1 Introduction
Over the past few years, China has witnessed the rapid growth and prosperity of third-party transaction platform, which ensures both the safety and security of online payments by acting as "credit intermediary". Although the licensing boundaries which limit the entry of start-up enterprises to this platform is extremely low, the third-party transaction market is still characterized by the multi-player oligopoly competition. In the context of large market share, the competition is vast for any third-party transaction enterprises that are determined to invest. The structure of the Chinese third-party transaction market is shaped by a small number of oligopoly enterprises that is built on the foundation of startup companies of smaller scales. We have the vision that this study on the competition of oligopoly enterprises in the third-party transaction market can provide readers with the understanding of the market structure with regard to the underlying process of third-party payment. Third party transaction enterprises thrive on optimizing market share of online transactions, making profit by pricing, and achieving maximal corporate gains. In connection with the current popularization of China's online commercial industries, this paper evaluates the oligopolistic competition mechanism of China's third-party transaction market with a clear emphasis on game theory.
2 Background and Literature Review
2.1 Electronic Commerce
Electronic commerce and third-party transaction share a same lineage in the sense that the former is the origin for the latter. Helander, et al. have provided a systematic review on the development of electronic commerce
[1]. Furthermore, they have presented a consumer-focused study that demonstrates the bargaining power of the client's demands in managing online market. On the other hand, Du and his team emphasize on the credit problems observed in e-commerce. By utilizing a microeconomics model, they have found that the core problems which sabotage the development of ecommerce is the absence of credit intermediaries
[2]. Additionally, Xie and Lu provide a fundamental definition for third party electronic transaction platform that modelize electronic business system structure and payment process
[3]. Through the employment of an online analytical mining methodology, Kwan, et al. have proposed an e-customer behavior model to identify e-customer behavioral changes that support internet marketing
[4]. By adopting a longitudinal survey, Tsai, Huang and Lin analyze, in three stages, the transformational impacts of emerging e-commerce on Taiwan's travel industry. They exhibited a strategic business model that maintains the competitive advantage of travel industries in Taiwan
[5]. Liu and Yan have evaluated the impact of e-commerce on conventional taxation policies. Moreover, they have made recommendations for taxation that adapt the ever-changing landscape of e-commerce
[6]. Pang has conceptualized the strategy that can increase the consumer-confidence in digitalized online market from the social, personal, technological, and political prospective
[7].
2.2 The Third-Party Transaction
The industrial structure of third-party transaction is determined by the theory. Upon examining the E-commerce Directive adopted in Europe's electronic marketplace, Kye's paper has discussed the reality of policy-making for online payment that promotes the regularization and standardization of third-party transaction
[8]. In his research on business-to-customer (B2C) e-commerce, Walton has explored the problems of third-party transactions which could place some measures to prevent any unnecessary detriments of commercial nature
[9]. Claycomb, Iyer and Germain have further explored the practical extension of B2C in the management of third-party transactions that expands the electronic market multidimensionally
[10]. By utilizing as an example in the study, Kim, Song, Braynov and Rao established a model that illustrates the function of American third-party licensing agency in promoting the public trust of online transaction
[11]. Ba, Whinston and Zhang have showed the unregularized aspect of current internet market which exhibits many potential risks as to the transparency and trustworthiness of making transactions online
[12]. By focusing on the feedback system in the third-party transaction, Dellarocas has systematically investigated the possibility of designing a reputation mechanism that could maintain the moral purity for online trading environment through the establishments of robust standards
[13]. In their paper, Miller, Resnick and Zeckhauser questioned the reliability and honesty of the existing recommender and reputation system. Alternatively, they have proposed payment-based system to induce truthful feedbacks
[14]. Through the examination of third-party transaction platform's internal environment, Wu qualitatively analyzes the layouts, operational managements, and competitive advantages of third-party payments to foresight that innovative input is the core of future advancement
[15]. Lamusi has stated that consumers and suppliers are the target market of online trading. Their immunity from unethical business practice and the engagement of internet commercialization are at the center of third-party transaction platforms
[16]. By incorporating practical cases with research, Chen has concluded that, instead of being a "financial institution, " the essence of third-party transaction platforms should be reviewed as the "credit intermediary"
[17].
