will buy in the advance selling period if |$E\left (v-p_{1}^{W}-\beta p_{1}^{W}\right ) \geq E\left (v-p_{2}^{W^{*}}\right )^{+}$|⁠. By inserting (4.3) into this constraint, we obtain

$$\begin{align} & p_{1}^{W} \leq \frac{(3-w-c)(1+w+c)}{8(1+\beta)}. \end{align}$$

(4.5)

Then, we set

$$\begin{align*} &p_{1}^{WU} = \frac{(3-w-c)(1+w+c)}{8(1+\beta)} \end{align*}$$

the probability that an informed consumer participates in the advance selling is |$\theta =P\left (p_{1}^{W} \leq p_{1}^{W U}\right )$| and the demand in the advance selling period is |$D_1=\lambda P\left (p_{1}^{W} \leq p_{1}^{W U}\right )$|⁠.

Since the consumers in the first period are assumed to be homogeneous (Cachon & Feldman, 2017; Lim & Tang, 2013; Zhao & Stecke, 2010; Zhao et al., 2016), the following two cases are discussed according to the different values of |$p_{1}^{W}$|⁠.

(1) When |$p_{1}^{W}> p_{1}^{W U}$|

The advance selling price is so high that all informed consumers do not buy in advance, and all consumers only consider buying in the spot selling period. At this time, |$\theta =0$| and |$D_{1}=0$|⁠. The profit is the same as that under the no advance selling situation. Thus, the e-retailer’s profit is

$$\begin{align} & \pi_{R}^{W, NAS}=\frac{(1-c-w)^{2}}{4}. \end{align}$$

(4.6)

(2) When |$p_{1}^{W} \leq p_{1}^{W U}$|

Since consumers are homogeneous in the advance selling period (Cachon & Feldman, 2017; Lim & Tang, 2013; Zhao & Stecke, 2010; Zhao et al., 2016), all informed consumers participate in the advance selling. Therefore, |$\theta =1$| and |$D_{1}=\lambda $| are satisfied and the profit in the two periods is

$$\begin{align} & \pi_{R}^{W, AS}=\left(p_{1}^{W}-w-c\right) \lambda+\left(p_{2}^{W}-w-c\right)\left(1-p_{2}^{W}\right)(1-\lambda). \end{align}$$

(4.7)

In Formula (4.7), the first part represents the e-retailer’s profit in the advance selling period and the second part represents her profit in the spot selling period. Inserting Formula (4.3) into Formula (4.7), we obtain the profit function and the constraint as follows:

$$\begin{align*} &\max_{p_{1}} \pi_{R}^{W, A S}=\left(p_{1}^{W}-w-c\right) \lambda+\frac{(1-c-w)^{2}(1-\lambda)}{4} \end{align*}$$

$$\begin{align*} &s.t.p_{1}^{W} \leq \frac{(3-w-c)(1+w+c)}{8(1+\beta)}. \end{align*}$$

Since |${{\partial \pi _{R}^{W, AS}}/ {\partial p_{1}^{W}}}>0$|⁠, we have the following equilibrium solution:

$$\begin{align*} &p_{1}^{W} =\frac{(3-w-c)(1+w+c)}{8(1+\beta)}. \end{align*}$$

By inserting |$p_{1}^{W*}$| into |$\pi _{R}^{W, AS}$|⁠, we can solve the e-retailer’s profit when she implements the advance selling strategy. Combining the results, a rational e-retailer chooses the marketing strategy that maximizes her profit as follows:

$$\begin{align*} & \pi_{R}^{W}=\max _{p_{1}, p_{2}}\left\{\pi_{R}^{W, A S}, \pi_{R}^{W, N A S}\right\}. \end{align*}$$

Proposition 4.1

Under the resale contract, there is a threshold |$\bar{w}$| for the manufacturer’s wholesale price and the e-retailer adopts the advance selling mode when |$w\leq{\bar{w}}$|⁠, where

$$\begin{align*} &\bar{w}=\frac{4}{3+2 \beta}-1-c.\end{align*}$$

The proof is shown in Appendix 1.

Proposition 4.1 shows that the e-retailer implements the advance selling strategy when the manufacturer charges a lower wholesale price. If consumers participate in the advance selling, then Formula (4.5) must be followed, which means that the e-retailer must charge a lower advance selling price so that consumers can be attracted to the advance selling. The e-retailer sacrifices her profit margin because of the low advance selling price. Only when the manufacturer also sacrifices his profit margin for the advance selling can the equilibrium exist.

4.2 Manufacturer’s strategy

According to Proposition 4.1, the e-retailer may sell in advance or not if the wholesale price is different. That is, the manufacturer’s optimal decision is related to the e-retailer’s response. Then, the different choices of the manufacturer are discussed based on the e-retailer’s response.

(1) When the e-retailer does not conduct advance selling (⁠|$w>{\bar{w}}$|⁠)

It is concluded that when the e-retailer does not choose advance selling, all consumers wait to purchase the product in the spot selling period. Since the manufacturer follows the make-to-order strategy, the total ordering quantity and demand are |$Q^{W,NAS}=D^{W,NAS}=1-p_{2}^{W*}$|⁠. Then, when the e-retailer does not conduct advance selling, the manufacturer’s profit is

$$\begin{align} &\pi_{M}^{W, NAS}=w(1-p_{2}^{W*}). \end{align}$$

(4.8)

Thus, the optimal wholesale price in no advance selling situation is

$$\begin{align} &w_{NAS}^{*}=\frac{1-c}{2}. \end{align}$$

(4.9)

After comparing |$\bar{w}$| and |$w_{NAS}^{*}$|⁠, we find that |$w_{NAS}^{*}\geq{\bar{w}}$| always exists. Thus, when the manufacturer sets the optimal wholesale price |$w_{NAS}^{*}$|⁠, the e-retailer does not conduct advance selling and the equilibrium exists.

