Competition between Green and Non-Green Travel Companies: The Role of Governmental Subsidies in Green Travel

Abstract

The problem of carbon emissions in transportation is an increasing concern, and consumers need to be encouraged towards green modes of travel to achieve low-carbon travel. To compete with non-green travel companies, green travel companies have considered implementing expensive green efforts to attract consumers. Decisions on travel prices, the green efforts of green travel companies to maintain their competitiveness, and the role of governmental subsidies in promoting green travel must be thoroughly investigated. To consider travel competitiveness and the role of governmental subsidies that support the increased expenses of green travel, this study defined four different decision-making scenarios. The Nash game model without governmental subsidies and the Stackelberg–Nash game model with governmental subsidies were built and solved to understand the effects on the pricing and green efforts of travel companies. The equilibrium results and the role of governmental subsidies were analyzed theoretically and numerically. The results showed that governmental subsidies could boost green efforts while increasing green and non-green travel prices. The competition between green and non-green travel companies both undermined the role of the governmental subsidies and reduced the green and non-green travel prices. A sufficiently large cost-sharing coefficient from the government caused the green travel demand to be higher than the non-green travel demand.

1. Introduction

With the increase in economic globalization and income levels worldwide, the scale and frequency of human travel have significantly increased [1]. The carbon emissions generated by travel have attracted increasing attention as well [2]. In addition, non-green modes of travel have generated undesirable carbon emissions and undermined green efforts to protect the environment. To respond to the growing calls and policies seeking to reduce the carbon emissions of countries worldwide, we must study the decision-making mechanisms that guide consumers to “go green”.

Green travel refers to the adoption of relatively environmentally friendly travel methods, which not only save energy, improve energy efficiency, and reduce pollution, but also benefit health and balance efficiency. In addition, green travel is a symbolic concept and a sustainable environmental concept, requiring everyone to seek to save resources and reduce pollution [3]. In order to reach their chosen destination, travelers can choose different modes of travel [4]. There are many modes available in the travel market, including road transport (e.g., buses, taxis, bicycles, etc.), rail transport (e.g., trains, subways, etc.), air transport, inland waterway transport, and sea transport. These modes of travel can be divided into green and non-green modes of travel. To date, the definition of green and non-green modes of travel has been determined [5,6,7]. The authors use the term “non-green mode of travel” in the further text to refer to a mode in which the passenger individually uses a traditional energy-driven vehicle to travel. The authors use the term “green mode of travel” in the further text to refer to a mode in which the passengers jointly use a traditional energy-driven vehicle or a new energy-driven vehicle to travel, as well as a passenger using a new energy vehicle to travel individually. This means that a travel mode with shared vehicles could always be considered to be green, regardless of whether the vehicle is fuelled by traditional energy or new energy. For example, the travel of two passengers using a fossil-fuel-based taxi coupled by the platform can be considered green. The travel of a family of three using a fossil-fuel-based taxi also could be considered green.

Green modes of travel provided by green travel companies have produced less carbon emissions as compared to non-green modes of travel provided by non-green travel companies. More importantly, green and non-green travel companies must compete in the market for travel consumers [8], which has introduced challenges for carbon reduction efforts in the travel industry. Therefore, studying the market strategies of green travel companies in a competitive environment has proven important [9].

To encourage consumers to adopt a green mode of travel [10], green travel companies have implemented environmentally responsible green efforts, such as increasing the availability of green transportation and shortening the wait time for consumers. This has, in turn, increased the consumer demand for green travel, while also imposing significant costs on these green travel companies, which could inhibit their green efforts. In particular, due to pricing competition among non-green travel companies, green travel companies must weigh travel prices against sustainable choices. Subsequently, finding an equilibrium between travel prices and green efforts, in order to remain competitive in the market, may fail to promote green travel among consumers. Therefore, the government’s sharing of the green effort costs can be an effective method of guiding green travel companies to enhance their green efforts [11]. In this study, a governmental subsidy to support green efforts was introduced to intervene in the competition between green and non-green travel companies, in order to promote consumers’ adoption of green modes of travel.

The main contributions of this study cover two aspects. First, we considered the competition between green and non-green modes of travel based on pricing and effort strategies used by travel companies. Second, we also examined the government cost-sharing subsidies that have been introduced to improve the competitive advantage of green travel.

This study focused on the travel market with green and non-green travel companies. Green travel companies are providers of green modes of travel, while non-green travel companies are providers of non-green modes of travel. There is competition between green and non green travel companies in terms of modes of travel, and the government has considered providing subsidies to green travel companies to promote green travel. Such practical application cases can be found in ride-sourcing platforms [12] and ride-sharing platforms [6]. The government subsidizes ride-sharing platforms to encourage individuals to buy electric vehicles, to improve the availability of green modes of travel and guide consumers towards green travel [13].

The rest of the paper is organized as follows. Section 2 reviews the relevant literature and shows a comparison of our study with the existing literature. Section 3 presents the problem description and notations of this study. Section 4 shows the optimal decisions without governmental subsidies. Section 5 demonstrates the optimal decisions with governmental subsidies. Section 6 investigates the impact of the governmental subsidies on green effort, travel prices, and travel demands. Section 7 numerically compares the results of different decision-making scenarios. Section 8 concludes this study and identifies future directions for study.

2. Literature Review

This study’s focus was relevant to three topics in the literature: pricing and effort strategies for green travel [14,15,16]; the competition among modes of travel [17,18,19,20]; and governmental subsidies for green travel [21,22]. The primary work of this research was to provide a bridge among these topics. Specifically, this study investigated the pricing and effort strategies of the green travel companies who compete with non-green travel companies. Governmental subsidies for the green effort costs of green travel companies are introduced to promote the company’s green efforts and the consumers’ green travel.In the following paragraphs, we provide a review of related research papers.

2.1. Pricing and Effort Strategies for Green Travel

Pricing and effort strategies are important decisions for the green travel service provider and are critical in maximizing the company’s profits and guiding consumers towards greener travel options. The pricing and effort strategies of green travel have been extensively explored and a number of achievements have been made [23,24,25,26,27]. The pricing of green modes of travel has primarily focused on bike sharing [28], vehicle sharing [29], ride sharing [30], and ride hailing [31]. The effort strategy of green travel has included the availability of shared bikes and vehicles [14], fleet management [32], and service-mode selection [33].

The pricing for green travel has been attracting increasing interest. The following references have focused on the pricing of bike-sharing services. In Haider et al. [28], the authors used pricing schemes to re-balance the inventory of bike-sharing systems, and they observed that the optimal price could ensure that customers obtained bikes from neighboring stations, rather than only their nearest stations. The authors of Chen et al. [15] studied the pricing of bike-sharing services by considering the perceived convenience of customers, and they found that more convenient bike-sharing services could set a higher price. In Zhang et al. [34], the researchers introduced an innovative dynamic pricing scheme for bike-sharing systems that included negative prices, and they found that their dynamic pricing strategy could effectively attract users.

The pricing of vehicle-sharing services has been another aspect of research on green travel. The authors of Miao et al. [29] studied the pricing of electric vehicle rental services by constructing a profit model, and they found that a differential pricing strategy could increase the firms’ profits as well as customer satisfaction. The authors of Zakharenko [24] studied the pricing of the shared vehicle market based on the spatial inequality of demand and argued that spatially explicit pricing enabled providers to expand their service areas into less profitable, low-density suburban areas. In Jiao et al. [25], the authors integrated price incentives and trip selection policies to enhance customer adoption of electric vehicle sharing, and they showed that price incentive policies could increase service adoption.

The pricing research of ride-sharing platforms has received much attention. In acob and Roet-Green [26], the researchers designed optimal price service menus for a ride-sharing platform based on a strategy that considered passengers and independent drivers. They found that offering both solo and pooled rides was optimal when the distribution of the passenger type was not skewed and congestion was not high. In Jiao and Ramezani [27], the authors proposed a dynamic discounted pricing strategy to incentivize ride-sharing platforms, and they found that dynamic discount pricing strategies created substantial economic benefits for a platform. The authors of Lin et al. [30] studied the pricing of ride-sharing platforms that cooperated with car rental companies and found that the optimal price of the platform was not necessarily monotonic in the potential number of drivers without a car. In Li et al. [35], the authors considered travel time variability and studied the pricing strategies of ride-sourcing services. The authors observed that the optimal prices for ride-sourcing services were higher under more reliable traffic conditions. The researchers in Gómez-Lobo et al. [23] studied the optimal prices for ride-sourcing that must compete with taxis and public transportation, and they suggested that optimal surcharges should be slightly higher if the average occupancy rate for ride-sourcing services is increased. The authors of Liu et al. [36] studied the curbside pricing for managing ride-hailing pick-ups and drop-offs, and they found that the optimal curbside pricing could effectively reduce curbside congestion and the total social cost of the traffic system. In Zhong et al. [31], the authors explored the role of the surcharge policy for a ride-hailing service platform, and argued that the platform could set a low surcharge to shift the demand to those customers with the surcharge policy. The authors of Ke et al. [37] studied pricing and equilibrium in on-demand ride-pooling markets and found that the decrease in travel prices in a ride-pooling market attracted more passengers than a non-pooling market.