2.3 Application of Game Theory in Third-Party Transactions
As the third-party transaction is still at the early stage of development, the literatures on its competitive mechanism are greatly limited. Currently, the third-party transaction is mostly discussed in the contexts of e-commerce, marketing, and commercial structure. Fu and Zhao have explored the competitive mechanism for third-party transactions from the prospective of pricing strategy, client targeting, and platform management
[18]. Liu confirmed that market share is the key to completing a successful online transaction
[19]. By applying game theory, Li has established the game binary tree to produce a dynamic game model which demonstrates that the third-party transaction platform can facilitate online payments
[20]. Piao, et al. presented an improved credit evaluation model for customer-to-customer (C2C) e-commerce website, and then proposed a corresponding credit evaluation algorithm to address credit problems that resist the development of e-commence
[21]. Zhang has employed evolutionary game model to explore the C2C mode observed in the management of third-party transaction. This serves as the conclusion that third-party transaction is consumers' first line choice of online payments
[22]. Wang et al have analyzed the relationship between commercial banks and third-party transaction companies and how the conflicts and competitions are the inevitable of such relationship
[23]. Lin utilized single and multiple game analyses to determine the importance of credit in the third-party transaction platforms
[24].
3 The Role of Third-Party Transaction in Chinese Market
As depicted in
Figure 1, the net transaction amount of the third-party payments has been increasing steadily and rapidly
[25] since its advent. This indicates a history-defining progress for third-party transaction market in Chinese economy. Adopting such indication, it is then observed in
Figure 2 that, online shopping has occupied the largest share in Chinese third-party transaction platform which is immediately followed by the ticketing market of public transportation. And the telecom payment is the third largest as to market share showed by the transaction scale. Although the emergence and introduction of novel business fields will lead to a diversified development of the third-party transaction platform, the online shopping, public transportation ticketing and telecom payment remain the majority that dominates more than 60% of the commercial payments made in Chinese third-party market. Consequently, the occupation and investment of these three markets aforementioned is the essence of a prospering third-party transaction company. Furthermore, it is our belief that the discussion that focuses on the input of Chinese third-party enterprises for online shopping, public transportation ticketing and telecom payment is of great significance in relation to the prospect study.
Figure 1 China's third party payment transaction scale |
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Figure 2 Industry structure of third party payment market |
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Based on the findings illustrated by
Figure 3, in 2016, it is confirmed that Alipay
[26], TenPay and UnionPay occupied over 79% of the market share in China's third-party transaction. At the time of writing this paper, the authors have concluded that Alipay is in the advantageous position of absolute domination for the reputation, the popularization, and the totality of economic strength in China. Alipay's quest for victory relies on Taobao, the largest online shopping platform, to acquire aggressive expansion that contributes to its absolute status in the third-party payment market. The driving engine of Alipay's success can be demonstrated by the number of users (outnumbering other competitors by a massive scale), adequate capital, and innovations in e-commerce. On the other hand, however, TenPay's survival depends on e-commerce platform which is built on the Tencent QQ's user group of vastly amount to provide a powerful resource base. Subsequently, with such powerful base in its hand, TenPay has capacity to penetrate into various industries efficiently
[27]. In comparison with Alipay and TenPay, the UnionPay business, which is owned by China UnionPay, has employed a conventional strategy that exploits the traditional mentality of bank users. Through the intrinsic commercial strength and business foundation, UnionPay business creates a strong presence in the ever-growing market of third-party transaction
[28].
Figure 3 Market shares of China's third party payment transactions in 2016 |
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As the three dominating companies that seek to monopolize the third-party transaction market in China, Alipay, TenPay and UnionPay are unavoidable to compete in the business fields of high profit
[29]. The key for such competition is characterized by the investments in the markets such as online shopping, public transportation ticketing and telecom payment. It is confirmed by numerous studies that these three markets have awarded the third-party transaction platforms with tremendous commercial returns that are represented by the gaining of the market share that is over 60%
[30]. The profitability pricing strategies of Alipay and TenPay are listed in
Tables 1 and
2 respectively.
Table 1 Alipay pricing strategy |
Market Segment | Profitability |
Online Shopping | |
Transport Ticketing | |
Telecom Payment | Around |
Account Transfer | | Service charge rate | Lower service charge (each transaction) | Upper limit of service charge (each transaction) |
Arrival in hours | | 1.00 RMB | 50.00 RMB |
Arrival the next day | | 0.9 RMB | 50.00 RMB |
Table 2 TenPay pricing strategy |
Market Segment | Profitability |
Online Shopping | |
Transport Tiketing | |
Telecom Payment | Around |
Account Transfer | for accounts more than a certain threshold |
For the strategic evaluation of the Chinese third-party transaction enterprises, the concentration ratio and Dahl Hirshman index are employed to analyze the outlay and the structure of third-party payment market. This is because both the concentration ratio and Dahl Hirshman index are able to reflect the reality of competition faced by companies in China's third-party platform.
