RETRACTED ARTICLE: Research on heterogeneous customer hotel supply chain channel selection model based on game theory

Abstract

In the context of the epidemic of New Coronavirus, customers have a heterogeneous preference for hotel consumption channels. Based on this, the hotel supply chain channel selection model was established, and the wholesale of hotels and online travel agencies (OTA) under the single-channel and dual-channel structures was analyzed. The optimal pricing under the cooperation mode with the agent provides a basis for the hotel’s channel and business model selection decision. On the basis of theoretical derivation, the use of Ctrip data to conduct numerical analysis and research found that: the choice of hotel channel structure and cooperation mode is affected by a variety of factors; when the hotel service capacity is low, the hotel will not cooperate with OTA, only Implement single-channel sales through direct sales channels; conversely, hotels will tend to cooperate with OTAs to implement dual-channel sales; when online shopping customers have a higher level of acceptance of online channels and a higher proportion or a lower commission rate, the agency model is better than wholesale Mode; otherwise, the wholesale mode is most beneficial to the hotel.The analysis shows that when the hotel service capacity is lower, the hotel only conducts direct sales through a single channel; otherwise, the hotel will tend to cooperate with OTA to sell as many rooms as possible through dual channels.

1 Introduction

With the continuous development of information and network technology, it is more convenient for customers to travel, more and more customers accept and get used to booking their flights and hotels Guo et al. (2021), for this reason, more and more hotels have begun to sell guest rooms to terminal customers with the OTA (such as Ctrip, eLong, etc.) network platform, for example, 35,000 hotels in China have sold hotel rooms to terminal passengers through the network platform of Ctrip. At present, the OTA website has become one of the main sales channels of many small and medium-sized hotel enterprises in China, and it is an effective supplement to the traditional channels of these small and medium-sized hotel enterprises (Gupta and Jana 2021; Alaybeyoglu and Kuntman 2020; Ylmaz and Erdem 2021; Li et al. 2021).

Small and medium-sized hotel enterprises can increase the sales volume of guest rooms with OTA’s network platform and maintain a high hotel occupancy rate, at the same time; however, small and medium-sized hotel enterprises and OTA have also created many problems in the cooperation process and face some new challenges, which mainly include (Kim 2021; Lee et al. 2013):

(1) Sales pricing conflict between hotel direct channel and OTA network channel; (2) Unreasonable interest distribution between hotel and OTA; (3) commercial modes of hotel and OTA cooperation are not perfect; as a result, Choice International Hotel abandoned its cooperation with Expedia.com in 2009. At present, the hotel and OTA mainly cooperate through two modes: wholesale mode and agent mode, both wholesale mode and agent mode have their own advantages and disadvantages for the hotel and the OTA. Under the wholesale mode, OTA first purchases the guest room from the hotel at wholesale and then sells them to the customers; therefore, the OTA needs to bear the inventory; risk of the unsold guest rooms that has been purchased, under the agent mode, the OTA charges the hotel agreed commission for each room booked through its own network channel, and the hotel assumes the inventory; risk of unsold room, so the main research problems in this paper are: under what conditions, should hotels increase OTA network channels to sell guest rooms? If the hotel chooses to cooperate with OTA, what cooperation mode should hotel cooperate with? (Wang and Shen 2004; Chiang and Hess 2003; Cattani et al. 2006; Liu and Li 2013).

Due to the booming development of e-commerce in recent years, whether or not to increase network distribution channels in the original traditional channels has attracted wide attention. Chiang et al. analyzed the influence on their own direct channels after manufacturers increased network channels, they pointed out that manufacturers are competing with retailers by introducing network channels, thereby reducing retailers’ pricing and reducing double marginal effects, thus achieving win-win of manufacturers and retailers. Similarly, the literatures study the influence of the introduction of direct channels on traditional retailers’ pricing strategies, and point out that the introduction of direct channels is not always harmful to traditional retailers. There is also some literature that considers the influence of consumer-related factors on manufacturers’ channel choices, such as literature (Ryan et al. 2012; Guo et al. 2008; Tsay and Agrawal 2004; Hendershott and Jie 2010; Smith et al. 2010). Chen et al. (2008). studied the optimal applicable environment for dual channels Chen et al. (2008) (such as the cost of managing network channels, the convenience of retailers, and the characteristics of products) when the manufacturer’s network channel competes with the retailer’s retail channel through service. Pu et al. (2014). considered physical store’ horizontal preference and vertical preference on the supply chain equilibrium strategy Pu et al. (2014). Cai (2010) discussed the choice of four channel modes for suppliers and retailers in the case of cooperation or no cooperation Cai (2010). They pointed out that the choice of channel mode for suppliers and retailers depends on the needs of each channel, the cost of channel operation and the alternatives degree of channel. However, none of the above references consider the influence of the manufacturers’ service ability on their channel selection and the heterogeneity of the customer’s acceptance for the network channel.

In addition, cooperation mode literature on manufacturers and retailers mainly focuses on the optimal decision of both parties under a certain cooperation mode at present; for example, Rubinstein et al. (1987) compared the supply chain efficiency consisting of many customers, retailer and intermediate institutions in agent mode and non-agent mode Prakash et al. (2021). Wang et al. (2009) studied the optimal conditions and optimal pricing for the cooperation between suppliers and retailers which provide monopoly services under the Name-Your-Own-Price mode (a form of wholesale mode) Esteves (2021). Lee and Chu (2010) explored the optimal decision of suppliers and retailers under two different agent strategies, pointed out that suppliers’ control of inventory; would be beneficial to suppliers and retailers Fang et al. (2020). However, these studies ignored the heterogeneous customer’s choice behaviors and the important influence of the manufacturer’s own service ability on the cooperation mode, and did not compare the influence of different cooperation modes on decision-making.

The research similar to this paper is research of Hsiao and Chen (2014), they pointed out when manufacturers and retailers should introduce network channels and the conditions and pricing strategies when they need to introduce network channels Esteves (2021). Tan et al. (2014) studied the optimal pricing problems of publishers and retailers under the agent mode, wholesale mode and fixed price mode, and found that the digital product agent mode can alleviate the double marginalization in the long run Chai et al. (2021). There are also related researches in China, for example, Cao et al. (2015). studied pricing and channel selection problems under the competition of brands and channels. But this study did not take into account the heterogeneity of different customers Cao et al. (2015). Shen et al. (2013), considering the dual heterogeneity of customer channel preferences and retailer acceptance, studied the retailer’s channel mode selection and pricing problems of different channels under the condition of horizontal competition of monopolistic retailers and duopoly retailers Shen et al. (2013). However, the study only considered that the customer’s maximum acceptance of the network channel is the same as the physical channel, and did not consider the influence of the retailer’s limited service capacity on the retailer’s channel mode choice.

This paper builds on the above research and is structured as follows: 1. Considering the dual heterogeneity of customer channel preferences and acceptance levels of online channels, we establish the case type of hotel supply chain channel selection, 2. On this basis, we analyse the optimal pricing of hotels and online travel agencies under single and dual channel structures in the wholesale and agency cooperation models respectively, 3. Finally, we analyse, through specific numerical arithmetic examples, the impact of the hotel’s service capacity, the level of customer acceptance of OTA online channels and the impact of the proportion of different types of customers on the hotel’s optimal decision.

2 Selection mode of hotel supply chain channel

2.1 Problem description

In a hotel and a hotel supply chain consisting of an OTA, the hotel not only carry out single-channel direct selling through its own store (mode A), but also cooperates with OTA to carry out dual channel sales through its network channel (mode B), as shown in the Fig. 1. In reality, consumers have individual preferences, and differences in preferences are consumer heterogeneity. With the development of online technology, this heterogeneity is becoming more and more evident and does have an impact on business competition. Because consumers have different buying habits, namely customers have preferences for channels, when dual channel sales are adopted; there will be demand competition among different channels. Moreover, because the number of hotel rooms is certain in a short period of time, therefore, considering the customers’ heterogeneity, the limited service capacity of the hotel and the following sequence of events: (1) the hotel should takes the goal of maximizing its own profits as goal to choose the channel mode, namely, single-channel direct selling mode or dual-channel mode. If the hotel selects the single-channel direct selling mode, then the hotel needs to set the optimal direct channel price; (2) If the hotel selects the dual channel mode, then the hotel needs to decide the cooperation mode with OTA at this time (wholesale mode or agent mode). Under the wholesale mode, the hotel needs to set the optimal wholesale price w and direct channel price $p_{\text {H}}$, and OTA sets the optimal online sales price $p_{\text {O}}$. Under the agent mode, under the condition of a given commission rate, the hotel needs to set the optimal direct channel price $p_{\text {H}}$, and the OTA sets the optimal online sales channel price $p_{\text {O}}$.

Fig. 1

The supply chain structure of direct channel and the OTA’s online channel

2.2 Channel demand function

Assuming that the customer is heterogeneous, namely different customers have differences in maximum payment willingness V for booking room through direct selling or online channel, and they are evenly distributed in [0, 1] without loss of generality, assuming that the potential number of customers in the market is 1. Moreover, customers are divided into two categories: one is online shopping customers (remarked as type H), which accounts for $\alpha \in [0,1]$ proportion in the whole market; the other is traditional customers (remarked as type L), which accounts for $1-\alpha$ proportion in the whole market, and these two types of customers’ payment willingness for the room reserved from the direct channel, namely the acceptance level of all customers to the direct channel is 1.