The following references focused on the dynamic and spatial pricing of ride-sourcing platforms. The authors of Chen et al. [16] studied the impact of dynamic optimization strategies on the ride-sourcing market and found that surge pricing could improve the optimization results. In Xu et al. [38], the authors studied the dynamic pricing of ride-sourcing services by considering time-dependent order cancellations, and they argued that dynamic pricing could sufficiently accommodate time-dependent systems such as these. In Afifah and Guo [39], the researchers investigated the impacts of spatial pricing for ride-sourcing services by considering traffic congestion and demonstrated optimal pricing strategies to minimize localized imbalances. In Li et al. [40], the authors studied the optimal spatial pricing for ride-sourcing platforms by considering a congestion charge and found that the one-directional cordon charge was effective for congestion mitigation. In Liang et al. [41], the researchers designed a pricing mechanism to incentivize passengers with spatially and temporally different demands to make different mobility choices, and they found that a dynamic pricing mechanism could achieve performance improvements.

While expanding the market demand by adjusting their prices, the providers of green travel services have also attracted consumers by displaying optimal green efforts. For example, they can increase the availability of green travel and shorten the waiting times of consumers by increasing the number of shared vehicles and the fleet size.

In Chen et al. [14], the authors studied the pricing and availability strategies of bike-sharing services for time-sensitive customers, and they suggested that a high availability rate encouraged potential customers to use bike-sharing services. This shows that the green travel demand is increasing with the green efforts of green travel providers. In Turan et al. [32], the authors studied dynamic pricing and fleet management for service providers of autonomous electric vehicles, and argued that it was probably better for the platform operator to set higher prices to prevent the queue from growing further. The authors of Zhang and Zhang [42] investigated optimal operations for ride-pooling services regarding the pricing, fleet size, and pooling size, and they observed that the pooling size should be optimized to mitigate congestion. In Guo et al. [33], the researchers studied the service mode selection of ride-hailing platforms and found that the platform could set the same prices for low-quality services, as compared to high-quality services.

The above references have extensively explored the pricing and effort strategies of green travel and have achieved significant findings overall. This study, however, investigated the pricing and effort decisions of green travel companies, versus those of non-green travel companies, in a competitive environment.

2.2. The Competition among Modes of Travel

There are many different modes of travel in the transportation market that compete against each other for the demand of consumers. The competition among different modes of travel includes public transit and private modes of travel [43], ride-sourcing platforms and taxis [23], and platform versus platform [44], among others. In addition, competition also emerges in other modes of travel, such as the competition between airlines [45,46] and competition between high-speed and conventional rail systems [47]. Furthermore, the competition between modes of travel can occur across different dimensions, including price, time, convenience, and accessibility, etc. This study focused on the price and effort competition between modes of travel.

The competition between public and private modes of travel includes several types, such as public versus private cars and public transit versus ride-sourcing platforms. In Emami et al. [44], the authors studied pricing competition between public and private cars and investigated the impact of transportation policies. They found that hybrid policies, such as increasing private car travel times coupled with lowered public in-vehicle travel times, could encourage consumers to choose public transit options. The authors of Yang et al. [48] investigated the competition and coordination behavior of public transportation modes, with both positive and negative externalities, and found that information affected the public transport mode choice behavior. In Rategh et al. [49], the authors investigated the pricing competition among airplanes, intercity buses, and high-speed railways. The authors found that the passengers’ heterogeneity was the main driver of the pricing competition between the three operators. In Sheu and Li [5], the authors studied the pricing and green transportation strategies of airlines under market competition, and they found that cost-inefficient companies with high operational costs should avoid pricing competition.

The competition between public transit and ride-sourcing platforms has attracted increasing attention. In Zhang and Nie [50], the authors studied the pricing of solo and pooling services of a transportation network company who competed with public transit, and they found that providing both solo and pooling rides could achieve the highest profit and trip production in most scenarios. The authors of Wei et al. [51] studied transit-planning optimization by considering ride-hailing competition and traffic congestion, and they found that optimized transit schedules led to system-wide cost reductions and achieved an optimal outcome. In Mo et al. [43], the researchers studied the competition between shared autonomous vehicles and public transit by considering adjustable fleet sizes and headways, and they found that the competition could improve both profits for operators and system efficiency. The authors of Li et al. [20] used a competitive game model to study the optimal pricing strategies of customized bus services and ride sharing, and they found that a firm’s profits were positively correlated with the proportion of platform-owned vehicles.

The competition between ride-sourcing platforms and taxis has also been explored. In Zhong et al. [17], the authors studied the pricing competition between ride-hailing platforms and taxi companies under government supervision, and they noted that the government should encourage competition between ride-hailing platforms and the traditional taxi industry. The authors of Guo et al. [52] optimized the operational decisions among shared autonomous vehicle systems that compete with human-driven private vehicles, and they argued that active relocation activities could increase the operating profits. In Yang et al. [53], the researchers used a multi-leader–follower game model to study pricing and relocation in a competitive car-sharing market, and they showed that the total profits of the market increased with the number of companies competing.

The following references investigated the competition between bike-sharing companies. In Jiang and Ouyang [54], the authors studied the operational decisions of bike-sharing companies by modeling their competition as a generalized Nash equilibrium problem, and they found that companies could deploy a surplus of bikes if they failed to recognize the competition stakes. In Jiang et al. [18], the researchers studied the competition of bike investment between two bike-sharing companies, and they developed a two-stage multi-period stochastic program to model the decision-making process. The authors of Cao et al. [19] studied the competition of pricing and bike investment between two bike-sharing firms, and they found that the competition could increase pricing and bike investments between the firms.

The competition between ride-sourcing platforms has also received attention. The researchers in Zhou et al. [55] studied the pricing competition between ride-sourcing platforms and found that market equilibrium was jointly governed by the degree of market fragmentation and the competition among platforms. The authors of Zhou et al. [56] studied the competition between ride-sourcing platforms by introducing third-party platform integration, and they found that platform integration could increase the total realized demand and improve social welfare. In Zhang and Nie [57], the authors studied the competition between two ride-hailing platforms, and they found that increased competition on the demand side offset the benefits of having a larger fleet. In Hong and Liu [6], the researchers studied the pricing strategies of ride-sharing platforms by considering the competition between green and basic ride services, and they suggested that the platform should set the price of green ride services to be higher than the price of basic ride services. This study focused on the competition between green and non-green modes of travel, and we investigated the impact of competition on pricing and green service strategies.

2.3. Government Subsidies for Green Travel

In order to encourage sustainable travel choices among consumers and reduce carbon emissions in the transportation industry, governments have introduced different types of subsidy mechanisms. Government subsidies can be classified according to their targets. For example, a government can subsidize enterprises that increase the availability of green travel options [14,58], or it can subsidize consumers who select green travel options [21].

Government subsidies have been used to encourage enterprises to improve the availability of green travel options. The authors of Chen et al. [14] considered governmental cost-sharing strategies to improve vehicle availability for bike-sharing companies, and they suggested that increasing the subsidy to improve the bike-sharing availability may not necessarily improve social welfare. In Mo et al. [12], the researchers studied the government’s compromise between subsidies for charging stations and subsidies for electric vehicle purchases, and they numerically showed that increasing both types of subsidies could achieve price reductions for consumers. The authors of Zhao et al. [13] evaluated governmental subsidies for the purchase of new vehicles by ride-sourcing platforms, and they found that the increase in governmental subsidies reduced the ride-fare rates of the two competitive platforms. In Srivastava et al. [59], the authors studied governmental incentives, such as subsidies and taxation schemes, in increasing the market penetration of electric vehicles, and they found that a mixed taxation–subsidy policy could maximize social welfare.

Government subsidies have been used to encourage consumers to choose green travel options. In Zhao et al. [22], the authors used an environmental protection subsidy to encourage passengers to use sustainable travel modes between cities, and they showed that a governmental subsidy had a significant impact on more sustainable intercity travel choices.In Zhu et al. [21], the researchers considered providing governmental subsidies for public transit riders who used ride sourcing to solve first- and last-mile problems, and they found that a strategic subsidy could boost ride-sourcing services. The authors of Fan et al. [11] analyzed governmental subsidies that promoted the sharing of electric vehicles, and they observed that allocating subsidies between companies and consumers in a certain proportion could effectively motivate residents to use shared electric vehicles.

The aforementioned references explored the impact of governmental subsidies on promoting green travel. This study introduced governmental subsidies into the competition between green and non-green travel companies. The governmental subsidies in this study appeared in the context of the governmental cost sharing of effort with green travel companies.

This study examined pricing and green effort strategies by considering the competition between green and non-green travel companies. A governmental subsidy for green effort was introduced, and its impact on travel company strategies and the effect of promoting green travel for consumers was discussed. The position of this study is presented in

Table 1. Position of this study.