3.1 Structural Evaluation in the Context of Concentration Ratio
Given a particular period of a particular industry, concentration ratio (CRn) of the top enterprises in the industry can be expressed as the sum of market shares of these enterprises, which can be represented by the following equation:
where, is the total sales of the industry, and are the business sale and market share of the th enterprise respectively.
With regard to microeconomics, the market structure for the industries of different fields is divided into four categories: Complete monopoly, oligopoly, monopolistic competition and perfect competition. Moreover, based on Bain's division method, the market structure can be further divided into different subtypes according to the value of CRn as shown in Table 3. This reflects the level of competition and the monopoly of whole market.
Table 3 Bain's market structure classification according to concentration ratio |
Range of CRn | | | | | | |
Market structure | Oligopoly type Ⅰ | Oligopoly type Ⅱ | Oligopoly type Ⅲ | Oligopoly type Ⅳ | Oligopoly type Ⅴ | Competitive type (No oligopoly) |
According to the market analysis of China's three largest third-party transaction platforms: Alipay, TenPay and China UnionPay, the values of CR3 in the past five years are listed in Table 4.
Table 4 Concentration ratio of China's third-party transaction market |
Based on the data presented in Table 4, it is showed that, on average, the annual CR in China, on the whole, is greater than . By considering Bain market structure classification in Table 3, this indicates that China's market structure is of Oligopoly Type Ⅰ. Therefore, it is our conclusion that the three third-party transaction platforms, i.e., Alipay, TenPay and UnionPay, are defined as oligopolistic competition in China's third-party transaction market.
3.2 Structural Evaluation with Herfindahl-Hirschman Index
Subsequently, we use Herfindahl-Hirschman Index (HHI) to divide the market structure for the insight of competitive mechanism and monopoly. HHI is defined as
where, is the total sales of the industry, and are the business sale and market share of the th enterprise respectively, is the total number of companies in this industry. It is obvious that the value of HHI ranges from 0 and 1. The closer the HHI value is to , the higher the monopoly degree of the industry is. Inversely, the closer the HHI value is to , the lower the monopoly degree of the industry is.
Table 5 Market structure classification according to Herfindahl-Hirschman Index |
Range of HHI | | | | | |
Market structure | High oligopoly degree type Ⅰ | High oligopoly degree type Ⅱ | Low oligopoly degree type Ⅰ | Low oligopoly degree type Ⅱ | Competitive type |
Given the HHI standard of the market structure classification, it is found from Table 6 that China's market is between High oligopoly degree type Ⅰ and High oligopoly degree type Ⅱ. As the market concentration is gradually diluted, the degree of oligopoly will be reduced, and the degree of competition will be increased. But, the overall market structure is still of high oligopoly.
Table 6 HHI of China's third party payment market |
In connection with CRn and HHI indicators, we can conclude that the market structure of China's third-party transaction platforms (with Alipay, TenPay and UnionPay as sampled representations) is of oligopolistic competition.
4 Modelization of Oligopolistic Competition for China's Third-Party Transaction Platform
Given that online shopping is a representation of the "one superpower and multi powers" market structure, this paper argues that Alipay (the leading enterprise), TenPay and UnionPay (the trailing enterprises) are in the position of oligopolistic competition. As third-party enterprises aim to strategically maximize the commercial gains by the means of optimizing the limited internal resources, we have established a model with enterprise profit as the target and enterprise resource investment as decision variable. The symbols represent Alipay, Tenpay and Unionpay respectively, and will be used to indicate the corresponding enterprise. Symbols and are investment resources and market share respectively. Symbols and denote functions of cost per-unit and number of users respectively. is used as profit function. All numerical simulation will be performed using Matlab.
As to the investment cost, there are no differences in the online shopping markets for Alipay, TenPay and UnionPay. These three companies have employed the Internet as the medium that is characterized by e-commerce based investment cost. Consequently, their unit investment costs are defined as
In comparison to the total population of China, the number of online shopping users for Alipay, TenPay and UnionPay is of small quantity. Therefore, the number of potentially convertible users is extremely large. Moreover, by investing more enterprise resources, more users can be converted. Furthermore, the investment of enterprise resources shares a positive proportion with number of users. In addition, the number of users is related to the market share of the third-party transaction enterprise. The bigger the market share is, the more difficult it becomes to convert potential users. We have characterized the functions of user numbers for Alipay, TenPay and UnionPay as
where, in association with Alipay, TenPay and UnionPay, denote the functions of user numbers for each company respectively, denote market share for each company respectively, denote investment resources for each company respectively, are respective impact factors in the online shopping market. The impact factors are in accordance with the Central Limit Theorem, therefore, they are subject to the normal distribution with the expectation and the variance . In addition, any other impact factors could be considered in the risk analysis of preferences for the third party payment enterprises.