Assuming that type H customers pay attention to convenience and speed, and think that there is no difference in the rooms booked through direct selling and online channels, and it is convenient and quick to book through network channels, therefore, their acceptance level $\theta ^{\text {H}}$ for OTA’s network channels is high ($\theta ^{\text {H}}>1)$, then this type of customers’ payment willingness booked from the network channel is $\theta ^{\text {H}}V$; type L customers pay attention to the quality of the room and service, think that the online booking cannot observe the actual situation of the guest room, there is a booking risk, so their acceptance level $\theta ^{\text {L}}$ for the OTA network channel is low ($0<\theta ^{\text {L}}<1)$, then this type of customers’ payment willingness booked from the network channel is $\theta ^{\text {L}}V$.

The customer utility theory is used to describe the customer’s selection behaviors for different channels, assuming that i customers obtain customer utility through direct selling and online channels, they are $U_{\text {H}}^i -V-p_{\text {H}}$, $U_{\text {OTA}}^i=\theta ^iV-p_{\text {O}}$, $i=H,L$, respectively. These two types of customers are completely rational, and their buying behaviors depend on the utility value, only when the customer utility is greater than 0, the customer will purchase, with the goal of maximizing utility, choose the channel that can bring the most utility to them to make a reservation. There are three conditions for type H customers:

• 1. $\xi =(p_0-p_{\text {H}})/(\theta ^{\text {H}}-1)$, when $U_{\text {H}}^{\text {H}} \geqslant U_{\text {OTA}}^{\text {H}}$, $U_{\text {H}}^{\text {H}} \geqslant 0$, namely $p_{\text {H}} \leqslant V\leqslant \xi$, the customers choose to purchase through the hotel direct channel. If V is non-empty, then require $p_{\text {H}} \leqslant \xi$ and $p_{\text {H}} \leqslant 1$, namely $p_{\text {O}} \geqslant \theta ^{\text {H}}p_{\text {H}}$ and $p_{\text {H}} \leqslant 1$;

• 2. When $U_{\text {H}}^{\text {H}}<U_{\text {OTA}}^{\text {H}}$, $U_{\text {OTA}}^{\text {H}} \geqslant 0$, namely $V>\max \{\xi , {p_{\text {O}} }/{\theta ^{\text {H}}}\}$, the customers choose to purchase through the network channel. If V is non-empty, then require $\xi <1$ and ${p_{\text {O}} }/{\theta ^{\text {H}}}<1$, namely $p_{\text {O}}<p_{\text {H}}+\theta ^{\text {H}}-1$ and $p_{\text {O}}<\theta ^{\text {H}}$;

• 3. Otherwise, give up buying.

There are also three conditions for type L customers:

• 1. $\zeta ={(p_0-p_{\text {H}})}/{(\theta ^{\text {L}}-1)}$, when $U_{\text {H}}^{\text {L}} \geqslant U_{\text {OTA}}^{\text {L}}$, when $U_{\text {H}}^{\text {L}} \geqslant 0$, namely when $V\geqslant \max \{\zeta , p_{\text {H}}\}$, the customers choose to purchase through the hotel direct channel. If V is non-empty, then require $\zeta \leqslant 1$ and $p_{\text {H}} \leqslant 1$, namely $p_{\text {O}} \geqslant p_{\text {H}}+\theta ^{\text {H}}-1$ and $p_{\text {H}} \leqslant 1$;

• 2. When $U_{\text {H}}^{\text {L}}<U_{\text {OTA}}^{\text {L}}$, when $U_{\text {OTA}}^{\text {L}} \geqslant 0$, namely when ${p_{\text {O}} }/{\theta ^{\text {L}}}<V<\zeta$, the customers choose to purchase through the network channel. If V is non-empty, then require ${p_{\text {O}} }/{\theta ^{\text {L}}}<\zeta$ and ${p_{\text {O}} }/{\theta ^{\text {L}}}<1$, namely $p_{\text {O}}<\theta ^{\text {L}}p_{\text {H}}$ and $p_{\text {O}}<\theta ^{\text {L}}$;

• 3. Otherwise, give up buying, therefore, according to the above constraint conditions, the requirements can be divided into the following five zones, as shown in Fig. 2.

Fig. 2

the feasible zones for online price $p_{\text {O}}$ and direct price $p_{\text {H}}$

Zone I: $p_{\text {O}} \geqslant p_{\text {H}}+\theta ^{\text {H}}-1$, then $U_{\text {H}}^i \geqslant U_{\text {OTA}}^i$, $i=H,L$, all customers will only book guest rooms through the hotel direct channel.

Zone II: $\theta ^{\text {H}}p_{\text {H}} \leqslant p_{\text {O}} \leqslant p_{\text {H}}+\theta ^{\text {H}}-1$, then, type H customers do not book rooms through the network channel, only book through the hotel direct channel; for type H customers, $\alpha (\xi -p_{\text {H}})$ part customers choose to book through the hotel direct channel, and $\alpha (1-\xi )$ part customers choose to book through the network channel.

Zone III: $\theta ^{\text {H}}p_{\text {H}} \leqslant p_{\text {O}} \leqslant \theta ^{\text {H}}p_{\text {H}}$, then $U_{\text {H}}^{\text {H}} \leqslant U_{\text {OTA}}^{\text {H}}$, $U_{\text {H}}^{\text {L}} \geqslant U_{\text {OTA}}^{\text {L}}$, type H customers only book rooms through online channels, while type L customers only book rooms through hotel direct channels.

Zone IV: $p_{\text {H}}+\theta ^{\text {H}}-1\leqslant p_{\text {O}} \leqslant \theta ^{\text {H}}p_{\text {H}}$, then $U_{\text {H}}^{\text {H}} \geqslant U_{\text {OTA}}^{\text {H}}$, type H customers only book rooms through the network channel; for type L customers, $(1-\alpha )(1-\zeta )$ part customers choose to book rooms through the hotel direct channel, and $(1-\alpha )(\zeta -{p_{\text {O}} }/{\theta ^{\text {L}}})$ part customers choose to book rooms through the network channel.

Zone V: $p_{\text {O}} \leqslant p_{\text {H}}+\theta ^{\text {H}}-1$, then $U_{\text {H}}^i \geqslant U_{\text {OTA}}^i$, $i=H,L$, all customers will only choose to book rooms through the network channel.

Therefore, the potential demand functions of the hotel and OTA can be obtained, as follows:

$$\begin{aligned}&\quad ~(Q_{\text {H}},Q_{\text {OTA}})\\&= \left\{ \begin{array}{@{}ll@{}} (1-p_{\text {H}}, 0),&{}(p_{\text {O}}, p_{\text {H}} )\in \mathrm {I} \\ (\alpha (\xi -p_{\text {H}})+(1-\alpha )(1-p_{\text {H}} ),\alpha (1-\xi )),&{}(p_{\text {O}}, p_{\text {H}} )\in \mathrm {II} \\ ((1-\alpha )(1-p_{\text {H}} ),\alpha (1-p_{\text {O}}/\theta ^{\text {H}})),&{}(p_{\text {O}}, p_{\text {H}} )\in \mathrm {III} \\ ((1-\alpha )(1-\zeta ),\alpha (1-p_{\text {O}}/\theta ^{\text {H}})+(1-\alpha )(\zeta -p_{\text {O}}/\theta ^{\text {H}})),&{}(p_{\text {O}}, p_{\text {H}} )\in \mathrm {IV} \\ (0,\alpha (1-p_{\text {O}}/\theta ^{\text {H}})+(1-\alpha )(1-p_{\text {O}}/\theta ^{\text {H}})),&{}(p_{\text {O}}, p_{\text {H}} )\in \mathrm {V} \\ \end{array}\right. \end{aligned}$$

(1)

2.3 Analysis of single-channel direct selling mode

First of all, when consider the hotel does not cooperate with OTA, only sell rooms to customers through their direct channels (namely Fig. 1, Mode A). At this time, the hotel sets an optimal direct selling price to maximize profit, according to the market demand under the single-channel direct selling mode; the hotel’s decision mode can be obtained.

$$\begin{aligned} \left\{ \begin{array}{@{}l} \mathop {\text {Max}}\limits _{p_{\text {H}} } \pi _{\text {H}}^S (p_{\text {H}} )=p_{\text {H}} (1-p_{\text {H}} ) \\ \text {s.t.}~~1-p_{\text {H}} \leqslant k. \\ \end{array}\right. \end{aligned}$$

(2)

According to the analysis and solving of the hotel’s decision mode, the following conclusions are obtained.

Theorem 1, under the single-channel direct selling mode, the hotel’s optimal direct selling price and corresponding profit are as follows:

• 1. When $k\geqslant {1}/{2}$, $p_{\text {H}}^*={1}/{2}$; $\pi _{\text {H}}^{S*}={1}/{4}$.

• 2. When $k<{1}/{2}$, $p_{\text {H}}^*=1-k$; $\pi _{\text {H}}^{S*}=k(1-k)$.