References	Green Effort	Travel Mode Competition	Government Subsidy
Fan et al. [11]	$\surd$		$\surd$
Chen et al. [14]	$\surd$		$\surd$
Mo et al. [12]	$\surd$		$\surd$
Zhao et al. [13]	$\surd$		$\surd$
Srivastava et al. [59]	$\surd$		$\surd$
Hong and Liu [6]	$\surd$	$\surd$
Rategh et al. [49]	$\surd$	$\surd$
Wei et al. [51]	$\surd$	$\surd$
Yang et al. [53]	$\surd$	$\surd$
Mo et al. [43]		$\surd$	$\surd$
Zhu et al. [21]		$\surd$	$\surd$
Zhong et al. [17]		$\surd$	$\surd$
Zhao et al. [22]		$\surd$	$\surd$
Present paper	$\surd$	$\surd$	$\surd$

.

3. Problem Description and Notations

This study considered a travel market consisting of a green travel company and a non-green travel company and studied their travel price decisions in a competitive environment, along with the green effort employed by the green travel company. When a consumer had to travel, they could select a green or non-green mode of travel. In this study, i represents the mode of travel, where $i=1$ and $i=2$ indicate that the consumer selects a green or non-green mode of travel, respectively.

The providers of green and non-green modes of travel were in competition with each other in this study. The green and non-green modes of travel were abstractly defined in the Introduction, though the modes of travel were not limited to specific vehicles. This approach facilitated the model construction and result analysis. However, it also limited our research to an extent.

Due to the successive introduction of environmental protection policies and the increasing consumer awareness of environmental protection, more sustainable modes of travel are gradually becoming preferred by consumers. Therefore, a green travel company implemented green effort e to increase the consumer demand for green travel. In addition, the green effort introduced a cost to the green travel company, and this incurred cost was defined as $k{e}^2/2$, where k represents the cost coefficient of the green effort. The cost of green effort might include the purchase of green transportation vehicles and technological investment in green transportation vehicles. For example, purchasing new energy vehicles on ride-sharing platforms incurred purchase cost [13], while improving the availability of bikes by bike-sharing companies incurred investment cost [14]. To avoid the loss of generality, we normalized the unit costs of green and non-green travel to zero. Similar treatments can be found in the works of [45,60]. The standardization of transport costs can simplify the mathematical model without losing generality. Considering that the transport cost is fixed, as long as the travel price is higher than the transport cost, companies always pursue the expansion of the market demand. At this point, there is no difference between a non-zero unit transport cost and a zero unit transport cost. When specific vehicles are considered in green and non-green modes of travel, the transport costs can be estimated from different aspects [24], such as movement costs, parking costs, fixed costs, etc.

In this study, $p_1$ and $p_2$ were used to denote green and non-green travel prices, which were decided by the green and non-green travel companies, respectively. Considering the pricing competition among travel companies, we assumed that both the green travel price $p_1$ and non-green travel price $p_2$ had an impact on the green and non-green travel demand. In addition, the green effort of the green travel company had a positive impact on the demand for green travel. Therefore, the demand for green travel options of the consumers was defined as the following:

$$D_1=a_1-b_1{p}_1+c_1{p}_2+ge$$

(1)

where $a_1$ represents the market size of green travel. To avoid the loss of generality, we assumed that $a_1$ was sufficiently large to ensure that the green travel demand would always be non-negative. The variable $b_1$ represents the marginal effect coefficient of the green travel price on the green travel demand, $c_1$ represents the marginal effect coefficient of the non-green travel price on the green travel demand, and g represents the marginal effect coefficient of the green effort on the green travel demand. The non-green travel demand of the consumers was defined as the following:

$$D_2=a_2-b_2{p}_2+c_2{p}_1$$

(2)

where $a_2$ represents the market size of non-green travel. To avoid the loss of generality, we assumed that $a_2$ was sufficiently large to ensure that the non-green travel demand was always non-negative. The variable $b_2$ represents the marginal effect coefficient of the non-green travel price on the non-green travel demand, and $c_2$ represents the marginal effect coefficient of the green travel price on the non-green travel demand. Considering that the impact of the non-green travel price on the green travel demand was higher than the impact of the green travel price on the non-green travel demand, this study assumed $c_1>c_2$. In addition, this study ignored the impact of the green travel company’s green effort on the non-green travel demand.

To reveal the competitive behavior between the green and non-green travel companies, this study examined the travel price and green effort decisions of the green and non-green travel companies in centralized and decentralized decision-making scenarios. In the centralized decision-making scenario, the green and non-green travel companies formed an integrated company and uniformly decided the green and non-green travel price schemes and green effort. In the decentralized decision-making scenario, the green travel company decided the green travel price and green effort, and the non-green travel company decided the non-green travel price.

Due to the additional expenses incurred by green effort, the green travel company implemented a green effort that maximized its own profit. However, the green effort at this time would not be socially optimal, i.e., it could not increase green travel to the greatest extent. Therefore, the government could subsidize the green travel company to improve this outcome. This study considered that the government could implement a cost-sharing approach to offset the additional expenses of the green travel company, which was denoted as the cost-sharing coefficient $\lambda$. In addition, we considered that both the green and non-green travel companies would introduce a carbon emission cost to the government. Therefore, we used $r_1$ and $r_2$ to denote the unit emission costs of green and non-green travel, respectively. To investigate the impact of governmental subsidies, this study investigated scenarios with and without governmental subsidies.

In summary, this study investigated four decision-making scenarios. We used $OC$ and $OD$ to represent the centralized and decentralized decision-making scenarios without governmental subsidies, respectively. We used $WC$ and $WD$ to represent the centralized and decentralized decision-making scenarios with the governmental subsidies, respectively. The notations used in this study are summarized in

Table 2. Notations and descriptions used in this study.

Notation	Description
Parameters
$D_i$	Demand of the ith mode of travel, where $i=1$ and $i=2$ denote the green and non-green modes of travel, respectively
$a_i$	Market size of the demand of the ith mode of travel
$b_i$	Marginal effect coefficient of the ith travel price on the demand of the ith mode of travel
$c_i$	Marginal effect coefficient of the (3-i)th travel price on the demand of the ith mode of travel
g	Marginal effect coefficient of the green effort on green travel demand
k	Cost coefficient of the green effort
$r_i$	Unit carbon emission cost of the ith mode of travel
Decision variables
$p_i$	Travel price of the ith mode of travel
e	Green effort of the green travel company
$\lambda$	Government’s sharing coefficient of the green effort cost
Superscripts
$OC$	Centralized decision-making without governmental subsidies
$OD$	Decentralized decision-making without governmental subsidies
$WC$	Centralized decision-making with governmental subsidies
$WD$	Decentralized decision-making with governmental subsidies

.

4. Decisions without Governmental Subsidies

This section describes the decision-making for the green and non-green travel companies in the absence of governmental subsidies. We first assumed that the green and non-green travel companies formed an integrated company and would make optimal decisions on travel prices and green effort in the OC scenario. The optimal results in the OC scenario provided a benchmark for system performance. Subsequently, because the green and non-green travel companies were independent economic entities, the Nash game equilibrium strategies of travel prices and green effort were provided in the OD scenario. By comparing decision results in the OC and OD scenarios, the impact of decentralized decision-making on system performance was revealed.

4.1. Centralized Decision-Making without Governmental Subsidies

The centralized decision-making without governmental subsidies (OC) was considered, i.e., the green and non-green travel companies formed an integrated company, which determined their travel prices and green effort. Therefore, the profit function of this integrated company was the following:

$$\begin{array}{cc}\hfill U^{OC}& =p_1^{OC}{D}_1^{OC}+p_2^{OC}{D}_2^{OC}-k{\left(e^{OC}\right)}^2/2\end{array}$$

(3)

where the first two items represent the benefits of the green and non-green travel demand to the integrated company, respectively, and the third item represents the green effort cost undertaken by the integrated company. The optimal results are placed in Proposition 1. All mathematical proofs are included in Appendix A.

Proposition 1.

In the scenario of centralized decision-making without a government subsidy, the green and non-green travel prices were $p_1^{OC}=k(2a_1{b}_2+a_2{c}_0)/[2b_2(2k{b}_1-g^2)-k{c}_0^2]$ and $p_2^{OC}=\left[k(2a_2{b}_1+a_1{c}_0)-a_2{g}^2\right]/[2b_2(2k{b}_1-g^2)-k{c}_0^2]$, respectively, and the green effort was $e^{OC}=g(2a_1{b}_2+a_2{c}_0)/\left[2b_2(2k{b}_1-g^2)-k{c}_0^2\right]$, where $c_0=c_1+c_2$.

Because the travel prices and green effort could not be negative, we assumed that $2b_2(2k{b}_1-g^2)>k{c}_0^2$. From Proposition 1, we observed that $p_1^{OC}$, $p_2^{OC}$, and $e^{OC}$ increased with $a_1$ as well as $a_2$. Regardless of the green or non-green travel demand, as the market size increased, this integrated company increased the green and non-green travel prices and green effort. The higher the number of travelers was, the higher the prices of green and non-green travel were. In addition, a better green effort could be implemented. We also observed that $p_1^{OC}$ and $e^{OC}$ decreased with $b_1$. As the marginal effect coefficient of the green travel prices on the green travel demand increased, this integrated company reduced its green travel prices and green effort. Similarly, with the increase in the marginal effect coefficient of the non-green travel prices on the non-green travel demand, the non-green travel prices were reduced.