(2) When the e-retailer conducts advance selling (⁠|$w\leq{\bar{w}}$|⁠)

When the e-retailer conducts advance selling, since the manufacturer follows the make-to-order strategy, the total ordering quantity and demand are |$Q^{W,AS}=D^{W,AS}=\lambda +(1-p_{2}^{W*})(1-\lambda )$|⁠. Then, the manufacturer’s profit is

$$\begin{align} &\pi_{M}^{W, AS}=w\left(\lambda+\left(1-p_{2}^{W^{*}}\right)(1-\lambda)\right). \end{align}$$

(4.10)

To ensure that the e-retailer is willing to sell in advance, the condition |$w\leq{\bar{w}}$| must be satisfied. Thus, we can conclude that the optimal wholesale price under the advance selling is

$$\begin{align} &w_{AS}^{*}=\bar{w}=\frac{4}{3+2 \beta}-1-c. \end{align}$$

(4.11)

The rational manufacturer chooses the suitable wholesale price that allows him to obtain the highest profit, that is,

$$\begin{align*} &\pi_{M}^{W}=\max _{w}\left\{\pi_{M}^{W, A S}, \pi_{M}^{W, N A S}\right\}. \end{align*}$$

By comparing the manufacturer’s profits under advance selling and no advance selling, we form the manufacturer’s strategy as follows.

Proposition 4.2

Under the resale contract, there are two thresholds |$\bar{\beta }^{W}$| and |$\bar{\lambda }^{W}$|⁠. When |$\beta \leq{\bar{\beta }^{W}}$| and |$\lambda \geq{\bar{\lambda }^{W}}$|⁠, the two members in the supply chain can achieve Pareto improvements through advance selling compared to no advance selling; otherwise, the manufacturer sets a higher wholesale price so that the e-retailer is not willing to sell in advance.

The proof is provided in Appendix 2.

According to Proposition 4.2, when the consumers’ loss aversion is not strong and there are enough informed consumers in the market, it is easier for the e-retailer to conduct advance selling and the manufacturer does not need to sacrifice too much to encourage the e-retailer to sell in advance. At this time, the two members in the supply chain can achieve Pareto improvements through advance selling compared with no advance selling. Further, considering the influence of the consumers’ loss aversion in advance selling on the decisions and the profits in the supply chain, we form Proposition 4.3.

Proposition 4.3

Under the resale contract, when the e-retailer conducts advance selling to release a new product, given the other parameters, the following properties related to the sensitivity analysis of the consumers’ loss aversion are satisfied: (1) |$\partial w_{A S}^{*} / \partial \beta <0$|⁠, |$\partial p_{1}^{W*} / \partial \beta <0$|⁠, and |$\partial p_{2}^{W*} / \partial \beta <0$|⁠; (2) |$\partial \pi _{M}^{W,AS} / \partial \beta <0$| and |$\partial \pi _{R}^{W,AS} / \partial \beta>0$|⁠.

The proofs are shown in Appendix 3.

According to Proposition 4.3 (1), under the resale contract, when the e-retailer selects advance selling, the wholesale price, the advance selling price and the spot selling price decrease as consumers’ loss aversion increases. That is, when consumers’ loss-averse behaviour is enhanced, because the informed consumers cannot experience the product on their own, it is more difficult to ensure that the informed consumers purchase the product in the advance selling period. The manufacturer and the e-retailer have to set a lower price to ensure that the consumers are willing to purchase the product during the advance selling period.

According to Proposition 4.3(2), the profit of the manufacturer decreases as the loss aversion of consumers increases, but the profit of the e-retailer increases as the loss aversion of consumers increases. This is a surprising result, since in order to ensure that the e-retailer conducts advance selling, the manufacturer gives a greater concession and drops the wholesale price more than the advance selling price and the spot selling price as consumers’ loss aversion increases. Why is the manufacturer willing to give a greater concession? According to the manufacturer’s choice, although he sharply reduces his wholesale price, which decreases his profit margin, he can also gain more profit from the e-retailer’s advance selling situation compared with that with no advance selling. Therefore, as consumers’ loss aversion increases, the manufacturer also prefers to participate in advance selling and the e-retailer can benefit from the manufacturer’s concession. Thus, under the resale contract, the consumers’ loss aversion in advance selling impacts the upstream member in the supply chain more.

5. Advance selling strategy under agency contract

Under the agency contract, first, the e-retailer sets the proportional fee rate |$a$| per unit of the product, which means that if the manufacturer sets the price |$p$|⁠, the e-retailer charges a proportional fee |$ap$|⁠. In reality, the e-retailer also charges a fixed fee |$F^A$|⁠. Since |$F^A$| is charged only once and the amount is far less than the total proportional fee, it has no effect on pricing (Tian et al., 2018). For simplification, we set |$F^A=0$|⁠. After observing the proportional fee rate, the manufacturer decides whether to use advance selling and makes his pricing decisions in the two periods. The time sequence is shown in Fig. 2, and we use the backward method to solve the equilibrium.

Fig. 2.

Game sequence under the agency contract.

5.1 Manufacturer’s strategy

The calculation process is similar to that in Section 4. First, we analyse the demand and profit in the spot selling period. To guarantee that the consumers who arrive in the spot selling period purchase the products, the condition |$v-p_{2}^{A}\geq 0$| should be satisfied. Thus, the demand function is similar to that in Section 4 and his profit in the spot selling period is

$$\begin{align} &\pi_{M, 2}^{A, A S}=\left((1-a) p_{2}^{A}-c\right)((1-\theta) \lambda+(1-\lambda)). \end{align}$$

(5.1)

Since |$\partial ^{2} \pi _{M,2}^{A, AS} / \partial p_{2}^{A 2}<0$|⁠, after setting |${{\partial \pi _{M,2}^{A, AS}}/ {\partial p_{2}^{A}}}=0$|⁠, we have the optimal spot selling price

$$\begin{align} & p_{2}^{A^{*}}=\frac{1-a+c}{2-2 a}. \end{align}$$

(5.2)

Inserting this price into Formula (5.1), we have the manufacturer’s profit in the advance selling period

$$\begin{align} \pi_{M, 2}^{A, A S}=\frac{(1-a-c)^{2}((1-\theta) \lambda+(1-\lambda))}{4(1-a)}. \end{align}$$

(5.3)

If he wants the informed consumers to buy in advance, the advance selling price must follow the constraint |$E\left (v-p_{1}^{A}-\beta p_{1}^{A}\right ) \geq E\left (v-p_{2}^{A^{*}}\right )^{+}$|⁠. Inserting (5.2) into this formula, we have

$$\begin{align} &p_{1}^{A} \leq \frac{(1-a+c)(3-3 a-c)}{8(1-a)^{2}(1+\beta)}. \end{align}$$

(5.4)

Referring to the references (Cachon & Feldman, 2017; Lim & Tang, 2013; Zhao & Stecke, 2010; Zhao et al., 2016), similar to that in Section 4, we set |$p_{1}^{AU} = \frac{(1-a+c)(3-3 a-c)}{8(1-a)^{2}(1+\beta )}$| and consider two cases according to the different values of |$p_{1}^{A}$|⁠.