Theorem 1 shows that if the hotel sells rooms through a single-channel direct selling mode, its optimal direct selling price is affected by the hotel’s service capability. When the hotel’s service capacity is less than half of the market size, namely when the demand exceeds supply, the hotel will set a higher direct selling price to obtain higher profits. Otherwise, the hotel will set a fixed direct selling price to maximize its profit.

2.4 Analysis of dual channel mode

This paragraph assumes that the hotel cooperates with OTA through wholesale mode and agency mode, namely the hotel sells rooms through the dual channel mode (namely Fig. 1, mode B), and the following mainly analyzes the optimal decision and the corresponding optimal profit of the hotel and OTA under different cooperation modes.

2.4.1 Dual-channel wholesale mode

Under the wholesale mode, the hotel and OTA are two independent decision-making bodies, and the decision-making process of the two is a two-stage Stackelberg game process. Among them, the hotel is the leader of the game, and the OTA is the follower of the game. It can be seen from formula (1) that OTA has no demand in interval I, namely the hotel makes the online sales price of OTA meet $p_{\text {O}} \geqslant p_{\text {H}}+(\theta ^{\text {H}}-1)$ by setting a higher wholesale price, this condition is the same as the single-channel direct selling mode, therefore, only the conditions in the zone II, III, IV, and V are discussed below.

Decision-making problem between hotel and OTA under wholesale mode in zone II;

According to the demand function of the hotel and OTA in formula (1), the optimization problem of this supply chain in this zone can be obtained as:

$$\begin{aligned} \left\{ \begin{array}{@{}l} \mathop {\text {Max}}\limits _{p_{\text {H}}, w} \pi _{\text {H}}^M=w\alpha (1-\xi )+p_{\text {H}} (\alpha (\xi -p_{\text {H}})+(1-\alpha )(1-p_{\text {H}} )) \\ \text {s.t.} \\ \mathop {\text {Max}}\limits _{p_{\text {O}} } \pi _{\text {OTA}}^M=(p_{\text {O}} -w)\alpha (1-\xi ) \\ p_{\text {O}} -(\theta ^{\text {H}}-1)\leqslant p_{\text {H}} \leqslant p_{\text {O}}/\theta ^{\text {H}}\leqslant 1,1-p_{\text {H}} \leqslant k. \\ \end{array}\right. \end{aligned}$$

(3)

The following lemma can be obtained from the solution of the optimization problem.

Lemma 1: when the online sales price and direct selling price are met, the optimal pricing and corresponding profit of the hotel and OTA at this time as follows:

• 1. when $k\geqslant \frac{1}{2}$, $p_{\text {H}}^*=\frac{1}{2}$, $w^*=\frac{\theta ^{\text {H}}}{2}$, $p_{\text {O}}^*=\frac{3\theta ^{\text {H}}-1}{4}$, $\pi _{\text {H}}^M=\frac{2+\alpha (\theta ^{\text {H}}-1)}{4}$, $\pi _{\text {OTA}}^M=\frac{\alpha (\theta ^{\text {H}}-1)}{16}$;

• 2. when $\frac{1+\alpha (\theta ^{\text {H}}-1)}{2+4\alpha (\theta ^{\text {H}}-1)}\leqslant k<\frac{1}{2}$ and $\alpha \leqslant \frac{3-2\theta ^{\text {H}}}{3(\theta ^{\text {H}}-1)}$, $p_{\text {H}}^*=\frac{1+3\alpha (\theta ^{\text {H}}-1)}{2+4\alpha (\theta ^{\text {H}}-1)}$, $p_{\text {O}}^*=\frac{\theta ^{\text {H}}(1+3(\theta ^{\text {H}}-1))}{2+4\alpha (\theta ^{\text {H}}-1)}$, $w^*=\frac{1-\alpha (1+\theta ^{\text {H}}-2\theta ^{H^2})}{2+4\alpha (\theta ^{\text {H}}-1)}$ $\pi _{\text {H}}^M=\frac{(1+\alpha (\theta ^{\text {H}}-1))^2}{4+8\alpha (\theta ^{\text {H}}-1)}$, $\pi _{\text {OTA}}^M=\frac{\alpha (\theta ^{\text {H}}-1)(1+\alpha (\theta ^{\text {H}}-1))^2}{4\left( {1+2\alpha (\theta ^{\text {H}}-1)} \right] ^2}$;

• 3. when $\frac{1+\alpha (\theta ^{\text {H}}-1)}{2+4\alpha (\theta ^{\text {H}}-1)}\leqslant k<\frac{1}{2}$ and $\alpha <\frac{3-2\theta ^{\text {H}}}{3(\theta ^{\text {H}}-1)}$, $p_{\text {H}}^*=1-k$, $w^*=\theta ^{\text {H}}+(1-2\theta ^{\text {H}})k$, $p_{\text {O}}^*=\theta ^{\text {H}}(1-k)$, $\pi _{\text {H}}^M=k(1+\alpha (\theta ^{\text {H}}-1)-k(1+2\alpha (\theta ^{\text {H}}-1)))$, $\pi _{\text {OTA}}^M=\alpha (\theta ^{\text {H}}-1)k^2$,

• 4. when $k<(1+\alpha (\theta ^{\text {H}}-1))/(2+4\alpha (\theta ^{\text {H}}-1))$, There is no solution that can meet the conditions.

Lemma 1 shows that in this price range $p_o -(\theta ^{\text {H}}-1)<p_{\text {H}} \leqslant p_o /\theta ^{\text {H}}$, all type L customers choose to purchase through the hotel direct channel, while type H customers can be divided into two parts, a part will be purchased through the network, a part will be purchased through the hotel direct selling; and with the reduction of hotel service capacity, hotel direct selling price, wholesale price and online sales price will increase accordingly; when the hotel service capacity is less than the critical value $(1+\alpha (\theta ^{\text {H}}-1))/(2+4\alpha (\theta ^{\text {H}}-1))$, the hotel will give up cooperation with OTA .

Decision-making issues for hotels and OTA in the wholesale mode of zone III

According to the demand function of the hotel and OTA in the formula (1), the optimization problem of this supply chain in this zone is

$$\begin{aligned} \left\{ \begin{array}{l} \mathop {\text {Max}}\limits _{p_{\text {H}}, w} \pi _{\text {H}}^M=w\alpha (1-\xi )+p_{\text {H}} (\alpha (\xi -p_{\text {H}})+(1-\alpha )(1-p_{\text {H}} )) \\ \text {s.t.} \\ \mathop {\text {Max}}\limits _{p_{\text {O}} } \pi _{\text {OTA}}^M=(p_{\text {O}} -w)\alpha (1-\xi ) \\ p_{\text {O}} -(\theta ^{\text {H}}-1)\leqslant p_{\text {H}} \leqslant p_{\text {O}}/\theta ^{\text {H}}\leqslant 1,1-p_{\text {H}} \leqslant k. \\ \end{array}\right. \end{aligned}$$

(4)

The following lemma can be obtained for solving this optimization problem,

Lemma 2: when the online sales price $p_o$ and direct selling price meet $p_o /\theta ^{\text {H}}\leqslant p_o /\theta ^{\text {L}}$, the optimal pricing and corresponding profit of the hotel and OTA at this time are as follows:

• 1. When $\frac{\theta ^{\text {H}}}{\widetilde{\theta }(\theta ^{\text {H}}+4\theta ^{\text {L}})}<\alpha <1$

  • (a) When $\widetilde{\theta }<\theta ^{\text {L}}$, $\frac{\alpha \widetilde{\theta }}{\theta ^{\text {H}}}\leqslant k\leqslant \frac{\theta ^{\text {L}}+(1-\alpha )\widetilde{\theta }}{2\theta ^{\text {L}}}$, $p_{\text {H}}^*=\frac{\theta ^{\text {H}}(1-k)}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $p_o^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}(1-k)}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $w*=\frac{\theta ^{\text {H}}(\theta ^{\text {L}}(1-2k)-(1-\alpha )\widetilde{\theta })}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $\pi _{\text {OTA}}^M=\frac{\alpha \theta ^{\text {H}}((1-\alpha )\widetilde{\theta }+k\theta ^{\text {L}})}{(\theta ^{\text {H}}-\alpha \widetilde{\theta })^2}$, $\pi _{\text {H}}^M=\frac{\theta ^M(1-k)(1-\alpha )(k\theta ^{\text {H}}-\alpha \widetilde{\theta })-\alpha ((1-\alpha )\widetilde{\theta }+k\theta ^{\text {L}})((1-\alpha )\theta -(1-2k)\theta ^{\text {L}})}{(\theta ^{\text {H}}-\alpha \widetilde{\theta })^2}$;

  • (b) When $\widetilde{\theta }>\theta ^{\text {L}}$ or $k>\frac{\theta ^{\text {L}}+(1-\alpha )\widetilde{\theta }}{2\theta ^{\text {L}}}$ or $k<\frac{\alpha \widetilde{\theta }}{\theta ^{\text {H}}}$, there is no solution that meets the conditions.