Proposition 1 also shows that $p_1^{OC}$, $p_2^{OC}$, and $e^{OC}$ increased with $c_0$. As the marginal effect coefficient of the non-green/green travel prices on the green/non-green travel demand increased, the green and non-green travel prices and green effort increased. When g increased, $p_1^{OC}$ and $e^{OC}$ increased. As the marginal effect coefficient of green effort on the green demand increased, the green travel price increased, and the green effort improved. In addition, $p_1^{OC}$ and $e^{OC}$ decreased with k. As the marginal cost coefficient of the green effort increased, this integrated company reduced the green travel prices and green effort.

Corollary 1 shows that the increase in the market size of green and non-green travel could increase the green travel demand. Green travel benefited from the large market size of both green and non-green travel. This was interesting. Due to the cross-influences of green and non-green travel prices on the travel demand, the increase in the market size of the non-green travel also increased the green travel demand. However, the non-green travel demand decreased with the market size of green travel. Based on $c_1>c_2$, the impact of the non-green travel price on the green travel demand was higher than the impact of the green travel price on the non-green travel demand. Here, the increase in the market size of green travel reduced the non-green travel demand. Corollary 1 also reveals that as the marginal effect coefficient of the green effort on the green travel demand increased, both the green and non-green travel demands increased. The increase in the marginal effect of the green effort on the green travel demand promoted both green and non-green travel.

Corollary 1.

In the scenario of centralized decision-making without a government subsidy, the green travel demand was $D_1^{OC}=[k{b}_1(2a_1{b}_2+a_2{c}_1-a_2{c}_2)+c_2(a_2{g}^2-k{a}_1{c}_0)]/[2b_2(2k{b}_1-g^2)-k{c}_0^2]$ and increased with $a_1$, $a_2$, and g. The non-green travel demand was $D_2^{OC}=[k{b}_2(2a_2{b}_1+a_1{c}_2-a_1{c}_1)-a_2(b_2{g}^2+k{c}_1{c}_0)]/[2b_2(2k{b}_1-g^2)-k{c}_0^2]$, which decreased with $a_1$ and increased with $a_2$ and g.

Corollary 2 shows that in the OC scenario, when the ratio of the market sizes of green travel to non-green travel was greater than the lower bound ${\Lambda }_1$, the integrated company could set a higher green travel price than a non-green travel price. In other words, as long as the market size of green travel was sufficiently larger than that of non-green travel, the green travel price could be higher than the non-green travel price. Conversely, when the ratio $a_1/a_2$ fell below the lower bound, the green travel price would be lower than the non-green travel price.

Corollary 2.

In the scenario of centralized decision-making without a government subsidy, the green travel price was higher than the non-green travel price when $a_1/a_2>{\Lambda }_1$, where ${\Lambda }_1=(2b_1-c_0-g^2/k)/(2b_2-c_0)$. Otherwise, the green travel price was lower than the non-green travel price.

Corollary 3 shows that in the OC scenario, the green travel demand was greater than the non-green travel demand, as long as the ratio of the market size of green travel to non-green travel $a_1/a_2$ was greater than the lower bound ${\Lambda }_2$. This was easy to observe. Once the market size of green travel was sufficiently larger than that of non-green travel, the travel prices and green strategic decisions could not change the size relationship between the green and non-green travel demands.

Corollary 3.

In the scenario of centralized decision-making without a government subsidy, the green travel demand was higher than the non-green travel demand when $a_1/a_2>{\Lambda }_2$, where ${\Lambda }_2=[b_1(2b_2+c_2-c_1)+c_1{c}_0-(c_2+b_2)g^2/k]/[b_2(2b_1-c_2-c_1)-c_2{c}_0]$. Otherwise, the green travel demand was lower than the non-green travel demand.

In the absence of governmental subsidies, the results of Proposition 1 and Corollary 1 provide benchmarks for system performance.

4.2. Decentralized Decision-Making without Governmental Subsidies

In the scenario of decentralized decision-making without a government subsidy (OD), the green and non-green travel companies were two companies with independent interests, and they made decisions on the premise of maximizing their individual profits. The green travel company determined the green travel price $p_1^{OD}$ and the green effort $e^{OD}$, and the non-green travel company determined the non-green travel price $p_2^{OD}$. In this scenario, the green and non-green travel companies had a competitive relationship. Without governmental subsidies, the green and non-green travel companies constituted a Nash game [61]. The profit function of the green travel company was the following:

$$\begin{array}{c}\hfill {\Pi }_1^{OD}=p_1^{OD}{D}_1^{OD}-k{\left(e^{OD}\right)}^2/2,\end{array}$$

(4)

where the first item represents the revenue obtained by the green travel company from the green travel demand, and the second item represents the green effort cost of the green travel company.

The profit function of the non-green travel company was the following:

$$\begin{array}{c}\hfill {\Pi }_2^{OD}=p_2^{OD}{D}_2^{OD}.\end{array}$$

(5)

The optimal results are shown in Proposition 2.

Proposition 2.

In the decentralized decision-making without a government subsidy scenario, the green and non-green travel prices were $p_1^{OD}=(2k{a}_1{b}_2+k{a}_2{c}_1)/[2b_2(2k{b}_1-g^2)-k{c}_1{c}_2]$ and $p_2^{OD}=[a_2(2k{b}_1-g^2)+k{a}_1{c}_2]/[2b_2(2k{b}_1-g^2)-k{c}_1{c}_2]$, respectively. The green effort was $e^{OD}=g(2a_1{b}_2+a_2{c}_1)/[2b_2(2k{b}_1-g^2)-k{c}_1{c}_2]$.

Proposition 2 shows that $p_1^{OD}$, $p_2^{OD}$, and $e^{OD}$ all increased with $a_1$ and $a_2$. For green and non-green travel, as the market size increased, both the green and non-green travel companies increased their travel prices. Simultaneously, the green travel company increased its green effort. For the green and non-green travel companies, a sufficiently large travel market size provided them with opportunities to their increase travel prices. As the green travel price increased, the green travel company also increased its green effort.

Proposition 2 also shows that $p_1^{OD}$, $p_2^{OD}$, and $e^{OD}$ all increased with $c_1$ and $c_2$. As the marginal effect coefficient of the non-green/green travel price on the green/non-green travel demand increased, the green travel price, non-green travel price, and green effort increased. When g increased, $p_1^{OD}$ and $e^{OD}$ increased. As the marginal effect coefficient of the green effort on the green travel demand increased, both the green travel price and green effort increased.

Corollary 4 shows that in the OD scenario, the market size of green travel, the market size of non-green travel, and the marginal influence coefficient of the green effort had a positive impact on the green and non-green travel demand. As the size of the travel market increased, both the green and non-green travel demands increased. In addition, the increasing marginal effect of the green effort on the green travel demand promoted both green and non-green travel.

Corollary 4.

In the scenario of decentralized decision-making without a government subsidy, the green travel demand was $D_1^{OD}=k{b}_1(2a_1{b}_2+a_2{c}_1)/[2b_2(2k{b}_1-g^2)-k{c}_1{c}_2]$, which increased with $a_1$, $a_2$, and g. The non-green travel demand was $D_2^{OD}=b_2[a_2(2k{b}_1-g^2)+k{a}_1{c}_2]/[2b_2(2k{b}_1-g^2)-k{c}_1{c}_2]$, which increased with $a_1$, $a_2$, and g.

Corollary 5 shows that the green travel company could set a higher travel price than the non-green travel price, but this was conditional. The condition was that the ratio of the market size of green travel to non-green travel $a_1/a_2$ had to be greater than the lower bound ${\Lambda }_3$, which was easy to observe. When the green travel market was sufficiently large, the green travel company had an advantage in travel competition. Therefore, it could withstand the losses caused by the decrease in green travel, which was caused by the increase in the green travel price. However, when $a_1/a_2$ fell below the lower bound, the green travel company had to set a lower green travel price.

Corollary 5.

In the scenario of decentralized decision-making without a government subsidy, the green travel price was higher than the non-green travel price when $a_1/a_2>{\Lambda }_3$, where ${\Lambda }_3=(2b_1-c_1-g^2/k)/(2b_2-c_2)$. Otherwise, the green travel price was lower than the non-green travel price.

Corollary 6 shows that when the ratio of the market size of green travel to non-green travel $a_1/a_2$ was greater than the threshold ${\Lambda }_4$, the green travel demand was greater than the non-green travel demand. This was intuitive. When the market size of green travel was sufficiently large, more consumers would choose green travel. Conversely, the non-green travel market would attract more consumers. Note that ${\Lambda }_4$ increased with the cost coefficient of the green effort k. Therefore, as k increased, it became difficult for the green travel demand to exceed the non-green travel demand. The reason was that the green travel company reduced its green effort at this time.

Corollary 6.

In the scenario of decentralized decision-making without a government subsidy, the green travel demand was higher than the non-green travel demand when $a_1/a_2>{\Lambda }_4$, where ${\Lambda }_4=[b_1(2b_2-c_1)-b_2{g}^2/k]/b_2(2b_1-c_2)$. Otherwise, the green travel demand was lower than the non-green travel demand.