(1) When |$p_{1}^{A}>p_{1}^{AU}$|

The advance selling price is so high that all informed consumers do not buy in advance and all consumers consider buying in the spot selling period. The profit is the same as in the no advance selling case, and the manufacturer’s profit is

$$\begin{align} & \pi_{M}^{A, N A S}=\frac{(1-a-c)^{2}}{4(1-a)}. \end{align}$$

(5.5)

(2) When |$p_{1}^{A}\leq p_{1}^{AU}$|

All informed consumers participate in the advance selling activities. The manufacturer’s profit in the two periods is

$$\begin{align} & \pi_{M}^{A, A S}=\left((1-a) p_{1}^{A}-c\right) \lambda+\left((1-a) p_{2}^{A}-c\right)\left(1-p_{2}^{A}\right)(1-\lambda), \end{align}$$

(5.6)

where the first part shows the manufacturer’s profit in the advance selling period and the second part shows his profit in the spot selling period. By inserting Formula (5.2) into Formula (5.6), we obtain the manufacturer’s profit function and the constraint as follows:

$$\begin{align*} & \max _{p_{1}} \pi_{M}^{A, A S}=\left((1-a) p_{1}^{A}-c\right) \lambda+\frac{(1-a-c)^{2}(1-\lambda)}{4(1-a)} \end{align*}$$

$$\begin{align*} &s.t. p_{1}^{A} \leq \frac{(1-a+c)(3-3 a-c)}{8(1-a)^{2}(1+\beta)}.\end{align*}$$

Since |${{\partial \pi _{M}^{A, AS}}/ {\partial p_{1}^{A}}}>0$|⁠, the optimal equilibrium solution is

$$\begin{align*} &p_{1}^{A*} = \frac{(1-a+c)(3-3 a-c)}{8(1-a)^{2}(1+\beta)}.\end{align*}$$

By inserting the above |$p_{1}^{A*}$| into |$\pi _{M}^{A, A S}$|⁠, we compute the manufacturer’s profit when he conducts advance selling. Combining the results of Cases (1) and (2), a rational manufacturer chooses the marketing strategy when he can maximize his profit as follows:

$$\begin{align*} & \pi_{M}^{A}=\max _{p_{1}, p_{2}}\left\{\pi_{M}^{A, A S}, \pi_{M}^{A, N A S}\right\}. \end{align*}$$

Proposition 5.1

There is a threshold |$\bar{a}$| for the e-retailer’s proportional fee rate and the manufacturer adopts the advance selling mode when |$a\leq{\bar{a}}$| and |$\bar{a}=1+c-\frac{4 c}{1-2 \beta }$|⁠.

The proof is shown in Appendix 4.

Proposition 5.1 is similar to Proposition 4.1. The manufacturer conducts advance selling when the e-retailer sets a lower proportional fee rate. This choice is made because if consumers participate in the advance selling under the agency contract, Formula (5.4) must be followed and the manufacturer must charge a lower advance selling price so that consumers can be attracted to purchase the product in the advance selling period. The manufacturer sacrifices his profit margin. A lower proportional fee rate means a lower profit margin for the e-retailer. Only when the e-retailer also sacrifices her profit margin, the manufacturer is willing to conduct advance selling.

5.2 E-retailer’s strategy

The e-retailer’s strategy is consistent with the manufacturer’s marketing choice. When the manufacturer does not conduct advance selling, all consumers make choices according to their own utility in the second period. Then, the e-retailer’s profit under no advance selling is

$$\begin{align} \pi_{R}^{A, N A S}=a p_{2}^{A^{*}}\left(1-p_{2}^{A^{*}}\right). \end{align}$$

(5.7)

Then, the optimal proportion fee rate under no advance selling mode is

$$\begin{align*} &a_{N A S}^{*}=1+\frac{Z}{3^{2 / 3}}-\frac{c^{2}}{Z},\end{align*}$$

where |$Z=\left (3 \sqrt{3} \sqrt{c^{4}\left (27+c^{2}\right )}-27 c^{2}\right )^{1 / 3}$|⁠.

When the manufacturer conducts advance selling, the e-retailer extracts the proportional fee from the revenue of the manufacturer in the two periods. The e-retailer’s profit under advance selling is

$$\begin{align}& \pi_{R}^{A, A S}=a p_{1}^{A^{*}} \lambda+a p_{2}^{A^{*}}\left(1-p_{2}^{A^{*}}\right)(1-\lambda). \end{align}$$

(5.8)

To ensure that the manufacturer conducts advance selling on the e-retailer’s platform, the condition |$a\leq{\bar{a}}$| should be satisfied. We find that when |$a\leq{\bar{a}}$|⁠, |${{\partial \pi _{R}^{A, AS}}/ {\partial a}}>0$| always exists. Thus, the optimal proportional fee rate under the advance selling mode is

$$\begin{align} a_{AS}^{*}=\bar{a}=1+c-\frac{4 c}{1-2 \beta}. \end{align}$$

(5.9)

A rational e-retailer chooses the suitable proportion fee rate that provides her with the highest profit, that is,

$$\begin{align*} \pi_{R}^{A}=\max _{a}\left\{\pi_{R}^{A, A S}, \pi_{R}^{A, N A S}\right\}. \end{align*}$$

By comparing the e-retailer’s profit under advance selling and no advance selling, we have Proposition 5.2.