• 2. When $\frac{\widetilde{\theta }}{\widetilde{\theta }+(\theta ^{\text {L}})^2}<\alpha <\frac{\theta ^{\text {H}}}{\widetilde{\theta }(\theta ^{\text {H}}+4\theta ^{\text {L}})}$,

  • (a) When $\widetilde{\theta }<\theta ^{\text {L}}$ and $\frac{\alpha ((\theta ^{\text {H}}+\widetilde{\theta })(1-\alpha )(1-3\theta ^{\text {L}})-(\theta ^{\text {L}})^2)}{2(\theta ^{\text {H}}(1-\alpha )+2\alpha (\theta ^{\text {L}})^2)}\leqslant k$, $p_{\text {H}}^*=\frac{\theta ^{\text {H}}(1-\alpha +3\alpha \theta ^{\text {L}})}{2(\theta ^{\text {H}}(1-\alpha )+2\alpha (\theta ^{\text {L}})^2)}$, $w^*=\frac{\theta ^{\text {H}}((1-\alpha )\widetilde{\theta }+\alpha (\theta ^{\text {L}})^2)}{\theta ^{\text {H}}(1-\alpha )+2\alpha (\theta ^{\text {L}})^2}$, $p_o^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha +3\alpha \theta ^{\text {L}})}{2(\theta ^{\text {L}}(1-\alpha )+2\alpha (\theta ^{\text {L}})^2)}$, $\pi _{\text {OTA}}^M=\frac{\alpha \theta ^{\text {H}}((1-\alpha )(\theta ^{\text {H}}+\widetilde{\theta })+\alpha (\theta ^{\text {L}})^2)^2}{4(\theta ^{\text {H}}(1-\alpha )+2\alpha (\theta ^{\text {L}})^2)^2}$, $\pi _{\text {H}}^M=\frac{\theta ^{\text {H}}((1-\alpha (1-\theta ^{\text {L}})^2-4\alpha \widetilde{\theta }(1-\alpha )))}{4(\theta ^{\text {H}}(1-\alpha )+2\alpha (\theta ^{\text {L}})^2)}$;

  • (b) When $\widetilde{\theta }>\theta ^{\text {L}}$ or $k<\frac{\alpha ((\theta ^{\text {H}}+\widetilde{\theta })(1-\alpha )(1-3\theta ^{\text {L}})-(\theta ^{\text {L}})^2)}{2(\theta ^{\text {H}}(1-\alpha )+2\alpha (\theta ^{\text {L}})^2)}$, there is no solution that meets the conditions.

• 3. When $\alpha \leqslant \frac{\widetilde{\theta }}{\widetilde{\theta }+(\theta ^{\text {L}})^2}$, there is no solution that meets the conditions. Among them, $\widetilde{\theta }=\theta ^{\text {H}}-\theta ^{\text {L}}$.

Lemma 2, in this price range, type H customers all choose to buy in the network, type L customers all choose to buy through the hotel direct channel; and only when the hotel service capacity is greater or proportion of type H customers is higher, the hotel is likely to choose to cooperate with OTA.

Decision problem of hotel and OTA under the wholesale mode in zone ?

According to the demand function of hotel and OTA in formula (1), the optimization problem of the supply chain in this zone can be obtained as

$$\begin{aligned} \left\{ \begin{array}{l} \mathop {\text {Max}}\limits _{p_{H,w} } \pi _{\text {H}}^M=w(\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(\zeta -p_o /\theta ^{\text {L}})+p_{\text {H}} (1-\alpha )(1-\zeta )) \\ \text {s.t.}\\ \mathop {\text {Max}}\limits _{p_o } \pi _{\text {OTA}}^M=(p_o -w)(\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(\zeta -p_o /\theta ^{\text {L}})) \\ p_o /\theta ^{\text {L}}<p_{\text {H}} \leqslant p_o (1-\theta ^{\text {L}}),p_o \leqslant \theta ^{\text {L}},\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(1-p_o /\theta ^{\text {L}})\leqslant k. \\ \end{array}\right. \end{aligned}$$

(5)

The following lemma can be obtained for solving this optimization problem.

Lemma 3: when the online sales price $p_o$ and direct selling price $p_{\text {H}}$ meet $p_o /\theta ^{\text {L}}<p_{\text {H}} \leqslant p_o+(1-\theta ^{\text {L}})$, the optimal pricing and corresponding profit of the hotel at this time and OTA are as follows:

• 1. When $A\leqslant 0$,

  • (a) When $k>\lambda _2 (2\lambda _1 )$, $p_o^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}(\lambda _1+(1-\theta ^{\text {L}})(\theta ^{\text {H}}-\alpha \widetilde{\theta }))}{2\lambda _1 (\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $p_{\text {H}}^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}\lambda _1+(2\lambda _1+\theta ^{\text {H}}\theta ^{\text {L}})(\theta ^{\text {H}}-\alpha \widetilde{\theta })}{2\lambda _1 (\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $w^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}}{2(\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $\pi _{\text {OTA}}^M=\frac{\lambda _2 \theta ^{\text {H}}\theta ^{\text {L}}(1-\theta ^{\text {L}})}{4\lambda _1^2 }$, $\pi _{\text {H}}^M=\frac{\lambda _2 \theta ^{\text {H}}\theta ^{\text {L}}}{4\lambda _1 (\theta ^{\text {H}}-\alpha \widetilde{\theta })}$;

  • (b) When $k\leqslant \lambda _2 (2\lambda _1 )$, there is no solution that meets the conditions.

• 2. When $A>0$,

  • (a) When $\alpha \leqslant \frac{\theta ^{\text {H}}}{\theta ^{\text {H}}+2\widetilde{\theta }+2(\theta ^{\text {L}})^2}$ and $\frac{\alpha \widetilde{\theta }}{\theta ^{\text {H}}}\leqslant k\leqslant k_1$ or $\alpha >\frac{\theta ^{\text {H}}}{\theta ^{\text {H}}+2\widetilde{\theta }+2(\theta ^{\text {L}})^2}$ and $\frac{\alpha \widetilde{\theta }}{\theta ^{\text {H}}}\leqslant k\leqslant \frac{\lambda _2 }{\lambda _1 }$, $p_o^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}(1-k)}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $w^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}(\lambda _2 -k\lambda _1 )}{\lambda _2 (\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $p_{\text {H}}^*=\frac{\alpha \widetilde{\theta }(1-\theta ^{\text {L}})+\theta ^{\text {H}}(1-k\theta ^{\text {L}})}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $\pi _{\text {OTA}}^M=\frac{k^2\theta ^{\text {H}}\theta ^{\text {L}}(1-\theta ^{\text {L}})}{\lambda _2 }$, $\pi _{\text {H}}^M=\frac{k\theta ^{\text {H}}\theta ^{\text {L}}(\lambda _2 -k\lambda _1 )}{\lambda _2 (\theta ^{\text {H}}-\alpha \widetilde{\theta })}$;

  • (b) When $\alpha \leqslant \frac{\theta ^{\text {H}}}{\theta ^{\text {H}}+2\widetilde{\theta }+2(\theta ^{\text {L}})^2}$ and $k_1 \leqslant k\leqslant k_2$, $p_o^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}(1-k)}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $p_{\text {H}}^*=\frac{\lambda _2 (2p_o^*-w^*)-\alpha \theta ^{\text {H}}\theta ^{\text {L}}(1-\theta ^{\text {L}})}{\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha )}$, $w^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}(\lambda _1+(1-\alpha )(2\theta ^{\text {H}}\theta ^{\text {L}}+\lambda _2+\alpha \theta ^{\text {L}}(\theta ^{\text {L}}-\widetilde{\theta }))-4\lambda _2 k)}{(\theta ^{\text {H}}-\alpha \widetilde{\theta })(\lambda _1+3\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha ))}$, $\pi _{\text {OTA}}^M=\frac{\lambda _2 (p_o^*-w^*)(2k-1+\alpha )}{\lambda _1+3\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha )}$, $\pi _{\text {H}}^M=\frac{w^*\lambda _2 (2k-1+\alpha )}{\lambda _1+3\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha )}+\frac{p_{\text {H}}^*(1-\alpha )(2k\theta ^{\text {H}}\theta ^{\text {L}}+\lambda _2 )}{\lambda _1+3\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha )}$.

  • (c) When $\alpha \leqslant \frac{\theta ^{\text {H}}}{\theta ^{\text {H}}+2\widetilde{\theta }+2(\theta ^{\text {L}})^2}$ and $k\geqslant k_2$ or $\alpha >\frac{\theta ^{\text {H}}}{\theta ^{\text {H}}+2\widetilde{\theta }+2(\theta ^{\text {L}})^2}$ and $k\geqslant \frac{\theta ^{\text {H}}-\alpha \widetilde{\theta }-\alpha (\theta ^{\text {L}})^2}{\lambda _1 }$ or $k<\frac{\alpha \widetilde{\theta }}{\theta ^{\text {H}}}$, there is no solution that meets the conditions; among them: $\lambda _1=\theta ^{\text {H}}(1-\alpha )(2-\theta ^{\text {L}})+2\alpha \theta ^{\text {L}}(1-\theta ^{\text {L}})$, $\lambda _2=\theta ^{\text {H}}-\alpha \widetilde{\theta }-\alpha (\theta ^{\text {L}})^2$, $A=\alpha \theta ^{\text {H}}(5\widetilde{\theta }+(\theta ^{\text {L}})^2-2\widetilde{\theta }\theta ^{\text {L}}(1-\alpha ))-4\widetilde{\theta }(\alpha \theta ^{\text {L}})^2-(\theta ^{\text {H}})^2$, $k_1=(\theta ^{\mathrm {H}}(\theta ^{\mathrm {H}}-\alpha (\theta ^{\mathrm {L}})^2)-\alpha ^2\widetilde{\theta }(\widetilde{\theta }+(\theta ^{\mathrm {L}})^2)+2\alpha \widetilde{\theta }\theta ^{\mathrm {H}}\theta ^{\mathrm {L}}(1-\alpha ))/(2\theta ^{\mathrm {H}}(\theta ^{\mathrm {H}}-2\theta -2(\theta ^{\mathrm {L}})^2))$, $k_2=(\lambda _1+(1-\alpha )(\theta ^{\text {H}}(1+2\theta ^{\text {L}})-\alpha \widetilde{\theta }(1-\theta ^{\text {L}})))/(4(\theta ^{\text {H}}-\alpha \widetilde{\theta }-\alpha (\theta ^{\text {L}})^2))$.