Corollary 7 shows that the profits of the green travel company were higher than those of the non-green travel company when the ratio of the market size of green travel to non-green travel $a_1/a_2$ was above the lower bound ${\Lambda }_5$. When the market size of green travel was sufficiently large, the green travel company would always obtain more profits than the non-green travel company.

Corollary 7.

In the scenario of decentralized decision-making without a government subsidy, the profit of the green travel company was greater than that of the non-green travel company when $a_1/a_2>{\Lambda }_5$, where ${\Lambda }_5=(2b_1\sqrt{b_2}-c_1\sqrt{b_1-\frac{g^2}{2k}})/(2b_2\sqrt{b_1-\frac{g^2}{2k}}-c_2\sqrt{b_2})$. Otherwise, the profit of the green travel company was lower than that of the non-green travel company.

Note that the ${\Lambda }_5$ decreased with $b_1-g^2/\left(2k\right)$ and $b_1-g^2/\left(2k\right)$ increased with k. Therefore, k had a negative effect on ${\Lambda }_5$. As k increased, it became easier for the green travel company to acquire more profit than the non-green travel company. This was counter-intuitive. It was easy to observe that a large cost coefficient of the green effort had a negative impact on the green travel company. Surprisingly, a large cost coefficient of the green effort also had a negative impact on the non-green travel company. Furthermore, the profit of the non-green travel company decreased more rapidly with the cost coefficient of the green effort than that of the green travel company’s profit.

4.3. Impact of Decision-Making Scenarios

This section compares the optimal results in the OC scenario with the equilibrium results in the OD scenario, in order to reveal the impact of OD decision-making on travel prices and green effort. Propositions 1 and 2 were compared, and the results are shown in Corollary 8.

Corollary 8.

Compared with centralized decision-making, decentralized decision-making reduced the green travel price, non-green travel price, and green effort.

Corollary 8 shows that the equilibrium results in the OD scenario deviated from the optimal results in the OC scenario. In the OD scenario, the green and non-green travel companies made decisions to maximize their individual profits, which resulted in a decrease in travel prices and green effort. Similar observations have been obtained in previous studies [54,57]. Furthermore, the competition between the green and non-green travel companies in the OD scenario caused the two companies to reduce their travel prices to compete in the travel market. In addition, the green travel company reduced its green effort in the OD scenario.

By comparing Corollaries 1 and 4, we easily observe that the impact of the market size of green travel on the non-green travel demand exhibited different laws in the OC and OD scenarios.

Corollary 9 provides an interesting conclusion. The increase in the market size of green travel in the OD scenario promoted the non-green travel demand, whereas the result in the OC scenario was the opposite. In either the OC or OD scenario, both the green and non-green travel prices increased with the market size of green travel (Propositions 1 and 2). Because the impact of the non-green travel price on the green travel demand was higher than the impact of the green travel price on the non-green travel demand ($c_1>c_2$), the green travel price increased more rapidly with the market size of green travel than that of the non-green travel price in the OC scenario. This caused the non-green travel demand in the OC scenario to decrease with the market size of green travel. However, the green travel price increased more gradually with the market size of green travel than the non-green travel price in the OD scenario. This caused the non-green travel demand in the OD scenario to increase with the market size of green travel. In the OD scenario, the existence of a double marginal effect caused the green and non-green travel companies to make travel price decisions that maximized their individual profits.

Corollary 9.

The market size of green travel had a negative impact on the non-green travel demand in the centralized decision-making scenario and a positive impact in the decentralized decision-making scenario.

5. Decisions with Governmental Subsidies

In this section, we describe the decision-making of the green and non-green travel companies with governmental subsidies. To incentivize the green travel company to increase its green effort, the government considered subsidizing the green travel company. This subsidy was manifested in the government’s cost-sharing approach. We assumed that the costs shared by the government were represented by $\lambda k{e}^2/2$, where $\lambda$ is the sharing coefficient and $0<\lambda <1$.

When the government provided a green effort subsidy, the government and travel companies constituted a Stackelberg game [62]. The government was the leader of the game, and the green and non-green travel companies were the followers. In addition, the green and non-green travel companies constituted a Nash game in the competition. The government first decided on the sharing coefficient of the green effort costs. Subsequently, the green travel companies determined the green travel prices and green effort, and the non-green travel company determined the non-green travel prices.

We considered the interest of the government from three aspects. First, we assumed that the stable operation of a transportation system would result in a social benefit ${\pi }_0$ for the government. Second, we assumed that both non-green and green travel generated carbon emissions, and the emissions generated per unit of green travel were less than that generated per unit of non-green travel. We used $r_1$ and $r_2$ to represent the carbon emissions generated per units of green and non-green travel, respectively. The carbon emissions generated by green and non-green travel options caused a loss for the government. To avoid the loss of generality, we assumed that a unit of carbon emissions resulted in one unit of lost profit for the government. Therefore, the losses generated by the carbon emissions of green travel options for the government could be expressed as $r_1{D}_1$, and the losses generated by non-green travel’s carbon emissions were $r_2{D}_2$. Finally, the government had to bear the green effort costs $\lambda k{e}^2/2$. From the above analysis, the government’s profit function was defined, as follows:

$$\begin{array}{c}\hfill \pi ={\pi }_0-r_1{D}_1-r_2{D}_2-\lambda k{e}^2/2.\end{array}$$

(6)

Correspondingly, the profit function of the green travel company was the following:

$$\begin{array}{c}\hfill {\Pi }_1=p_1{D}_1-\left(1-\lambda \right)k{e}^2/2.\end{array}$$

(7)

Similar to Section 4, we first considered the centralized decision-making scenario and determined the optimal results to provide a benchmark for the performance of the system. Subsequently, we presented the equilibrium strategies of the green and non-green travel companies in the decentralized decision-making scenario.

5.1. Centralized Decision-Making with Governmental Subsidies

In the scenario of centralized decision-making with a government subsidy (WC), the green and non-green travel companies formed an integrated company. The integrated company and the government constituted a Stackelberg game. The government was the leader, and the integrated company was the follower. The government first determined ${\lambda }^{WC}$. Subsequently, the integrated company determined $p_1^{WC}$, $p_2^{WC}$, and $e^{WC}$. In this scenario, the profit function of the integrated company was the following:

$$\begin{array}{c}\hfill U^{WC}=p_1^{WC}{D}_1^{WC}+p_2^{WC}{D}_2^{WC}-k\left(1-{\lambda }^{WC}\right){\left(e^{WC}\right)}^2/2.\end{array}$$

(8)

Proposition 3 shows that $e^{WC}$ increased with ${\lambda }^{WC}$. As the government’s sharing coefficient of the green effort cost increased, the integrated company increased its green effort. In the WC scenario, the green and non-green travel prices also increased with ${\lambda }^{WC}$. When ${\lambda }^{WC}=0$, the green effort, green travel price, and non-green travel price were all the same as those in Proposition 1. Therefore, when ${\lambda }^{WC}>0$, the green effort, green travel prices, and non-green travel prices were higher than those in the OC scenario. This showed that governmental subsidies effectively incentivized the integrated company to increase its green effort. This result was consistent with Chen et al. [14]. A subsidy given by the government improved the green effort of the company. The government’s cost sharing of the green effort enabled the integrated company to increase the green and non-green travel prices. In addition, Proposition 3 shows that $e^{WC}$ increased with $a_1$ and $a_2$, when ${\lambda }^{WC}$ was fixed.

Proposition 3.

In the scenario of centralized decision-making with a government subsidy, the government’s sharing coefficient of the green effort cost was ${\lambda }^{WC}=[2b_2{g}^2({\Theta }_1+4b_2{\Theta }_2-2{\Theta }_3{\Theta }_4)+k{\Theta }_4(12b_2{\Theta }_2+2{\Theta }_3-{\Theta }_1)]/k{\Theta }_4({\Theta }_1+12b_2{\Theta }_2+2{\Theta }_3{\Theta }_4)$, where ${\Theta }_1={(2a_1{b}_2+a_2{c}_0)}^2$, ${\Theta }_2=(r_1{b}_1-r_2{c}_2)(2a_1{b}_2+a_2{c}_0)+(r_2{b}_2-r_1{c}_1)(2a_2{b}_1+a_1{c}_0)$, ${\Theta }_3=2b_2(r_2{b}_2-r_1{c}_1)+r_1(2a_1{b}_2+a_2{c}_0)$, and ${\Theta }_4=4b_1{b}_2-c_0^2$. The green travel price was $p_1^{WC}=(2a_1{b}_2+a_2{c}_0)/\{4b_1{b}_2-c_0^2-2b_2{g}^2/\left[k(1-{\lambda }^{WC})\right]\}$ and increased with ${\lambda }^{WC}$. The green effort was $e^{WC}=g(2a_1{b}_2+a_2{c}_0)/\{4b_1{b}_2-c_0^2-2b_2{g}^2/\left[k(1-{\lambda }^{WC})\right]\}$ and increased with ${\lambda }^{WC}$. The non-green travel price was $p_2^{WC}=\{2a_2{b}_1+a_1{c}_0-a_2{g}^2/\left[k(1-{\lambda }^{WC})\right]\}/\{4b_1{b}_2-c_0^2-2b_2{g}^2/\left[k(1-{\lambda }^{WC})\right]\}$ and increased with ${\lambda }^{WC}$.