If we used to define the expected number of users in the online shopping market for the third-party transaction platform, and to denote the demand observed in the third-party transaction market. Given the oligopolistic game model and the expected number of users, the inverse demand function is obtained as
where, represents the value of services provided for users in the online shopping market by the third-party transaction platform. When the value of services in certain market area offered by a third-party transaction platform is unsatisfied, users will abandon the said service, and the third-party transaction platform will suffer the detriment by losing users in this market area.
By analyzing the market structure of the third-party transaction, we have concluded that Alipay occupies the dominant position to obtain the leading role in strategy-planning within the online shopping market. The other enterprises will only start to strategize after observing Alipay's strategy. In the other word, Alipay is the leading enterprise, and TenPay and UnionPay are the trailing enterprises. Hence, Alipay, TenPay and UnionPay are in the dynamic game of perfect information with regard to online shopping market.
Profit functions for Alipay, TenPay and UnionPay in the online shopping market can be respectively defined by
As the leading enterprise in the online shopping market, Alipay will first choose to invest resources into the online shopping market. After TenPay and UnionPay confirm Alipay's strategy, the optimal decision can be made in accordance with Equations and
Taking the first derivative respectively in and with respect to and , using the conditions and , we can obtain
Solving and , we can obtain
Based on the static game of perfect information, Alipay will predict the investment decisions and made by TenPay and UnionPay before making investment decision , so the maximum profit for Alipay can be represented by
Substituting into yields
From the optimal first order condition , we obtain
Substituting into gives
Substituting into profit functions, we obtain
which produce the profit functions as
We can make the following conclusions based on the establishment and solution of our model.
Conclusion 1 From , we see
Therefore, it is concluded that the more enterprise resources the third-party transaction platform invests in online shopping markets, the higher the profit earned will be. The profit growth rate of online shopping markets of the third-party transaction enterprises will accelerate in the presence of the increasing invested enterprise resources.
Furthermore,
Therefore, it is concluded that the greater market share in online shopping markets of the third-party transaction platform is, the higher profit will be earned. The profit growth rate of online shopping markets of the third-party payment enterprises also keeps accelerating in accordance with the expansion of market share.
Conclusion 2 If , and , we obtain .
If the third-party transaction enterprises made an investment in online shopping markets for commercial maintenance, then the gap of market share in online shopping market for the third-party transaction enterprises will continue to increase given the undisrupted free development. As the result, in the context of this paper, the market share of the leading company (such as Alipay) will exhibit dominance in the online shopping market. Eventually, the online shopping market will be monopolized.
Conclusion 3 Based on Conclusions and , if we made the assumption that the profits earned in the online shopping markets by the third-party transaction enterprises are the same, then the enterprises' resources invested are inversely proportional to the market share. This indicates that governmental agencies can, through policy-making, regularize the profit margins of potentially monopolizing third-party enterprises to promote the growth and prosperity of smaller third-party transaction companies with less market share in online shopping market. Subsequently, as a responding strategy to this hypothesized governmental policy interference, the third-party transaction enterprises will reduce their investments in the online shopping market. As an alternative, there exists a possibility that they will invest in other market segments. This will prevent the monopolization of third-party transaction enterprises in online shopping market to promote a more diversified competition structure that additionally will motivate the development of other market segments.
Conclusion 4 Taking the telecom payment market as an example, for the multi powers market structure, the market shares of Alipay, TenPay and UnionPay are similar to each other. Hence, in order to maximize their profits, these three dominating third-party transaction enterprises will calculate the strategies by predicting their competitors moves. Therefore, this is a static game of perfect information.
Analogously, the equilibrium solution of enterprises' resources can be obtained as
Substituting into profit formula gives the profit values of Alipay, TenPay and UnionPay respectively as
Conclusion 5 From , we get
Therefore, it is concluded that the investment of resources by the third-party transaction enterprises in the telecom payment market are directly proportional to the economical returns. The profit growth rate of telecom payment markets for the third-party transaction enterprises will be accelerated given the increased investment of enterprise resources.