Lemma 3: all type H customers choose to purchase through the network channel in this price range, and the type L customer will be divided into two parts, part of the purchase through the network, part of the purchase through the hotel direct channel; at this time, the optimal decision of the hotel and OTA is the combined effect of the proportion of type H customers, the acceptance of the two types of customers on the network channel and the service capacity of the hotel.

Decision-making problem between hotels and OTA in the wholesale mode of zone V

According to the demand function of the hotel and OTA in the formula (1), the optimization problem of this supply chain in this zone is

$$\begin{aligned} \left\{ \begin{array}{l} \mathop {\text {Max}}\limits _{p_{H,w} } \pi _{\text {H}}^M=w(\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(1-p_o /\theta ^{\text {L}})) \\ \text {s.t.}\\ \mathop {\text {Max}}\limits _{p_o } \pi _{\text {OTA}}^M=(p_o -w)(\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(1-p_o /\theta ^{\text {L}})) \\ p_{\text {H}} >p_o+(1-\theta ^{\text {L}}),p_o \leqslant \theta ^{\text {L}},\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(1-p_o /\theta ^{\text {L}})\leqslant k. \\ \end{array}\right. \end{aligned}$$

(6)

The following lemma can be obtained for solving this optimization problem.

Lemma 4: when the online sales price $p_o$ and direct selling price meet $p_{\text {H}} >p_o+(1-\theta ^{\text {L}})$, at this time, the optimal pricing and corresponding profit of the hotel and OTA are as follows:

• 1. When $\alpha >\theta ^{\text {H}}/(2\widetilde{\theta })$,

  • (a) When $k\geqslant 1/4$, $w^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}}{2(\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $p_o^*=\frac{3\theta ^{\text {H}}\theta ^{\text {L}}}{4(\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $\pi _{\text {H}}^M=\frac{\theta ^{\text {H}}\theta ^{\text {L}}}{8(\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $\pi _{\text {OTA}}^M=\frac{\theta ^{\text {H}}\theta ^{\text {L}}}{16(\theta ^{\text {H}}-\alpha \widetilde{\theta })}$;

  • (b) When $\alpha \widetilde{\theta }/\theta ^{\text {H}}\leqslant k<1/4$, $w^*=\frac{(1-2k)\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $p_o^*=\frac{(1-k)\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $\pi _{\text {H}}^M=\frac{k(1-2k)\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $\pi _{\text {OTA}}^M=\frac{k^2\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$;

• 2. When $\theta ^{\text {H}}/(4\widetilde{\theta })\leqslant \alpha <\theta ^{\text {H}}/(2\widetilde{\theta })$ and $k\geqslant \alpha \widetilde{\theta }/\theta ^{\text {H}}$, $w^*=\frac{(\theta ^{\text {H}}-2\alpha \widetilde{\theta })\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \widetilde{\theta }}$, $p_o^*=\theta ^{\text {L}}$, $\pi _{\text {H}}^M=\frac{(\theta ^{\text {H}}-2\alpha \widetilde{\theta })\theta ^{\text {L}}\alpha \widetilde{\theta }}{\theta ^{\text {H}}(\theta ^{\text {H}}-\alpha \widetilde{\theta })}$, $\pi _{\text {OTA}}^M=\frac{(\alpha \widetilde{\theta })^2\theta ^{\text {L}}}{\theta ^{\text {H}}(\theta ^{\text {H}}-\alpha \widetilde{\theta })}$

• 3. When $\alpha \leqslant \theta ^{\text {H}}/(4\widetilde{\theta })$ or $k<\alpha \widetilde{\theta }/\theta ^{\text {H}}$, there is no solution that meets condition.

Lemma 4, only when the proportion of type H customers is higher and the hotel service capacity is higher, the hotel is likely to set a higher direct selling price, so that all customers can purchase through the channel, it can be seen from Lemma 1 to Lecture 4 when the hotel and OTA cooperate through the wholesale mode, the hotel’s profit in the II, III, IV and V zone, respectively, the best decision of the hotel can obtained under the wholesale mode.

Theorem 2: for a given k, $\alpha$, $\theta ^{\text {H}}$, $\theta ^{\text {L}}$, by comparing the hotel’s profit in the II, III, IV and V zone, the maximum corresponding $w^*$, $p_{\text {H}}^*$ and $p_o^*$ to the hotel’s profit is the optimal pricing of the hotel under the wholesale mode, at this time, the hotel’s revenue is recorded as $\pi _{\text {H}}^{M*}$.

2.4.2 Dual-channel agent mode

Under the agent mode, the decision-making process between the hotel and OTA is also Stackelberg game process. Drawing on the research of Wang et al. (2009), OTA has strong bargaining power in the agent mode. Therefore, assuming that OTA is the leader of the game, then the hotel is the follower of the game. At this time, OTA first set the optimal online sales price $p_o$; then the hotel sets the optimal direct selling price. It can be seen from the I zone in Fig. 2: $p_o \geqslant p_{\text {H}} (\theta ^{\text {H}}-1)$, $U_{\text {OTA}}^{\text {L}}<0,U_{\text {OTA}}^{\text {H}}<0$, at this time, the customer will never get from the network, so for OTA, OTA will not set the online sales price to zone I. Therefore, in the following discussion, only the zones II, III, IV, V are discussed.

Decision-making problem of hotel and OTA under agent mode in zone II.

According to the demand function of the hotel and OTA IN the formula (1), the optimization problem of the supply chain in this zone can be obtained as:

$$\begin{aligned} \left\{ \begin{array}{l} \mathop {\text {Max}}\limits _{p_o } \pi _{\text {OTA}}^A=rp_o \alpha (1-\xi ) \\ \text {s.t.}\\ \mathop {\text {Max}}\limits _{p_{\text {H}} } \pi _{\text {H}}^A=(1-r)p_o \alpha (1-\xi )+p_{\text {H}} (\alpha (\xi -p_{\text {H}})+(1-\alpha )(1-p_{\text {H}} )) \\ p_o -(\theta ^{\text {H}}-1)>p_{\text {H}} \leqslant p_o /\theta ^{\text {H}}\leqslant 1,1-p_{\text {H}} \leqslant k. \\ \end{array}\right. \end{aligned}$$

(7)

The following lemma can be obtained from the solution of this optimization problem.

Lemma 5: when the online sales price $p_o$ and direct selling price meet $p_o -(\theta ^{\text {H}}-1)<p_{\text {H}} \leqslant p_o /\theta ^{\text {H}}$, at this time, the optimal pricing and corresponding profit of the hotel and OTA are as follows:

• 1. When $B\geqslant 0$ and $k\geqslant k_3$, $p_{\text {H}}^*=\frac{\beta }{2\beta +r\alpha \theta ^{\text {H}}}$, $p_o^*=\frac{\beta \theta ^{\text {H}}}{2\beta +r\alpha \theta ^{\text {H}}}$ $\pi _{\text {OTA}}^A=\frac{r\alpha \beta \theta ^{\text {H}}(\beta +r\alpha \theta ^{\text {H}})}{(2\beta +r\alpha \theta ^{\text {H}})}$, $\pi _{\text {H}}^A=\frac{\beta (\beta +\alpha \theta ^{\text {H}})(\beta +\theta ^{\text {H}}(1-r\alpha ))}{(2\beta +r\alpha \theta ^{\text {H}})^2}$;

• 2. When $B\geqslant 0$ and $\frac{\beta +r\alpha \theta ^{\text {H}}}{2(\theta ^{\text {H}}-1)+r\alpha }\leqslant k<k_3$ or $B<0$ and $\frac{\beta +r\alpha \theta ^{\text {H}}}{2(\theta ^{\text {H}}-1)+r\alpha }\leqslant k\leqslant k_4$, $p_o^*=\frac{\alpha \theta ^{\text {H}}+(1-2k)(\alpha +\theta ^{\text {H}}-1)}{(2-r)\alpha }$, $p_{\text {H}}^*=1-k$, $\pi _{\text {OTA}}^A=\frac{rp_o^*(k(r\alpha +2\theta ^{\text {H}}-2)-\beta -r\alpha \theta ^{\text {H}})}{(2-r)(\theta ^{\text {H}}-1)}$, $\pi _{\text {H}}^A=\frac{(1-r)p_o^*(k(r\alpha +2\theta ^{\text {H}}-2)-\beta -r\alpha \theta ^{\text {H}})}{(2-r)(\theta ^{\text {H}}-1)}+\frac{(1-k)(\beta +r\alpha \theta ^{\text {H}}-rk(\beta -\alpha \theta ^{\text {H}}))}{(2-r)(\theta ^{\text {H}}-1)}$;