Corollary 10 shows that in the WC scenario, when the ratio of the market size of green travel to non-green travel $a_1/a_2$ was greater than the lower bound ${\Lambda }_6$, the integrated company could set a higher green travel price than the non-green travel price. When the market size of green travel was much larger than that of non-green travel, the green travel price could be higher than the non-green travel price. Note that ${\Lambda }_6$ decreased with ${\lambda }^{WC}$; thus, a larger sharing coefficient could cause the green travel price to exceed the non-green travel price. In particular, when the government’s cost-sharing coefficient was sufficiently large, the non-green travel price was likely to be lower than the green travel price.

Corollary 10.

In the scenario of centralized decision-making with a government subsidy, the green travel price was higher than the non-green travel price when $a_1/a_2>{\Lambda }_6$, where ${\Lambda }_6=[2b_1-c_0-g^2/k(1-{\lambda }^{WC})]/(2b_2-c_0)$. Otherwise, the green travel price was lower than the non-green travel price.

Corollary 11 shows that in the WC scenario, when the ratio of the market size of green travel to non-green travel $a_1/a_2$ was greater than the lower bound ${\Lambda }_7$, the green travel demand was greater than the non-green travel demand. Note that ${\Lambda }_7$ decreased with ${\lambda }^{WC}$. With the increase in the government’s sharing coefficient, the green travel demand had more opportunities to exceed the non-green travel demand. In particular, a sufficiently large government cost-sharing coefficient induced a higher green travel demand, as compared to the non-green travel demand. This result was similar to that in Fan et al. [11]. Therefore, a subsidy could encourage consumers to choose a green mode of travel.

Corollary 11.

In the scenario of centralized decision-making with a government subsidy, the green travel demand was higher than the non-green travel demand when $a_1/a_2>{\Lambda }_7$, where ${\Lambda }_7=[b_1(2b_2+c_2-c_1)+c_1{c}_0-(c_2+b_2)g^2/k(1-{\lambda }^{WC})]/[b_2(2b_1-c_2-c_1)-c_2{c}_0]$. Otherwise, the green travel demand was lower than the non-green travel demand.

5.2. Decentralized Decision-Making with Governmental Subsidies

In the scenario of decentralized decision-making with a government subsidy (WD), the green and non-green travel companies were independent. The government, the green travel company, and the non-green travel company constituted a Stackelberg–Nash game. The government was the leader, and the two travel companies were the followers. The game was played in two stages. In the first stage, the government determined ${\lambda }^{WD}$. In the second stage, the green travel company determined $p_1^{WD}$ and $e^{WD}$, and the non-green travel company determined $p_2^{WD}$. The profit function of the green travel company was the following:

$$\begin{array}{c}\hfill {\Pi }_1^{WD}=-b_1{\left(p_1^{WD}\right)}^2+a_1{p}_1^{WD}+g{e}^{WD}{p}_1^{WD}+c_1{p}_1^{WD}{p}_2^{WD}-k\left(1-{\lambda }^{WD}\right){\left(e^{WD}\right)}^2/2.\end{array}$$

(9)

The profit function of the non-green travel company was the following:

$$\begin{array}{c}\hfill {\Pi }_2^{WD}=-b_2{\left(p_2^{WD}\right)}^2+a_2{p}_2^{WD}+c_2{p}_1^{WD}{p}_2^{WD}\end{array}$$

(10)

Proposition 4 shows that $e^{WD}$ increased with ${\lambda }^{WD}$ in the WD scenario. As the government’s sharing coefficient of the green effort cost increased, the green travel company increased its green effort. In the WD scenario, the green and non-green travel prices also increased with ${\lambda }^{WD}$. This showed that governmental subsidies effectively incentivized the green travel company to implement green effort. This result was consistent with that in Zhao et al. [22]. Correspondingly, the green travel company could increase the green travel price. Interestingly, the non-green travel company could also increase the non-green travel price. The reason could have been that the governmental subsidies caused the green travel company to increase the green travel price, which created an opportunity for the non-green travel company to increase the non-green travel price.

Proposition 4.

In the scenario of decentralized decision-making with a government subsidy, the government’s sharing coefficient of the green effort cost was ${\lambda }^{WD}=[2b_2{g}^2({\Phi }_1+4b_2{\Phi }_2-2{\Phi }_3{\Phi }_4)+k{\Phi }_4(12b_2{\Phi }_2+2{\Phi }_3-{\Phi }_1)]/k{\Phi }_4({\Phi }_1+12b_2{\Phi }_2+2{\Phi }_3{\Phi }_4)$, where ${\Phi }_1={(2a_1{b}_2+a_2{c}_1)}^2$, ${\Phi }_2=(r_1{b}_1-r_2{c}_2)(2a_1{b}_2+a_2{c}_1)+(r_2{b}_2-r_1{c}_1)(2a_2{b}_1+a_1{c}_2)$, ${\Phi }_3=2b_2(r_2{b}_2-r_1{c}_1)+r_1(2a_1{b}_2+a_2{c}_1)$, and ${\Phi }_4=4b_1{b}_2-c_1{c}_2$. The green travel price was $p_1^{WD}=(2a_1{b}_2+a_2{c}_1)/\{(4b_1{b}_2-c_1{c}_2)-[2b_2{g}^2/k(1-{\lambda }^{WD})]\}$ and increased with ${\lambda }^{WD}$. The green effort was $e^{WD}=g(2a_1{b}_2+a_2{c}_1)/[k(1-{\lambda }^{WD})(4b_1{b}_2-c_1{c}_2)-2b_2{g}^2]$ and increases with ${\lambda }^{WD}$. The non-green travel price was $p_2^{WD}=[k(1-{\lambda }^{WD})(2a_2{b}_1+a_1{c}_2)-a_2{g}^2]/[k(1-{\lambda }^{WD})(4b_1{b}_2-c_1{c}_2)-2b_2{g}^2]$ and increased with ${\lambda }^{WD}$.

In addition, Proposition 4 showed that $e^{WD}$ increased with $a_1$ and $a_2$, when ${\lambda }^{WD}$ was fixed. This observation was consistent with that in Propositions 2–4, which did not depend on the decision-making scenarios. Both the market sizes of green and non-green travel could boost the green effort.

Corollary 12 shows that when the ratio of the market size of green travel to non-green travel $a_1/a_2$ was greater than the threshold ${\Lambda }_8$, the green travel price was greater than the non-green travel price. Furthermore, we observed that the government’s sharing coefficient had a negative effect on ${\Lambda }_8$. As the government’s sharing coefficient increased, the green travel price easily exceeded the non-green travel price. Therefore, governmental subsidies offered the green travel company the opportunity to set a higher travel price. This result was different from that in Mo et al. [12], where governmental subsidies had been found to reduce travel prices.

Corollary 12.

In the scenario of decentralized decision-making with a government subsidy, the green travel price was higher than the non-green travel price when $a_1/a_2>{\Lambda }_8$, where ${\Lambda }_8=\left[2b_1-c_1-g^2/k(1-{\lambda }^{WD})\right]/\left(2b_2-c_2\right)$. Otherwise, the green travel price was lower than the non-green travel price.

Corollary 13 shows that when the ratio of the market size of green travel to non-green travel $a_1/a_2$ was greater than the threshold ${\Lambda }_9$, the green travel demand was greater than the non-green travel demand. Therefore, a sufficiently large market size of green travel could always induce more consumers to choose green travel. Note that ${\Lambda }_9$ decreased with ${\lambda }^{WD}$. Therefore, with the increase in the government’s sharing coefficient, the green travel demand was more likely to exceed the non-green travel demand. The reason was that governmental subsidies incentivized the green travel company to implement more green effort.

Corollary 13.

In the scenario of decentralized decision-making with a government subsidy, the green travel demand was higher than that of non-green travel when $a_1/a_2>{\Lambda }_9$, where ${\Lambda }_9=[b_1(2b_2-c_1)-b_2{g}^2/k(1-{\lambda }^{WD})]/b_2(2b_1-c_2)$. Otherwise, the green travel demand was lower than that of non-green travel.

Corollary 14 shows that when the ratio of the market size of green travel to non-green travel was not less than the threshold, the profit of the green travel company was higher than that of the non-green travel company. When the green travel market was sufficiently large, the green travel company was always more profitable than the non-green travel company. Note that ${\Lambda }_{10}$ decreased with $b_1-g^2/\left[2k(1-{\lambda }^{WD})\right]$ and $b_1-g^2/\left[2k(1-{\lambda }^{WD})\right]$ decreased with ${\lambda }^{WD}$. Therefore, we found that ${\lambda }^{WD}$ had a positive effect on ${\Lambda }_{10}$. With the increase in the government’s sharing coefficient, it was difficult for the profit of the green travel company to exceed the profit of the non-green travel company. This was interesting. A larger share of the cost covered by the government benefited the non-green travel company.

Corollary 14.