Proposition 5.2

Under the agency contract, when consumers’ loss aversion |$\beta \leq{\bar{\beta }^{A}}$| and the number of informed consumers |$\lambda \geq{\bar{\lambda }^{A}}$|⁠, advance selling can achieve a Pareto improvement compared with no advance selling.

The proof is shown in Appendix 5.

According to Proposition 5.2, similar to that in Section 4, when the consumers’ loss aversion is not strong and there are enough informed consumers in the market, it is easier for the manufacturer to conduct advance selling and the e-retailer does not need to sacrifice too much to encourage the retailer to sell in advance. Therefore, when the consumers’ loss aversion is not strong and there are enough informed consumers in the market, advance selling can achieve a Pareto improvement relative to no advance selling.

Proposition 5.3

With the agency contract, when the manufacturer conducts advance selling to release a new product through an e-retailer’s platform, given the other parameters, the following are satisfied. (1) |${\partial a^{*}}/ {\partial{\beta }}<0$|⁠, |${\partial p_{1}^{A*}}/ {\partial{\beta }}<0$| and |${\partial p_{2}^{A*}}/ {\partial{\beta }}<0$|⁠. (2) |${\partial \pi _{M}^{A, A S}}/ {\partial{\beta }}>0$|⁠. (3) There are thresholds |$c_1$| and |$\lambda _1$|⁠,

(i) when |$c<c_1$| and |$\lambda <\lambda _1$|⁠, |${\partial \pi _{R}^{A, A S}}/ {\partial{\beta }}>0$|⁠;

(ii) when |$c\geq{c_1}$| or |$\lambda \geq{\lambda _1}$|⁠, |${\partial \pi _{R}^{A, A S}}/ {\partial{\beta }}\leq{0}$|⁠. where |$c_{1}=\frac{1-6 \beta +12 \beta ^{2}-8 \beta ^{3}}{15+22 \beta +20 \beta ^{2}+8 \beta ^{3}}, \lambda _{1}=\frac{15 c+6 \beta +22 c \beta -12 \beta ^{2}+20 c \beta ^{2}+8 \beta ^{3}+8 c \beta ^{3}-1}{3 c+22 \beta -10 c \beta -28 \beta ^{2}+4 c \beta ^{2}+8 \beta ^{3}+8 c \beta ^{3}-5}$|⁠.

The proofs are shown in Appendix 6.

Proposition 5.3(1) shows that as the consumers’ loss aversion increases, the e-retailer’s proportional fee rate and the manufacturer’s price reduce and the proportional fee rate declines faster. This occurs because when consumers’ loss aversion is high, it is more difficult for the manufacturer to sell in advance through the e-retailer’s platform, and so all the supply chain members need to sacrifice their profit margins.

Proposition 5.3(2) reveals that as consumers’ loss aversion increases, the proportional fee rate declines faster and the e-retailer sacrifices more than the manufacturer, so that the manufacturer can achieve more profit as the consumers’ loss aversion increases. Proposition 5.3(3) states that when the order fulfilment costs are low and the scale of informed consumers is small, the profit of the e-retailer increases as the consumers’ loss aversion increases. However, as the order fulfilment costs and the number of informed consumers increase, the profit of the e-retailer decreases as the consumers’ loss aversion increases. We can easily find that similar to the conclusion in Proposition 4.3, the negative impact of consumers’ loss aversion is always higher for the indirect pricing member in the supply chain than for the direct pricing member. However, as the consumers’ loss aversion increases, even if the manufacturer’s profit is considerably harmed, he may achieve more profit under the e-retailer’s advance selling compared with that with no advance selling. Furthermore, for the e-retailer, due to the popularity of the online shopping, an increasing number of consumers are becoming informed, that is, when |$\lambda \geq{\lambda _1}$|⁠, the e-retailer’s profit decreases as the consumers’ loss aversion increases. Thus, the consumers’ loss-averse behaviour has an enormous influence on members’ decisions and profits in the supply chain.

6. Contract comparisons

This section compares the results obtained under the resale contract and the agency contract. We can obtain Proposition 6.1 by comparing the pricing equilibrium results under these two contracts in the supply chain.

Proposition 6.1

Whether the e-retailer chooses the resale contract or the agency contract for the advance selling of new products, the prices in the advance selling period and in the spot selling period are same for the consumers, that is,

$$\begin{align*} &p_{1}^{W*}=p_{1}^{A*},p_{2}^{W*}=p_{2}^{A*}.\end{align*}$$

Regarding the modelling, according to the analysis in Sections 4 and 5, when the manufacturer or e-retailer conducts advance selling for consumers, the other member sets a boundary solution in order to ensure that the equilibrium of the advance selling does not deviate. The wholesale price or the proportional fee rate needs to meet the consumer’s utility constraints and the utility constraints are related only to the consumers but not to the contracts in supply chains. The upstream decision directly affects the downstream pricing strategies for consumers, which leads to the same downstream pricing strategy. For example, in a real-world situation, Huawei, one of the largest cell phone manufacturers, released its new Mate 30 mobile phone through an advance selling strategy,² and resellers (JD.com and Suning) and platform vendors (Tmall) set the same advance selling price and the same spot selling price for this cell phone.

The pricing results for consumers directly determine the total demand and total profit in the supply chain. According to the conclusion in Proposition 6.1, we can further find that the total profits in the supply chain under the resale contract and agency contract are equal. However, under these two contracts, the profits shared by each member in the supply chain are different. The analysis in Sections 4 and 5 shows that the loss aversion has a greater impact on the profits of the two members. Figures 3 and 4 show the proportional share of each member’s profit in the supply chain considering consumers’ loss aversion under the different contracts.

$The profits of two players under the resale contract $c=0.1,\lambda =0.5$.$

Fig. 3.

The profits of two players under the resale contract |$c=0.1,\lambda =0.5$|⁠.

$The profits of two players under the agency contract $c=0.1,\lambda =0.5$.$

Fig. 4.

The profits of two players under the agency contract |$c=0.1,\lambda =0.5$|⁠.

Figure 3 shows that when the resale contract is applied for advance selling, as consumers’ loss aversion increases, the manufacturer’s profit decreases and the e-retailer’s profit increases, which is the same as the results in Proposition 4.3. If the consumers’ loss aversion is low, then the manufacturer can obtain more profit in the supply chain. However, when the consumers’ loss aversion is high, the e-retailer can obtain more profit.