• 3. When $B<0$ and $k\geqslant k_4$, $p_{\text {H}}^*=\frac{((1-\alpha )(3r\alpha -2\alpha -4)+2\theta ^{\text {H}}(2-r\alpha ))(\theta ^{\text {H}}-1)}{4(\theta ^{\text {H}}-1+\alpha )(2(\theta ^{\text {H}}-1)+r\alpha )}$, $p_o^*=\frac{(\alpha +2\theta ^{\text {H}}-1)(\theta ^{\text {H}}-1)}{4(\theta ^{\text {H}}-1)+2r\alpha }$, $\pi _{\text {OTA}}^A=(r\alpha (\theta ^{\text {H}}-1)(\alpha +2\theta ^{\text {H}}-1)^2)(8(\alpha +\theta ^{\text {H}}-1)(r\alpha +2\theta ^{\text {H}}-2))$, $\pi _{\text {H}}^A=\frac{(1-r)\alpha (\theta ^{\text {H}}-1)(\alpha +2\theta ^{\text {H}}-1)^2}{8(\alpha +\theta ^{\text {H}}-1)(r\alpha +2\theta ^{\text {H}}-2)}+\frac{p_{\text {H}}^*(4\beta +r\alpha (1-\alpha +2\theta ^{\text {H}}))}{4(r\alpha +2\theta ^{\text {H}}-2)}$;

• 4. When $k<(\beta +r\alpha \theta ^{\text {H}})/(2(\theta ^{\text {H}}-1)+r\alpha )$, There is no solution that meet the conditions.

  Among them, $\beta =(\theta ^{\text {H}}-1)(1-\alpha )$, $B=(1-\alpha )(2\beta +3r\alpha \theta ^{\text {H}}-2(1-\alpha ))$ $k_3=\frac{r^2\alpha ^2\theta ^{\text {H}}+\alpha \beta (r+2\theta ^{\text {H}})+(\theta ^{\text {H}}-1)(r\alpha \theta ^{\text {H}}(1+\alpha )+2\beta )}{2(\theta ^{\text {H}}-1+\alpha )(2\alpha +r\alpha \theta ^{\text {H}})}$, $k_4=\frac{4(\theta ^{\text {H}}-1)^2+\alpha (\theta ^{\text {H}}-1)(6+r+2r\theta ^{\text {H}})+\alpha ^2(2+r\theta ^{\text {H}}(3r-2))}{4(\theta ^{\text {H}}-1+\alpha )(2\theta ^{\text {H}}-2+r\alpha )}$,

Similar to Lemma 1, Lemma 5 also shows that only when the hotel’s service capacity is higher, it is possible for the hotel to set a lower direct selling price to attract all type L and some type H customers to purchase rooms through the hotel direct sales channel.

Decision-making problem of hotel and OTA under agent mode in the zone III.

According to the demand function of the hotel and OTA in the formula (1), the optimization problem of this supply chain in this zone can be obtained as:

$$\begin{aligned} \left\{ \begin{array}{l} \mathop {\text {Max}}\limits _{p_o }\pi _{\text {OTA}}^A=rp_o \alpha (1-p_o /\theta ^{\text {H}}) \\ \text {s.t.}\\ \mathop {\text {Max}}\limits _{p_{\text {H}} } \pi _{\text {H}}^A=(1-r)p_o \alpha (1-p_o /\theta ^{\text {H}})+p_{\text {H}} (1-\alpha )(1-p_{\text {H}} ) \\ p_o /\theta ^{\text {H}}<p_{\text {H}} \leqslant p_o /\theta ^{\text {L}},p_o \leqslant \theta ^{\text {H}},\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(1-p_{\text {H}} )\leqslant k. \\ \end{array}\right. \end{aligned}$$

(8)

The following lemma can be obtained from the solution of this optimization problem.

Lemma 6: when the online sales price $p_o$ and direct selling price meet $p_o /\theta ^{\text {H}}<p_{\text {H}} \leqslant p_o /\theta ^{\text {L}}$, at this time, the optimal pricing and corresponding profit of the hotel and OTA are as follows:

• 1. When $k\geqslant 1/2$, $p_{\text {H}}^*=1/2$, $p_o^*=\theta ^{\text {H}}/2$, $\pi _{\text {H}}^A=2+\alpha (\theta ^{\text {H}}-1)/4$, $\pi _{\text {OTA}}^A=\alpha (\theta ^{\text {H}}-1)/16$;

• 2. When $k<1/2$, There is no solution that meet the conditions.

Similar to Lemma 2, Lemma 6 also shows that only when the hotel’s service capacity is higher ($k\geqslant 1/2)$, it is possible for the hotel to set a lower direct selling price to attract all type L customers to purchase rooms through the hotel direct sales channel.

Decision-making problem of hotel and OTA under agent mode in the zone IV

According to the demand function of the hotel and OTA in the formula (1), the optimization problem of the supply chain in this zone is

$$\begin{aligned} \left\{ \begin{array}{l} \mathop {\text {Max}}\limits _{p_o } \pi _{\text {OTA}}^A=rp_o (\alpha (1-p_o /\theta ^{\text {H}}))+(1-\alpha )(\zeta -p_o /\theta ^{\text {L}}) \\ \text {s.t.}\\ \mathop {\text {Max}}\limits _{p_{\text {H}} } \pi _{\text {H}}^A=(1-r)p_o (\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(\zeta -p_o /\theta ^{\text {L}})+p_{\text {H}} (1-\alpha )(1-\zeta )) \\ \frac{p_o }{\theta ^{\text {L}}}<p_{\text {H}} \leqslant p_o+(1-\theta ^{\text {L}}),p_o \leqslant \theta ^{\text {L}},\alpha (1-p_o /\theta ^{\text {H}})+(1-\alpha )(1-p_o /\theta ^{\text {L}})\leqslant k. \\ \end{array}\right. \end{aligned}$$

(9)

The following lemma can be obtained from the solution of this optimization problem.

Lemma 7: when the online sales price and direct selling price meet $p_o /\theta ^{\text {L}}<p_{\text {H}} \leqslant p_o+(1-\theta ^{\text {L}})$, at this time, the optimal pricing and corresponding profit of the hotel and OTA are as follows:

• 1. When $C\geqslant 0$ and $k\geqslant ((\alpha \widetilde{\theta }+\theta ^{\text {H}})(1-\theta ^{\text {L}})+r\theta ^{\text {H}}\theta ^{\text {L}})/(\theta ^{\text {H}}(2(1-\theta ^{\text {L}})+r\theta ^{\text {L}}))$ $p_o^*=(\theta ^{\text {L}}(1-\theta ^{\text {L}})/2(1-\theta ^{\text {L}})+r\theta ^{\text {L}})$, $p_{\text {H}}^*=(1-\theta ^{\text {L}})/(2(1-\theta ^{\text {L}})+r\theta ^{\text {L}})$, $\pi _{\text {OTA}}^A=(rp_o^*\alpha (r\theta ^{\text {H}}\theta ^{\text {L}}+(\theta ^{\text {H}}+\widetilde{\theta })(1-\theta ^{\text {L}})))/(\theta ^{\text {H}}(2(1-\theta ^{\text {L}})+r\theta ^{\text {L}}))$, $\pi _{\text {H}}^A=\frac{(1-r)p_o^*\alpha (r\theta ^{\text {L}}\theta ^{\text {L}}+(\theta ^{\text {H}}+\widetilde{\theta })(1-\theta ^{\text {L}}))}{\theta ^{\text {H}}(2(1-\theta ^{\text {L}})+r\theta ^{\text {L}})}+\frac{(1-\alpha )(1-\theta ^{\text {L}})(1-(1-r)\theta ^{\text {L}})}{(2(1-\theta ^{\text {L}})+r\theta ^{\text {L}})}$;

• 2. When $C<0$,

  • (a) When $k\geqslant k_5$, $p_o^*=(\theta ^{\text {H}}\theta ^{\text {L}}(1+\alpha )(1-\theta ^{\text {L}}))/((1+\alpha )\theta ^{\text {H}}(2+2\theta ^{\text {L}}-r\theta ^{\text {L}})-C),p_{\text {H}}^*=(1-\theta ^{\text {L}}+p_o^*)/2$, $\pi _{\text {OTA}}^A=(r\theta ^{\text {H}}\theta ^{\text {L}}(1+\alpha )^2(1-\theta ^{\text {L}}))/(8((1+\alpha )\theta ^{\text {H}}(2+2\theta ^{\text {L}}-r\theta ^{\text {L}})-C))$, $\pi _{\text {H}}^A=\frac{(1-r)\theta ^{\text {H}}\theta ^{\text {L}}(1+\alpha )^2(1-\theta ^{\text {L}})}{8((1+\alpha )\theta ^{\text {H}}(2+2\theta ^{\text {L}}-r\theta ^{\text {L}})-C)}+\frac{(1-\alpha )p_{\text {H}}^*(4(1-\theta ^{\text {L}})(\theta ^{\text {H}}-\alpha \widetilde{\theta })-r\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha ))}{8(1-\theta ^{\text {L}})(\theta ^{\text {H}}-\alpha \widetilde{\theta })+4r\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha )}$;