In the scenario of decentralized decision-making with a government subsidy, the profit of the green travel company was greater than that of the non-green travel company when $a_1/a_2>{\Lambda }_{10}$, where ${\Lambda }_{10}=\frac{2b_1\sqrt{b_2}-c_1{[b_1-\frac{g^2}{2k(1-{\lambda }^{WD})}]}^{\frac{1}{2}}}{2b_2{[b_1-\frac{g^2}{2k(1-{\lambda }^{WD})}]}^{\frac{1}{2}}-c_2\sqrt{b_2}}$. Otherwise, the profit of the green travel company was less than that of the non-green travel company.

5.3. Impact of Decision-Making Scenarios

To reveal the impact of WD on travel prices and green effort, this section compares the optimal results in the WC scenario with the equilibrium results in the WD scenario. The endogenous government’s sharing coefficient $\lambda$ was difficult to theoretically analyze due to its complicated expression. Therefore, we assumed that $\lambda$ was exogenous.

Corollary 15 shows that in the WD scenario, the green travel company reduced its green effort and set a lower green travel price, as compared to the WC scenario. In addition, the non-green travel price was reduced. Due to the existence of a double marginal effect, the green and non-green travel companies made decisions on travel prices and green effort to maximize their individual profits. By combining Corollaries 8 and 15, we could show that with or without governmental subsidies, decentralized decision-making reduced the travel prices and green effort. This result was inconsistent with that in Cao et al. [19].

Corollary 15.

When λ was exogenous, decentralized decision-making reduced the green travel price, non-green travel price, and green effort.

A question that still remained was whether the effect of decentralized decision-making on the travel prices and green effort was related to $\lambda$ being endogenous. However, there were theoretical difficulties involved in answering this question. In the Numerical Experiments section, we provide a detailed discussion of the optimal results by considering $\lambda$ to be endogenous.

6. Impact of Governmental Subsidies

6.1. Impact on Green Effort

Based on Propositions 3 and 4, the governmental subsidies promoted green effort both in the WC and WD scenarios. Therefore, we could directly obtain Corollary 16.

Corollary 16.

In both the centralized and decentralized decision-making scenarios, the governmental subsidies boosted the green effort.

Corollary 16 shows that governmental subsidies were effective. The government’s cost sharing with the green travel company enabled the green travel company to increase its green effort. The increase in green effort promoted green travel and environmental protection.

We then investigated whether there was a difference in the promotion of the green effort through governmental subsidies in the centralized and decentralized decision-making scenarios. Therefore, we compared the proportions of the green effort improvement in the centralized and decentralized decision-making scenarios, and the result is shown in Corollary 17.

Corollary 17.

As compared to decentralized decision-making, centralized decision-making could achieve a greater boost to green effort through governmental subsidies.

Corollary 17 showed that centralized decision-making was more effective than decentralized decision-making in realizing the promotion of green effort through governmental subsidies. In other words, decentralized decision-making weakened the effect of governmental subsidies on green effort improvement. Therefore, the government would prefer that the green and non-green travel companies form an integrated company.

6.2. Impact on Travel Prices

Propositions 1 and 3 indicated that in the centralized decision-making scenario, governmental subsidies increased both the green and non-green travel prices. When the green and non-green travel companies formed an integrated company, the government’s cost-sharing of the green effort prompted the integrated company to increase the green and non-green travel prices simultaneously. Propositions 2 and 4 indicate that the governmental subsidies increased the green and non-green travel prices in the WD scenario. In the WD scenario, the governmental subsidies enabled the green travel company to increase the green travel price and the non-green travel company to increase the non-green travel price. Therefore, we could directly obtain Corollary 18.

Corollary 18.

For the centralized and decentralized decision-making scenarios, the governmental subsidies increased the green and non-green travel prices.

Corollary 18 presents an interesting conclusion. The government’s cost sharing of the green effort increased the green and non-green travel prices. This was contrary to the results in Zhao et al. [13]. The authors found that governmental subsidies could reduce travel prices. The green travel company could increase the green travel price as the governmental subsidies boosted the green effort of the green travel company. Correspondingly, the non-green travel company could also increase the non-green travel price. However, an increase in the travel price was detrimental to travelers. For non-green travelers, the increase in travel prices increased their travel costs. For green travelers, the increase in travel prices also increased their travel costs, whereas an increase in green effort improved their travel experience.

Next, we investigated whether the governmental subsidies affected the green travel price differently than the non-green travel price. Therefore, we compared the green and non-green travel prices in the OC and WC scenarios (Corollaries 2 and 10) and those in the OD and WD scenarios (Corollaries 5 and 12). The results are shown in Corollary 19.

Corollary 19.

In both the centralized and decentralized decision-making scenarios, the green travel price exceeded the non-green travel price when the government’s cost-sharing coefficient was sufficiently large.

Corollary 19 provided a significant observation. As long as the government was willing to share a sufficiently large cost, the green travel price was unconditionally higher than the non-green travel price. The result was similar to that in Hong and Liu [6]. This could have been due to the increasing proportion of cost sharing also increasing the green effort, which created an opportunity for an increase in the green travel price. However, green effort had no direct impact on the non-green travel prices. The increase in the non-green travel price was attributed only to the increase in the green travel price.

6.3. Impact on Travel Demand

We investigated whether governmental subsidies affected the green travel demand differently than the non-green travel demand. Therefore, we compared the green and non-green travel demands in the OC and WC scenarios (Corollaries 3 and 11, respectively), and those in the OD and WD scenarios (Corollaries 6 and 13, respectively).The results are shown in Corollary 20.

Corollary 20.

In both the centralized and decentralized decision-making scenarios, the green travel demand exceeded the non-green travel demand when the government’s cost-sharing coefficient was sufficiently large.

Corollary 20 provides a significant conclusion. As long as the government was willing to sufficiently share the costs, the green travel demand was higher than the non-green travel demand. The government’s cost sharing boosted the green effort of the green travel company, further boosting the green travel demand. Therefore, governmental subsidies promoted green travel. This was similar to the result of Zhu et al. [21].

7. Numerical Experiments

To reveal the impact of governmental subsidies and decision-making on travel company strategies, this section presents the numerical experiments used to compare the performance of the green effort, green travel price, and non-green travel price in the four different decision-making scenarios. We examined not only the independent effects of governmental subsidies and decision-making but also their cross-effects. In addition, we provide the numerical results of the travel demands and travel companies’ profits in the four different decision-making scenarios. Considering that the increase in green effort could promote the green demand and the increase in the cost coefficient of the green effort restricted the green effort, we varied the cost coefficient of the green effort within a range to observe the effect of the cost coefficient on system performance. Specifically, we assumed $k\in [2,20]$. Other parameters were considered as constants, and the specific values are shown in

Table 3. Parameter settings.

Parameter	${\mathit{a}}_1$	${\mathit{a}}_2$	${\mathit{b}}_1$	${\mathit{b}}_2$	${\mathit{c}}_1$	${\mathit{c}}_2$	g	${\mathit{r}}_1$	${\mathit{r}}_2$
Value	90	60	25	7	6	5	3	20	25

.

Figure 1, Figure 2 and Figure 3 show the variation trends of the green effort, the green travel prices, and the non-green travel prices with the cost coefficient k in the four decision-making scenarios. Figure 4 and Figure 5 present the numerical results of the green and non-green travel demands, respectively, in the four decision-making scenarios. Figure 6 and Figure 7 depict the profits of the green and non-green travel companies in the four decision-making scenarios, respectively. Figure 8 shows the changes in the government’s sharing coefficient with the cost coefficient of the green effort in the WC and WD scenarios.

Figure 1 shows that governmental subsidies promoted the green effort in both the WC and WD scenarios. Specifically, the green effort in the WC scenario was the largest, followed closely by the green effort in the WD scenario. This indicated that governmental subsidies caused the green effort in the WD scenario to exceed that in the OC scenario. As expected, the green effort was lowest in the OD scenario.

Figure 1 also shows that decentralized decision-making reduced the green effort, as compared to centralized decision-making. In the decentralized decision-making scenarios, the green travel company decided the green effort by maximizing its own profit, which deviated from the optimal green effort in the centralized decision-making scenarios. Interestingly, when the government provided a subsidy, the decrease in the green effort by decentralized decision-making was limited. This suggested that governmental subsidies weakened the impact of decentralized decision-making. Furthermore, we observed that the green effort decreased with its cost coefficient in the four decision-making scenarios. This was intuitive. The increased effort cost hindered the green effort of the travel company.

Figure 2 shows that in both the WC and WD scenarios, the governmental subsidies increased the green travel price. Specifically, the green travel price in the WC scenario was the largest, whereas the green travel price in the OD scenario was the smallest. The governmental subsidies enabled the green effort in the WD scenario to exceed that in the OC scenario, although this was conditional.

Figure 2 also shows that decentralized decision-making reduced the green travel price, as compared to centralized decision-making. In the decentralized decision-making scenarios, the travel price determined by the green travel company deviated from the optimal green travel price in the centralized decision-making scenarios. We can see an intersection in Figure 2. When the cost coefficient of the green effort exceeded the horizontal coordinates of this intersection, the green travel price in the OC scenario was higher than that in the WD scenario. This indicated that decentralized decision-making weakened the effect of governmental subsidies on the green travel price. In addition, we observed that the green travel price decreased with the cost coefficient of the green effort in the four decision-making scenarios. The decrease in travel price was reasonable as the green effort decreased with the cost coefficient.