Figure 4 shows that when the agency contract is adopted for advance selling, the manufacturer’s profit increases and the e-retailer’s profit decreases as the consumers’ loss aversion increases, which is same as the conclusions in Proposition 5.3. Unlike the linear trends of the two members’ profit shares under the resale contract in Fig. 3, here, convex downward and upward curves appear in Fig. 4. We can see that if the consumers’ loss aversion is not too high, then the e-retailer can achieve a higher profit share. When the consumers’ loss aversion is higher, the manufacturer can obtain a greater profit share, that is, the consumers’ loss aversion has a greater negative impact on the e-retailer when indirect pricing exists.

Comparing Fig. 3 with Fig. 4, we find that when the consumers’ loss aversion is low, the e-retailer can obtain a higher profit share if she chooses the agency contract. When the consumers’ loss aversion is high, the e-retailer has a higher profit share under the resale contract. When the loss aversion is medium, regardless of which contract is chosen, the e-retailer can obtain more profit than the manufacturer.

Fig. 5.

Pareto region under different contracts when |$c=0.1$|⁠.

Fig. 6.

Pareto region under different contracts when |$c=0.2$|⁠.

Fig. 7.

E-retailer’s contract choice when |$c=0.1$|⁠.

Fig. 8.

E-retailer’s contract choice when |$c=0.2$|⁠.

Fig. 9.

Pareto zone considering demand uncertainty.

Combined with the analysis in Sections 4 and 5, in order to find which contract is better in advance selling, we use numerical analysis to determine the Pareto regions of different contracts in Figs 5 and 6.

It is not difficult to find that if the advance selling is adopted, it is much easier to achieve Pareto improvement in the supply chain under the resale contract than under the agency contract (the Pareto region under the agency contract is larger than that under the resale contract in Figs 5 and 6). That is, it is better to apply the agency contract than the resale contract when the supply chain members consider advance selling to launch new products. Many scholars have also found that the agency contract is much better than the resale contract at mitigating the double marginalization in the supply chain (Abhishek et al., 2015; Geng et al., 2018; Li et al., 2019).

Regarding real-world conditions, we explain why the advance selling in the Double Eleven Festival has become increasingly popular in recent years and the scale of its advance selling is larger than those on other platforms that adopt resale contracts (Sun et al., 2018). Tmall is one of the largest e-commerce trading platforms in China that uses agency contracts to cooperate with his suppliers. Tmall’s Double 11 presale period in 2018 involved 71 brands with a gross merchandise value that exceeded $14.37 million. In total, 15 of those 71 brands were from the apparel branch in Tmall, e.g. Converse, Nike, Puma, Adidas and Lining. Both Tmall and the manufacturers are willing to achieve higher profits through advance selling.

Further, the e-retailer considers not only the consumers’ loss aversion attitude but also the characteristics of the products when she selects the contracts. By comparing the profits of the e-retailer under these two contracts, Proposition 6.2 is given as follows.

Proposition 6.2

When both agents in the supply chain adopt the advance selling mode to release a new product, thresholds exist regarding the order fulfilment cost |$\bar{c}$| and the proportion of the informed consumers in the market |$\bar{\lambda }$|⁠. (1) When |$c\leq{\bar{c}}$| and |$\lambda \geq \max \{\bar{\lambda }^{W},\bar{\lambda }\}$|⁠, the e-retailer prefers the agency contract. (2) When |$c>\bar{c}$| and |$\bar{\lambda }^{W}<\lambda <{\bar{\lambda }}$|⁠, the e-retailer prefers the resale contract.

The proofs are shown in Appendix 7.

To more clearly represent the optimal contract choice of the e-retailer under different parameter ranges in Proposition 6.2 and Figs 7 and 8 has been plotted to show the e-retailer’s contract choices under the common Pareto zone in the advance selling mode. In Figs 7 and 8, because the thresholds are within the scope of the conditions in Proposition 6.2(1) and (2) and |$\bar{\lambda }^{W}$| is always larger than |$\bar{\lambda }^{A}$|⁠, i.e. when |$\lambda \geq{\bar{\lambda }^{W}}$|⁠, both agents can achieve Pareto improvement under two contracts. As shown in Fig. 7, when the order fulfilment cost |$c$| is small, the e-retailer always prefers the agency contract. Meanwhile, as shown in Fig. 8, in most cases, the e-retailer also prefers the agency contract, but when order fulfilment cost |$c$| is relatively large and when |$\bar{\lambda }^{W}<\lambda <{\bar{\lambda }}$|⁠, the e-retailer chooses the resale contract.

We can see that in most cases, under the common Pareto zone, the e-retailer chooses the agency contract to conduct advance selling. When the order fulfilment cost is small, the e-retailer prefers to choose the agency contract to release new products through advance selling. When the order fulfilment cost is large, she begins to consider the resale contract when consumers’ loss aversion is large, which explains why JD.com, one of the largest B2C e-retailers in China, has tended to sell products in advance through its self-operated model in recent years. JD.com owns two selling channels: the self-operated channel with resale contracts and the third-party channel with agency contracts. When new products such as mobile phones, computers and furniture are released, JD.com often advance sells products through self-operated channels. These products have higher order fulfilment costs due to their own value characteristics and logistics characteristics, making it more beneficial for e-retailers to choose the resale contract (Tian et al., 2018). This effect occurs because as the order fulfilment cost and consumers’ loss aversion increase, the e-retailer obtains a lower profit margin and seeks to obtain pricing power for consumers to cover the negative impact of high order fulfilment costs on her own profits.