  • (b) When $\frac{(\alpha \tilde{\theta }+\theta ^{\text {H}})(1-\theta ^{\text {L}})+r\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}(2(1-\theta ^{\text {L}})+r\theta ^{\text {L}})}\leqslant k<k_5$, $p_o^*=\frac{(1-k)\theta ^{\text {H}}\theta ^{\text {L}}}{(\theta ^{\text {H}}-\alpha \tilde{\theta })}$, $p_{\text {H}}^*=\frac{1-\theta ^{\text {L}}+p_o^*}{2}$, $\pi _{\text {OTA}}^A=\tau p_o^*(\frac{k-(1-\alpha )(1-\theta ^{\text {L}}+3p_o^*)}{(2(1-\theta ^{\text {L}}))})$, $\pi _{\text {H}}^A=(1-r)p_o^*(k-\frac{(1-\alpha )(1-\theta ^{\text {L}}+3p_o^*)}{2(1-\theta ^{\text {L}})})+\frac{p_{\text {H}}^*(1-\alpha )(1-\theta ^{\text {L}}+3p_o^*)}{2(1-\theta ^{\text {L}})}$;

• 3. When $k<\frac{(\alpha \tilde{q}+\theta ^{\text {H}})(1-\theta ^{\text {L}})+r\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}(2(1-\theta ^{\text {L}})+r\theta ^{\text {L}})}$, There is no solution that meet the conditions, among them,

  $C=2(1-\theta ^{\text {L}})(2\alpha \tilde{\theta }+\alpha \theta ^{\text {H}}-\theta ^{\text {H}})+r\theta ^{\text {L}}\theta ^{\text {H}}(3\alpha -1)$, $k_5=\frac{(3-\alpha )(1-\theta ^{\text {L}})(\theta ^{\text {H}}-\alpha \tilde{\theta })+2r\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha )}{2(2(1-\theta ^{\text {L}})(\theta ^{\text {H}}-\alpha \tilde{\theta })+r\theta ^{\text {H}}\theta ^{\text {L}}(1-\alpha ))}$.

Decision-making problem of hotel and OTA under agent mode in the zone V

According to the demand function of the hotel and OTA in the formula (1), the optimization problem of the supply chain in this zone can be obtained as:

$$\begin{aligned} \left\{ \begin{array}{l} \mathop {\max }\limits _{p_o } \pi _{\text {OTA}}^A=rp_o (\alpha (1-\frac{p_o }{\theta ^{\text {H}}})+(1-\alpha )(1-\frac{p_o }{\theta ^{\text {L}}})) \\ \text {s.t.}\\ \mathop {\max }\limits _{p_{\text {H}} } \pi _{\text {H}}^A=(1-r)p_o (\alpha (1-\frac{p_o }{\theta ^{\text {H}}})+(1-\alpha )(\zeta -\frac{p_o }{\theta ^{\text {L}}})) \\ p_{\text {H}} >p_o+(1-\theta ^{\text {L}}),p_o \leqslant \theta ^{\text {L}},\alpha (1-\frac{p_o }{\theta ^{\text {H}}})+(1-\alpha )(1-\frac{p_o }{\theta ^{\text {L}}})\leqslant k \\ \end{array}\right. \end{aligned}$$

(10)

The following lemma can be obtained from the solution of this optimization problem.

Lemma 8: when the online sales price and the direct selling price meet $p_{\text {H}} >p_o+(1-\theta ^{\text {L}})$, at this time, the optimal pricing and corresponding profit of the hotel and OTA are as follows:

• 1. When $p_{\text {H}} \geqslant \frac{\tilde{\theta }(1-2\alpha (1-\theta ^{\text {L}}))}{2(\theta ^{\text {H}}-\alpha \tilde{\theta })}$ and $\alpha <\frac{\theta ^{\text {H}}}{2\tilde{\theta }}$,

  • (a) When $k\geqslant \frac{1}{2}$, $p_o^*=\frac{\theta ^{\text {H}}\theta ^{\text {L}}}{2(\theta ^{\text {H}}-\alpha \tilde{\theta })}$, $\pi _{\text {OTA}}^A=\frac{r\theta ^{\text {H}}\theta ^{\text {L}}}{4(\theta ^{\text {H}}-\alpha \tilde{\theta })}$, $\pi _{\text {H}}^A=\frac{(1-r)\theta ^{\text {H}}\theta ^{\text {L}}}{4(\theta ^{\text {H}}-\alpha \tilde{\theta })}$;

  • (b) When $\frac{\alpha \tilde{\theta }}{\theta ^{\text {H}}}\leqslant k<\frac{1}{2}$, $p_o^*=\frac{(1-k)\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \tilde{\theta }}$, $\pi _{\text {OTA}}^A=\frac{rk(1-k)\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \tilde{\theta }}$, $\pi _{\text {H}}^A=\frac{(1-r)k(1-k)\theta ^{\text {H}}\theta ^{\text {L}}}{\theta ^{\text {H}}-\alpha \tilde{\theta }}$;

• 2. When $p_{\text {H}} \geqslant \frac{\tilde{\theta }(1-2\alpha (1-\theta ^{\text {L}}))}{2(\theta ^{\text {H}}-\alpha \tilde{\theta })}$ and $\alpha \geqslant \frac{\theta ^{\text {H}}}{2\tilde{\theta }}$, $k\geqslant \frac{\alpha \tilde{\theta }}{\theta ^{\text {H}}}$, $p_o^*=\theta ^{\text {L}}$, $\pi _{\text {OTA}}^A=\frac{r\alpha \theta ^{\text {L}}\tilde{\theta }}{\theta ^{\text {H}}}$, $\pi _{\text {H}}^A=\frac{(1-r)\alpha \theta ^{\text {L}}\tilde{\theta }}{\theta ^{\text {H}}}$;

• 3. When $p_h \geqslant \frac{\tilde{\theta }(1-2\alpha (1-\theta ^{\text {L}}))}{2(\theta ^{\text {H}}-\alpha \tilde{\theta })}$ and $k<\frac{\alpha \tilde{\theta }}{\theta ^{\text {H}}}$, There is no solution that meet the conditions;

• 4. When $(1-\theta ^{\text {L}})<p_{\text {H}}<\frac{\tilde{\theta }(1-2\alpha (1-\theta ^{\text {L}}))}{2(\theta ^{\text {H}}-\alpha \tilde{\theta })}$,

  • (a) When $k\geqslant k_6$ $p_o^*=p_{\text {H}} -(1-\theta ^{\text {L}})$, $\pi _{\text {OTA}}^A=\frac{rk_6 (p_{\text {H}} -(1-\theta ^{\text {L}}))}{\theta ^{\text {H}}\theta ^{\text {L}}}$, $\pi _{\text {H}}^A=\frac{(1-r)k_6 (p_{\text {H}} -(1-\theta ^{\text {L}}))}{\theta ^{\text {H}}\theta ^{\text {L}}}$;

  • (b) When $k<k_6$, here is no solution that meet the conditions among them, $k_6=\frac{\theta ^{\text {H}}(1-p_{\text {H}} )+\alpha \tilde{\theta }(p_{\text {H}}+\theta ^{\text {L}}-1)}{\theta ^{\text {H}}\theta ^{\text {L}}}$.

It can be seen from Lemma 5 to Lemma 8 that when the hotel and OTA cooperate through the agent mode, the hotel and OTA will have profits in the zone II, III, IV and V, respectively, and thus the optimal decision-making of hotel in the agent mode can be obtained.

Theorem 3: For given k, $\alpha$, $\theta ^{\text {H}}$, $\theta ^{\text {L}}$, by comparing the profit of the OTA in the zone II, III, IV, and V, When profit of OTA are greatest, the corresponding profit of the hotel is the profit of the hotel under the agent wholesale mode, at this time, the hotel’s profit is recorded as $\pi _{\text {H}}^{A*}$.

2.4.3 Special cases

Paragraph 2.4.1 and 2.4.2 studied the pricing problem of hotels and OTAs under wholesale and agent modes in general condition, and a special case is discussed below: when the market share $\alpha$ of type H customers is smaller, namely when extreme condition $\alpha =0$, then the demand function of hotel and OTA:

$$\begin{aligned} (Q_{\text {H}},Q_{\text {OTA}})=\left\{ \begin{array}{ll} (1-p_{\text {H}}, 0), &{}(p_{\text {H}}, p_{\text {H}} )\in ~\mathrm {I}~ \& ~\mathrm {II}~ \& ~\mathrm {III}\\ (1-\zeta , \zeta -{p_o}/{\theta ^{\text {L}}}) &{} (p_o, p_{\text {H}} )\in \mathrm {IV} \\ (0,1-{p_o}/{\theta ^{\text {L}}}) &{} (p_o, p_{\text {H}} )\in V \\ \end{array}\right. \end{aligned}$$

(11)

Similar to Lemma 1 to Lemma 8, it is possible to obtain the best price and profit of hotel and OTA in single-channel direct selling mode, dual-channel wholesale mode and dual-channel agent mode. The following conclusions can be obtained Through comparative analysis.