Figure 3 shows that governmental subsidies increased the non-green travel prices in both the WC and WD scenarios. Specifically, the non-green travel price in the WC scenario was the largest, followed by that in the OC scenario, and the non-green travel price in the OD scenario was the smallest. Because the green travel price had been increased by the governmental subsidies, the non-green travel price also increased. The increase in governmental subsidies for the non-green travel price in the WD scenario was smaller than that in the WC scenario. This suggested that decentralized decision-making reduced the effect of governmental subsidies on the non-green travel price.

Figure 3 also shows that decentralized decision-making reduced the non-green travel price, as compared to centralized decision-making. In the decentralized decision-making scenarios, the non-green travel company determined the travel price by maximizing its own profit, which deviated from the optimal non-green travel price in the centralized decision-making scenarios. In addition, we observed that the non-green travel price decreased with the cost coefficient of the green effort in all four decision-making scenarios. Considering the cross-influence between the green and non-green travel prices, when the green travel price decreased with the cost coefficient, the non-green travel price also decreased.

Figure 4 shows that for both the WC and WD scenarios, the governmental subsidies increased the green travel demand. The governmental subsidies were reasonable to promote green travel. Whether or not the governmental subsidies existed, the green travel demand was higher in the decentralized decision-making scenario than in the centralized decision-making scenario. This suggests that decentralized decision-making promoted green travel.

Figure 4 also shows that the green travel demand in the WD scenario was the largest, whereas the green travel demand in the OC scenario was the smallest. In the WD scenario, the green travel demand was the highest because of the joint promotion effect of governmental subsidies and decentralized decision-making on green travel. We noted that the green travel demand in the OD scenario could exceed the green travel demand in the WC scenario, although this was conditional. As compared to the OD scenario, the green travel demand decreased more rapidly with k in the WC scenario when k was large. This suggested that centralized decision-making hindered the promotion of the green travel demand through governmental subsidies. In addition, we observed that the green travel demand decreased with the cost coefficient of the green effort in the four decision-making scenarios. An increase in the green effort cost was detrimental to green travel.

Figure 5 shows that the impact of the governmental subsidies on the non-green travel demand in the WC scenario was different from that in the WD scenario. The governmental subsidies promoted the non-green travel demand in the WD scenario and reduced the non-green travel demand in the WC scenario. Considering the increase in the green travel demand through the governmental subsidies in the WD scenario, it was not surprising that the governmental subsidies increased the non-green travel demand. However, in the WC scenario, the governmental subsidies increased the green travel demand while reducing the non-green travel demand. Therefore, the non-green travel demand in the WD scenario was the highest, followed by the non-green travel demand in the OD scenario, and the non-green travel demand in the WC scenario was the lowest.

Figure 5 also shows that whether the governmental subsidies existed or not, the non-green travel demand in the decentralized decision-making scenario was higher than that in the centralized decision-making scenario. This suggested that decentralized decision-making promoted non-green travel. Interestingly, the impact of the cost coefficient of the green effort on the non-green travel demand in the decentralized decision-making scenarios differed from that in the centralized decision-making scenarios. The non-green travel demand decreased with the cost coefficient of the green effort in the decentralized decision-making scenarios and increased with the cost coefficient of the green effort in the centralized decision-making scenarios. Because the green travel demand in the centralized decision-making scenarios decreased with the cost coefficient of the green effort, the integrated company prompted travelers to select non-green travel.

Figure 6 shows that in both the WC and WD scenarios, the governmental subsidies increased the profit of the green travel company. The government’s cost sharing of the green effort benefited the green travel company. Figure 6 also shows that whether the governmental subsidies existed or not, decentralized decision-making reduced the profit of the green travel company, as compared to centralized decision-making. This suggested that decentralized decision-making was not beneficial to the green travel company. The profit of the green travel company was the largest in the WC scenario and the smallest in the OD scenario. When the cost coefficient of the green effort was small, the profit of the green travel company in the WD scenario could be higher than that in the OC scenario. This showed that the governmental subsidies boosted the profit of the green travel company. However, when the cost coefficient of the green effort was large, the profit of the green travel company in the WD scenario was lower than that in the OC scenario. This suggested that decentralized decision-making hindered the promotion of the green travel company’s profit through governmental subsidies. In addition, we observed that the profit of the green travel company decreased with the cost coefficient of the green effort in the four decision-making scenarios. The increase in cost was clearly detrimental to the green travel company.

Figure 7 shows that in both the WC and WD scenarios, the governmental subsidies increased the profit of the non-green travel company. The government’s cost sharing of the green effort also benefited the non-green travel company. This was interesting. The governmental subsidies increased the green effort and also prompted the green travel company to increase the green travel price, which was beneficial to the non-green travel company. Figure 7 also shows that whether the governmental subsidies existed or not, decentralized decision-making reduced the profit of the non-green travel company, as compared to centralized decision-making. This suggested that decentralized decision-making was not beneficial for the non-green travel company. The profit of the non-green travel company was the largest in the WC scenario and the smallest in the OD scenario. When the cost coefficient of the green effort was small, the profit of the non-green travel company in the WD scenario could be higher than that in the OC scenario. This showed that the governmental subsidies could boost the profit of the non-green travel company. However, when the cost coefficient of the green effort was large, the profit of the non-green travel company in the WD scenario was lower than that in the OC scenario. This suggested that decentralized decision-making hindered the promotion of the profit of the non-green travel company through the governmental subsidies. In addition, we observed that the profit of the non-green travel company decreased with the cost coefficient of the green effort in the four decision-making scenarios. The increase in effort cost was clearly detrimental to the non-green travel company.

Figure 8 shows that the sharing coefficient of the government in the WD scenario was lower than that in the WC scenario. As compared to the WC scenario, the government was more reluctant to share the green effort cost in the WD scenario. Considering the weakening effect of decentralized decision-making on the governmental subsidies, the government shared a lower green effort cost than in the centralized decision-making. We also observed that the government’s cost-sharing coefficient increased with the cost coefficient in both the WC and WD scenarios. As the cost coefficient of the green effort increased, the green travel company was increasingly reluctant to implement green effort, which resulted in decreasing green effort. Therefore, to motivate the green travel company to implement green effort, the government must increase the sharing coefficient.

8. Conclusions

Green travel plays an important role in alleviating traffic congestion and reducing carbon emissions. This study analyzed the travel prices and green strategic decision-making of travel companies from the perspective of travel competition. A green travel company determined the green travel prices and green effort, and a non-green travel company determined the non-green travel prices. To promote green travel, governmental subsidies were introduced in the form of sharing the costs related to green efforts. The decisions on green effort and travel prices were investigated in four decision-making scenarios: centralized decision-making without governmental subsidies, decentralized decision-making without governmental subsidies, centralized decision-making with governmental subsidies, and decentralized decision-making with governmental subsidies. The Nash game model without governmental subsidies and the Stackelberg–Nash game model with governmental subsidies were built and solved. The optimal results and the role of governmental subsidies in promoting green travel were analyzed theoretically and numerically. We obtained the following conclusions.

First, the governmental subsidies could both boost the green effort of the green travel company and increase the green and non-green travel prices. This observation was similar to that in Fan et al. [11]. The optimal travel price increased with the subsidy sharing coefficient. Specifically, as compared to the decentralized decision-making scenario, the governmental subsidies allowed a more significant improvement in green effort in the centralized decision-making scenario. The governmental subsidies motivated the green travel company to implement more green efforts.

Second, the competition between the green and non-green travel companies undermined the role of the governmental subsidies and reduced the green and non-green travel prices. As compared to decentralized decision-making, centralized decision-making provided a greater boost for green effort through the governmental subsidies. As compared to centralized decision-making, decentralized decision-making reduced the green and non-green travel prices, with or without the governmental subsidies.

Third, a sufficiently large cost-sharing coefficient of the government could make the green travel demand higher than the non-green travel demand. When the government’s cost-sharing coefficient was sufficiently large, the green travel price exceeded the non-green travel price. This observation was consistent with that of Emami et al. [44], and an incentive policy in the form of governmental subsidies could increase the green travel demand.

Fourth, the increase in the effort cost of green travel inhibited the green effort, making it difficult for the green travel demand to exceed the non-green travel demand. Meanwhile, a large cost coefficient of the green effort was detrimental to both the green and non-green travel companies. This observation was similar to that of Chen et al. [14]. The increase in the strategy cost coefficient was unfavorable to the travel companies. In particular, the profit of the non-green travel company decreased more rapidly with the cost coefficient of the green effort than that of the profit of the green travel company.

Finally, with or without the governmental subsidies, the market sizes of both green and non-green travel boosted the green effort. In the absence of governmental subsidies, the non-green travel demand decreased with the market size of green travel in the centralized decision-making scenario and increased with the market size of green travel in the decentralized decision-making scenario.

Future research could consider the income of travelers and the competition among multiple modes of travel. The competition between two green travel companies could be further studied. In addition, other types of governmental subsidies should be considered in future studies. A limitation of this study was that despite considering green efforts as the CSR/ESG performance of green travel companies [63], the concept of CSR/ESG was not mentioned in the main text. Another limitation was the failure to consider the CSR/ESG performance of non-green travel companies.