7. Extension

7.1 Considering demand uncertainty

In the above analysis, we assume that the market demand is determined only by consumers’ utilities. However, the demand is often influenced by many factors that cause demand uncertainty, which impacts the pricing decisions and the e-retailer’s contract selection in the supply chain. Consistent with Petruzzi & Dada (1999) and Pan et al. (2009), we consider demand uncertainty to extend our model and assume the real demand functions |$X_{t}$|⁠, where |$t=1,2$|⁠, in the two periods are as follows:

$$\begin{align*} & \left\{\begin{array}{l} X_{1}=D_{1}\left(p_{1}\right)+\xi_{1} \\ X_{2}=D_{2}\left(p_{2}\right)+\xi_{2}, \end{array}\right. \end{align*}$$

where |$D_{1}\left (p_{1}\right )$| and |$D_{2}\left (p_{2}\right )$| respectively describe the functions that capture the interdependency between demand and price, which can be calculated using consumers’ utilities in two periods. |$\xi _{1}$| and |$\xi _{2}$| are the random variables that are independent of price, where |$\xi _{1} \sim N\left (0, \sigma _{1}^{2}\right )$| and |$\xi _{2} \sim N\left (0, \sigma _{2}^{2}\right )$|⁠. The market demand in the two periods can be regarded as the sum of the price-dependent demand and the price-independent demand, which reflects the uncertainty of consumers’ demand (Pan et al., 2009). For the decision maker who determines the advance selling price and the spot selling price, he or she specifies a minimum target sales volume |$q_{1}=D_{1}\left (p_{1}\right )-\mu \sigma _{1}$| and |$q_{2}=D_{2}\left (p_{2}\right )-\mu \sigma _{2}$| in two periods, which are used as the turning point for price decline, where |$\mu $| is a positive parameter of both members, and we assume that both have the same |$\mu $| to simplify the calculation. If the realized demands during the two periods satisfy |$X_{t}>q_{t}, t=1,2$|⁠, then the sales volume is |$q_{t}$| and the ordering quantity is also |$q_{t}$|⁠. Otherwise, the sales volume is |$X_{t}$| and the ordering quantity is |$q_{t}$|⁠.

We use a similar calculation method as that in Sections 4 and 5, as shown in Appendix 8. After setting |$\mu =0.1,\sigma _{1}=0.1,\sigma _{2}=0.1,c=0.1$| we can draw the Pareto improvement if advance selling is performed in the supply chain compared with that with no advance selling under different contracts considering the demand uncertainty, as shown in Fig. 9.

From Fig. 9, we can conclude that the Pareto zone considering demand uncertainty is similar to that in Fig. 5. The difference is that the proportion of the Pareto zone under the agency contract in Fig. 9 is larger than that in Fig. 5. Thus, when demand is uncertain, both members prefer the agency contract, and this is in accordance with the real-world phenomenon adopted by the larger e-platforms. This finding shows that our model is robust when we consider the demand uncertainty.

Further, we analyse the conditions under which both agents can realize Pareto improvements from advance selling. We surprisingly find that with the demand uncertainty, the e-retailer always chooses the agency contract to avoid the risk, even though the risk is very low. This occurs because under the resale contract, the products may not all be sold in the market; however, the e-retailer has to pay the wholesale price for all products, including the unsold products. Therefore, to avoid the risk from the demand uncertainty, the e-retailer always chooses the agency contract to transfer the risk to the manufacturers.

7.2 Considering consumers’ heterogeneous loss aversion

$$\begin{align*} & \left\{\begin{array}{l} U_{1 L}=E\left[v-p_{1}-\beta_{L} F\left(p_{1}\right)\right] \\ U_{1 H}=E\left[v-p_{1}-\beta_{H} F\left(p_{1}\right)\right] \\ U_{2}=v-p_{2}. \end{array}\right. \end{align*}$$

Then, there are three potential situations in our model. When |$U_{1 H}> \max \left \{U_{2}, 0\right \}$|⁠, all informed consumers buy in the advance selling period. When |$U_{1 H} \leq \max \left \{U_{2}, 0\right \} \leq U_{1 L}$|⁠, only informed consumers with a low degree of loss aversion buy in the advance selling period, and the informed consumers with high degrees of loss aversion wait, which is the same as that for the uninformed consumers. When |$U_{1 L} < \max \left \{U_{2}, 0\right \}$|⁠, all informed consumers wait until the spot selling period. Therefore, the pricing decisions by consumers can be classified into three situations. The calculation process is given in Appendix 9. After setting |$c=0.2,\beta _{L}=0.01,\beta _{H}=0.02$|⁠, we obtain the Pareto zone under the two contracts and illustrate the results in Fig. 10.

Fig. 10.

Pareto zone considering consumers’ heterogeneous loss aversion.

There are two pricing strategies for informed consumers in the advance selling period: when |$\lambda \geq \lambda _{0}^{\prime }$| under the resale contract and when |$\lambda \geq \lambda _{0}$| under the agency contract, all informed consumers buy the product in the advance selling period; otherwise, only consumers with a low degree of loss aversion |$\beta _L$| buy the product in the advance selling period. From Fig. 10, we can see that when considering a heterogeneous degree of loss aversion for consumers, a Pareto improvement can be achieved easily under the agency contract compared with that under the resale contract. This condition is similar to that in Fig. 5, and we can show that the result is robust.

After setting |$c=0.2,\beta _{L}=0.01,\beta _{H}=0.02$|⁠, Fig. 11 is plotted to show the e-retailer’s contract choice under the common Pareto zone in the advance selling mode considering consumers’ heterogeneous degree of loss aversion.

Fig. 11.

E-retailer’s contract choice with consumers’ heterogeneous loss aversion.

http://www.syntun.com/about.html

The conclusion is similar to that in Proposition 6.2. That is, in most cases, the e-retailer chooses the agency contract, and when |$\lambda $| is smaller than a threshold, she chooses the resale mode. However, as the proportion of consumers with |$\beta _L$| (low loss aversion) increases, decision makers in the supply chain change their pricing strategy from advance selling for all informed consumers to only advance selling for consumers with |$\beta _L$|⁠. This decision is made because their marginal profits are higher when advance selling occurs only for consumers with |$\beta _L$|⁠. When the proportion of these consumers increases, the total profit of advance selling only for consumers with |$\beta _L$| is greater. When choosing to conduct advance selling only for low loss aversion consumers, the agency contract is better than the resale contract for the e-retailer.