Theorem 4: when all customers in the market have low acceptance levels for the network channel $(\alpha =0)$, the hotel will choose the single-channel direct selling mode, namely the hotel will give up the cooperation with OTA to maximize the revenue.

Theorem 4 shows that if all customers have low acceptance levels for OTA’s network channels, OTA can only attract customers by setting a lower online sales price, the hotel join the network channel, which will not only obtain higher marginal revenue but will brings competition to the offline channel of hotel, so the hotel will not cooperate with OTA and choose the single-channel direct selling mode to sell the rooms.

3 Numerical analysis

Considering the complexity of the above theoretical mode, this section intends to verify the hotel service capabilities through the data of Ctrip.com. Ctrip.com is a large travel website in China. It was founded in 1999 and its headquarter is located in Shanghai. The company’s business scope covers hotel booking, air ticket booking, vacation booking and other fields. In 2003, Ctrip was listed on the NASDAQ in the United States; in 2015, Ctrip acquired 37.6% of the shares in Elong and merged with Qunar.this paragraph intends to analyze the hotel service capacity k type H and type L customer’s acceptance level for network channels $\theta ^{\text {H}}$, $\theta ^{\text {L}}$, market share $\alpha$ of type Hcustomers, and the influence of the commission rate r in the agent mode on the profit of the hotel in different modes, and explores that hotels should cooperate with OTA under which circumstances, if cooperation should be in which mode.

First, the interaction effect of the capacity k and the market scale $\alpha$ of H-type customer on the hotel’s strategic choice is analyzed, the other parameters assignment as follows: $\theta ^{\text {H}}=1.5$, $\theta ^{\text {L}}=0.8$. Moreover, in order to analyze the influence of the commission rate on hotel decision-making through comparison, the commission rates take $r=0.2$ and $r=0.1$, respectively, as shown in Fig. 3a, b.

Fig. 3

The interaction effect of the capacity and the market scale of H-type customer on the hotel’s strategic choice

Figure 3a shows that when the hotel’s service capacity is relatively low, the limited rooms can only meet the customer needs of the hotel store, and the room marginal profit obtained by the hotel direct selling is higher than marginal profit obtained through the OTA network channel, so the hotel will choose the single channel direct selling mode at this time, namely give up cooperation with OTA; otherwise, cooperation with OTA can help the hotel to sell excess rooms, there are also such cases in actual sales, for example, some family hotels in popular tourist attractions are not willing to cooperate with OTA because of the small number of rooms and large demand; and some larger hotels often choose to cooperate with OTA. When the hotel service capacity k is relatively high, the wholesale mode is more favorable to the hotel, because the hotel first sells to the OTA at a lower wholesale price under the wholesale mode, and the marginal profit obtained by the OTA through wholesale sales is higher than the marginal profit obtained through the agent, therefore, OTA’s sales enthusiasm under the wholesale mode is definitely higher than that in the agency mode, moreover, the wholesale mode can reduce the inventory risk of the hotel’s excess rooms, when the hotel service capacity k is relatively moderate and the proportion of type H customers is relatively large, the agent mode is more favorable to the hotel. Because when the proportion of online shopping customers is high, OTA can set a higher online sales price to increase profits, although the OTA network channel increases competition to direct selling channels, the hotel’s marginal profit under the agent mode is higher than that under the wholesale mode, so the hotel will choose the proxy mode in limited room resources.

Similar to Fig. 3a, b shows that when the hotel service capacity k is relatively low, the hotel will give up cooperation with OTA; when the hotel service capacity is relatively high and the proportion $\alpha$ of type customers H is relatively small, then the wholesale mode is more favorable to the hotel; when the hotel service capacity k is relatively moderate or higher and the proportion $\alpha$ of type customers H is relatively large, then the agent mode is more favorable to the hotel. Figure 3a is compare with Fig. 3b, it can be seen that when the commission rate is low, the profit of the hotel under the agent mode will increase accordingly, so if the commission rate drops, the range of optimal choices for the agent mode will be expanded for hotel.

Secondly, the interaction effect of the capacity k and H-type consumer acceptance $\theta ^{\text {H}}$ of online channel on the hotel’s strategic choice is analyzed, $\alpha =0.5$, $\theta ^{\text {L}}=0.8$, $r=0.2$, as shown in Fig. 4.

Fig. 4

The interaction effect of the capacity and H-type consumer acceptance of online channel on the hotel’s strategic choice

Similar to Figs. 3 and 4 shows that when the hotel’s service capacity is relatively low, the hotel will abandon cooperation with OTA. When the hotel service capacity kis relatively high and the type H customers’ acceptance for network channel OH is lower $(\theta ^{\text {H}}\leqslant 1.65)$, then the wholesale mode is more favorable to the hotel. Because type H customers have lower valuations for rooms booked through online channels, at this time, the OTA must set a lower online sales price to attract more customers, and because the profit margin of OTA sales through wholesale mode is higher than the profit margin obtained through agent mode, at this time, if the hotel adopts the agent mode to cooperate with OTA, OTA’s sales enthusiasm is low, which leads to the decline of the hotel’s total profit, so the wholesale mode will be the most favorable for the hotel. When the hotel service capacity k is relatively high and the type H customers’ acceptance for network channel OH is higher $(\theta ^{\text {H}}>1.65)$, at this time, the OTA can set a higher online sales price and the OTA sales enthusiasm is higher, moreover, The marginal profit obtained by the hotel through agent mode is higher than the marginal profit obtained through the wholesale mode, so at this time the hotel mode has the highest profit under the agent mode.

Finally, this paper analyzes the interaction effect of the market scale $\alpha$ and acceptance $\theta ^{\text {H}}$ of online channel of H-type customer on the hotel’s strategic choice when the hotel service capacity is certain, the other parameters assignment as follows: $k=0.4$, $\theta ^{\text {L}}=0.8$, $r=0.2$, as shown in Fig. 5.

Fig. 5

The interaction effect of the market scale and acceptance of online channel of H-type customer on the hotel’s strategic choice

4 Discussion

Although this article explored problems on whether hotels cooperate with OTA, there are still some shortcomings that need further study, future research can be extended to a hotel and collaboration of many OTA and explored the impact of commission rates on hotel decisions. In addition, when the market demand is random, the selection of hotel channels and their equilibrium decision-making problems remain to be studied.

let’s analyse what advantages an agent has compared to direct sourcing.

First, operational professional advantage: we have a professional OTA online operations team, Internet search optimization and OTA operations and promotion, to reduce the pressure of hotel OTA operations, increase the professional degree of operation to save hotel promotion costs to improve the amount of online orders.

Second, the channel advantage (online and offline combination): online in addition to the United States group Ctrip other sites such as: Touniu, Ma Hive, where to go, flying pig, Yilong, Touniu, the same city, booking, etc. more than 20 different channels and offline travel agency partners, especially the local community cooperation is frequent, business, such as travel agency partners of business travel customers, tour groups. More than one distribution channel more than one traffic entrance, many hotels direct collection no distribution channels of the port, and our hotel agents have, this is our hotel agents distribution channels more advantages.

Third, the settlement is flexible: agents with the hotel settlement more flexible, can be a single settlement, daily, weekly, semi-monthly, monthly, reducing the hotel cash flow pressure.

Next, we analyze why hotels are willing to cooperate with agents.

First, the agents have multiple channels.Generally speaking, agents have more than 20 different distribution channels online and offline to increase the number of nights and occupancy rate for hotels, which can effectively solve the problem of insufficient guest sources in the off-season.

Second, the agent settlement is flexible.Compared with direct procurement, the agent settlement is more flexible, which can reduce the pressure of hotel capital flow to a considerable extent.

Third, the agent has great operational advantages.The agent has a professional OTA operation team, which can solve the problem of high OTA operation cost and lack of professionalism of most hotels.This can solve the problem of high OTA operation costs and lack of professionalism of most hotels, and increase the amount of OTA orders on the hotel line.

Fourth, the hotel fixed costs are too high.The hotel industry is an asset-intensive industry. The hotel occupancy rate is too low, which can easily cause the hotel to lose money. In order to prevent losses, the hotel has to find some travel agencies and third-party agents to seek cooperation to increase hotel income and prevent losses.

5 Conclusion

Based on the dual heterogeneity of customer channel preferences and acceptance of network channels, this paper studied the optimal pricing of hotels and OTA under single-channel direct selling mode, dual-channel wholesale mode and dual-channel agent mode. According to the principle of maximizing hotel profits, the optimal channel structure and the optimal cooperation mode of the hotel are analyzed. The analysis shows that when the hotel service capacity is lower, the hotel only conducts direct sales through a single channel; otherwise, the hotel will tend to cooperate with OTA to sell as many rooms as possible through dual channels. For the choice of cooperative business model, when the customer acceptance for network channels is higher and a higher proportion, the agent mode is better than the wholesale mode for the hotel; otherwise, the wholesale mode is most beneficial to the hotel. Under special circumstances, if all customers have low acceptance for OTA’s network channels, the hotel join the network channel, which will not only achieve higher marginal profit but will bring competition to the hotel’s direct selling channels, so the hotel will not cooperate with OTA, rooms sold only through their own direct sales channels.