8. Conclusion

With the rapid development of e-commerce technology, advance selling is becoming more popular among merchants and consumers. Many e-retailers and manufacturers have been willing to launch new products and conduct festival promotions through advance selling under different contracts. Finding the pricing strategies under different contracts and identifying the more suitable contract for the supply chain members in advance selling mode are meaningful for both academic studies and real-world decision making. Considering consumers’ loss aversion in advance selling under different supply chain contracts, this paper establishes Stackelberg game models under the resale contract and the agency contract and obtains the following conclusions.

(1) The supply chain conducts advance selling when the upstream member gives a concession on the wholesale price or the proportional fee rate because the upstream member has more pricing choice modes by advance selling and the concession can earn more demand and more profit. As consumers’ loss aversion increases, supply chain decision makers set lower prices to cater to consumers. The consumers’ loss aversion has a positive impact on the profit of the member who directly sets the price for consumers, but it has a negative impact on the indirect pricing side because of the concession of the upstream member by conducting advance selling. The bad effect of consumers’ loss aversion shifts to the upstream of the supply chain.

(2) Under different supply chain contracts, advance selling can achieve a Pareto improvement in the supply chain when the loss aversion is low enough and the number of informed consumers is sufficiently large. The lower loss aversion and larger number of informed consumers can result in a higher price for consumers and a lower concession of the upstream member.

(3) When considering different supply chain contracts, we find that the agency contract more easily achieves a Pareto improvement from advance selling in the supply chain than the resale contract, which explains why more merchants are willing to advance sell through the e-commerce platform using agency contracts, such as Tmall. When the order fulfilment cost is large, it is more advantageous for the e-retailer to choose the resale contract for advance selling, which explains why JD.com conducts advance selling through his self-operated channel rather than his third-party platform. When considering the demand uncertainty or the heterogeneous loss aversion degree of consumers, the results do not change.

Although our findings have some management insights for e-retailers and manufacturers when using advance selling to release new products under different supply chain contracts considering consumers’ loss aversion, our research still has some shortcomings. For example, we assume that the order fulfilment costs are the same for the manufacturer and the e-retailer; however, the costs can be different because of the different scale of the executor. In future research, it may be worthwhile to consider the different order fulfilment costs for the supply chain members and the economies of scale for the order fulfilment costs.

9. Appendix

The detail process is shown in the electronic companion.

Funding

This research is supported by Major Program of the National Social Science Foundation of China (Grant No. 18ZDA060).

Footnotes

1

2

https://www.cnbc.com/2019/09/19/huawei-mate-30-announced-specs-price-android.html

References

Abhishek

,

V.

,

Jerath

,

K.

&

Zhang

,

Z. J.

(

2015

)

Agency selling or reselling? Channel structures in electronic retailing

.

Manag. Sci.

,

62

,

2259

–

2280

.

Agatz

,

N. A.

,

Fleischmann

,

M.

&

Van Nunen

,

J. A.

(

2008

)

E-fulfillment and multi-channel distribution—a review

.

European J. Oper. Res.

,

187

,

339

–

356

.

Asgari

,

N.

,

Nikbakhsh

,

E.

,

Hill

,

A.

&

Farahani

,

R. Z.

(

2016

)

Supply chain management 1982–2015: a review

.

IMA J. Manag. Math.

,

27

,

353

–

379

.

Baron

,

O.

,

Hu

,

M.

,

Najafi-Asadolahi

,

S.

&

Qian

,

Q.

(

2015

)

Newsvendor selling to loss-averse consumers with stochastic reference points

.

Manuf. Serv. Oper. Manag.

,

17

,

456

–

469

.

Cachon

,

G. P.

(

2003

)

Supply chain coordination with contracts

.

Handbooks in Operations Research and Management Science

, vol. 11. Philadelphia, USA: Wharton School of Business, University of Pennsylvania, pp.

227

–

339

.

Cachon

,

G. P.

&

Swinney

,

R.

(

2009

)

Purchasing, pricing, and quick response in the presence of strategic consumers

.

Manag. Sci.

,

55

,

497

–

511

.

Cachon

,

G. P.

&

Feldman

,

P.

(

2017

)

Is advance selling desirable with competition?

Market. Sci.

,

36

,

214

–

231

.

Chiang

,

W. Y. K.

,

Chhajed

,

D.

&

Hess

,

J. D.

(

2003

)

Direct marketing, indirect profits: a strategic analysis of dual-channel supply-chain design

.

Manag. Sci.

,

49

,

1

–

20

.

Cho

,

S. H.

&

Tang

,

C. S.

(

2013

)

Advance selling in a supply chain under uncertain supply and demand

.

Manuf. Serv. Oper. Manag.

,

15

,

305

–

319

.

Geng

,

X.

,

Tan

,

Y.

&

Wei

,

L.

(

2018

)

How add-on pricing interacts with distribution contracts

.

Prod. Oper. Manag.

,

27

,

605

–

623

.

Guo

,

X.

,

Cheng

,

L.

&

Liu

,

J.

(

2019

)

Green supply chain contracts with eco-labels issued by the sales platform: profitability and environmental implications

.

Int. J. Prod. Res.

,

58

,

1485

–

1504

.

Ghadimi

,

S.

,

Szidarovszky

,

F.

&

Farahani

,

R. Z.

(

2013

)

Coordination of advertising in supply chain management with cooperating manufacturer and retailers

.

IMA J. Manag. Math.

,

24

,

1

–

19

.

He

,

B.

,

Gan

,

X.

&

Yuan

,

K.

(

2019

)

Entry of online presale of fresh produce: a competitive analysis

.

European J. Oper. Res.

,

272

,

339

–

351

.

Huang

,

K. L.

,

Kuo

,

C. W.

&

Shih

,

H. J.

(

2017

)

Advance selling with freebies and limited production capacity

.

Omega

,

73

,

18

–

28

.

Kahneman

,

D.

(

1979

)

Prospect theory: an analysis of decisions under risk

.

Econometrica

,

47

,

278

.

Kapner

,

S.

(

2014

)

How the web drags on some retailers

.

The WallStreet Journal. Available at http://www.wsj.com/articles/how-the-web-drags-on-some-retailers-1417477790 (accessed date 30 November 2015)

.

Karle

,

H.

&

Möller

,

M.

(

2018

)

Selling in advance to loss averse consumers

.

Int. Econ. Rev.

,

61

, 441–468.

Kauffman

,

R. J.

,

Li

,

T.

&

Van Heck

,

E.

(

2010

)

Business network-based value creation in electronic commerce

.

Int. J. Electron. Commer.

,

15

,

113

–

144

.

Khouja

,

M.

&

Zhou

,

J.

(

2015

)

Channel and pricing decisions in a supply chain with advance selling of gift cards

.

European J. Oper. Res.

,

244

,

471

–

489

.

Li

,

Y.

,

Shan

,

M.

&

Li

,

M. Z.

(

2016

)

Advance selling decisions with overconfident consumers

.

J. Ind. Manag. Optim.

,

12

,

891

–

905

.

Li

,

Z.

,

Ho

,

Y. C.

,

Nan

,

G.

&

Li

,

M.

(

2019

)

Agency or resale: effects of a platform-performance investment for frenemy platforms

.

Decis. Support Syst.

,

124

,

113098

.

Lim

,

W. S.

&

Tang

,

C. S.

(

2013

)

Advance selling in the presence of speculators and forward-looking consumers

.

Prod. Oper. Manag.

,

22

,

571

–

587

.

Lin

,

Z.

&

Heng

,

C. S.

(

2015

)

The paradoxes of word of mouth in electronic commerce

.

J. Manag. Inf. Syst.

,

32

,

246

–

284

.

Ma

,

S.

,

Lin

,

J.

&

Zhao

,

X.

(

2016

)

Online store discount strategy in the presence of consumer loss aversion

.

Int. J. Prod. Econ.

,

171

,

1

–

7

.

Ma

,

S.

,

Li

,

G.

,

Sethi

,

S. P.

&

Zhao

,

X.

(

2019

)

Advance selling in the presence of market power and rise-averse consumers

.

Decision Sci.

,

50

,

142

–

169

.

Nie

,

J.

&

Zhang

,

J.

(

2017

)

Distribution channel selection considering advertising productiveness

.

IMA J. Manag. Math.

,

28

,

437

–

450

.

OpenURL Placeholder Text

Pan

,

K.

,

Lai

,

K. K.

,

Liang

,

L.

&

Leung

,

S. C.

(

2009

)

Two-period pricing and ordering policy for the dominant retailer in a two-echelon supply chain with demand uncertainty

.

Omega

,

37

,

919

–

929

.

Petruzzi

,

N. C.

&

Dada

,

M.

(

1999

)

Pricing and the newsvendor problem: a review with extensions

.

Oper. Res.

,

47

,

183

–

194

.

Safari

,

E.

,

Babakhani

,

M.

,

Sadjadi

,

S. J.

,

Shahanaghi

,

K.

&

Naboureh

,

K.

(

2015

)

Dynamic pricing of a web service in an advance selling environment

.

Math. Probl. Eng.

,

2015

, 783149.

OpenURL Placeholder Text

Scholz

,

M.

,

Dorner

,

V.

,

Franz

,

M.

&

Hinz

,

O.

(

2015

)

Measuring consumers’ willingness to pay with utility-based recommendation systems

.

Decis. Support Syst.

,

72

,

60

–

71

.

Shi

,

X.

,

Dong

,

C.

&

Cheng

,

T. C. E.

(

2018

)

Does the buy-online-and-pick-up-in-store strategy with pre-orders benefit a retailer with the consideration of returns?

Int. J. Prod. Econ.

,

206

,

134

–

145

.

Shugan

,

S. M.

&

Xie

,

J.

(

2005

)

Advance-selling as a competitive marketing tool

.

Int. J. Res. Market.

,

22

,

351

–

373

.

Su

,

B. C.

(

2007

)

Consumer e-tailer choice strategies at on-line shopping comparison sites

.

Int. J. Electron. Commer.

,

11

,

135

–

159

.

Sun

,

Y.

,

Siqin

,

T.

&

Mu

,

L.

(

2018

)

Advance selling with part prepayment and consumer returns

.

Math. Probl. Eng.

,

2018

, 2934698.

OpenURL Placeholder Text

Tang

,

W.

&

Ang

,

S.

(

2017

)

Advance selling with part payment for new to-be-released products

.

J. Model. Manag.

,

12

,

455

–

474

.

Tian

,

L.

,

Vakharia

,

A. J.

,

Tan

,

Y.

&

Xu

,

Y.

(

2018

)

Marketplace, reseller, or hybrid: strategic analysis of an emerging e-commerce model

.

Prod. Oper. Manag.

,

27

,

1595

–

1610

.

Wang

,

R. F.

,

Li

,

B.

&

Li

,

Z. H.

(

2018

)

Selection policy for a manufacturer’s online channel: do it oneself or cooperate with retailers

.

IMA J. Manag. Math.

,

29

,

393

–

414

.

Wei

,

M. M.

&

Zhang

,

F.

(

2018

)

Advance selling to strategic consumers: preorder contingent production strategy with advance selling target

.

Prod. Oper. Manag.

,

27

,

1221

–

1235

.

Wong

,

H.

&

Lesmono

,

D.

(

2017

)

Conflicting quality attributes, distribution channel structure and product line length in quality-based segmentation

.

IMA J. Manag. Math.

,

30

,

125

–

147

.

Xu

,

M.

,

Tang

,

W.

&

Zhou

,

C.

(

2019

)

Procurement strategies of e-retailers under different logistics distributions with quality- and service-dependent demand

.

Electron. Commer. Res. Appl.

,

35

,

100853

.

Zennyo

,

Y.

(

2020

)

Strategic contracting and hybrid use of agency and wholesale contracts in e-commerce platforms

.

European J. Oper. Res.

,

281

,

231

–

239

.

Zhao

,

X.

&

Stecke

,

K. E.

(

2010

)

Pre-orders for new to-be-released products considering consumer loss aversion

.

Prod. Oper. Manag.

,

19

,

198

–

215

.

Zhao

,

X.

,

Pang

,

Z.

&

Stecke

,

K. E.

(

2016

)

When does a retailer’s advance selling capability benefit manufacturer, retailer, or both?

Prod. Oper. Manag.

,

25

,

1073

–

1087

.