Furthermore,
Therefore, it is concluded that the market share of the third-party transaction platform in telecom payment markets positively contributes to the totality of profit gained. The profit growth rate of telecom payment markets for the third-party transaction enterprises also will present consistent acceleration given the expansion of market share.
Conclusion 6 If , and , we obtain .
If the third-party transaction enterprises made an investment in telecom payment market, the market shares for Alipay, TenPay and UnionPay will simultaneously expand at a steady rate given the free development of third-party transaction platforms. In the long term, Alipay, TenPay and UnionPay will gradually occupy over the entire telecom payment market that will form an oligopoly dominance for the third-party payment enterprises.
Conclusion 7 Based on Conclusions and , the market share for the telecom payment market is inversely proportional to the enterprises' resource investments if the profits gained are the same. Certain governmental agencies may exhibit control and adjustment over the enterprises' profits through policies. As the result, the third-party transaction enterprises will internally reduce the resource investments, thereby reducing market share. This will promote a healthy environment for competition in the market. Meanwhile, with regard to telecom payment market, Alipay, TenPay and UnionPay are radically unconventional from the prospective of traditional industries. To elaborate, third-party transaction platforms are not limited by physical factors. For instance, third-party transaction platforms have the luxury to not consider many tangible problems such as the costly management (which understandably is an inevitable for many premise-based businesses). What is more, for Alipay, TenPay and UnionPay, we argue that the only cost behind their day-to-day operation is the utilization of e-commerce. It is suggested that there is a need for national supervision that serves to eradicate the collusive oligopoly strategy which Alipay, TenPay and UnionPay may employ, thus constructing a healthy environment for competition in the telecom payment market.
5 Pricing Model for China's Third-Party Transaction Platform in the Context of Multidimensional Game Theory
Given the making of practical decisions, the third-party transaction enterprises strategize their competitive mechanisms by simultaneously comprehending multiple market segments. The profit made by the third-party transaction enterprises is strongly correlated to its pricing in the market. Therefore, the decision for price employed by enterprises is a determining prerequisite that affects its gains and expansions in the third-party transaction market that is of oligopolistic competition.
We have sampled the third-party transaction platforms that are monopolized by the two oligopoly enterprises, Alipay and TenPay, to experiment our model analysis. Our model will also integrate the online shopping market and the ticketing market of public transportation. By taking the maximum profit of the third-party transaction enterprises as the target and the price factor as the strategy variable, we theorize a pricing model that examines the competitive effects that impact factors of the price have on the internal and external environments for the given companies.
For modelizing our theories, we have proposed the following hypotheses:
Let be the price of Alipay for online shopping market;
Let be the price of TenPay for the online shopping market;
Let be the price of Alipay for the ticketing market of public transportation;
Let be the price of TenPay for the ticketing market of public transportation;
Let the total demand in the online shopping market be ;
Let the price for the ticketing market of public transportation be .
The decision as to the pricing determined by a third-party transaction enterprise in the market segments will complementarily affect the number of clients in the multiple markets for both the said enterprise and its competitors. Table 7 illustrates the impact factors for different markets.
Table 7 Impact factors of impact relations in different markets |
Impact factor | Impact relation |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
The demand functions for Alipay in the online shopping market and the ticketing market of public transportation are defined as
The demand functions for TenPay in the online shopping market and the ticketing market of public transportation are defined as
Unit costs for Alipay and TenPay in the online shopping market and the ticketing market of public transportation are said to be the same:
Then, the profit function for Alipay in the online shopping market can be derived from Equations and
The profit function for Alipay in the ticketing market of public transportation can be derived from Equations and
Adding and gives the total profit function of Alipay
Taking the first derivative of the profit function (5.6) with respect to and , and letting and , we can obtain
which is reformulated in matrix form as
yielding the reaction function for Alipay
For convenience of calculation and expression, letting
We can re-write the reaction function in matrix formulation for Alipay
Analogously, we can also derive the reaction function in matrix formulation for TenPay:
Consequently, the following results of the game equilibrium can be obtained based on Equations and .
Conclusion 8 If and , we get
If we assumed that Alipay and TenPay only make policy decisions through the online shopping market, then the impact factors would meet the following conditions:
Meanwhile, the cost and market demand for the ticketing market of public transportation are both zero, that is,
Substituting and into the matrices and, we obtain the next conclusion.
Conclusion 9
is the equilibrium pricing result for Alipay and TenPay that reflects the competition for price in the online shopping market only. Here, . This indicates that Alipay and TenPay do not invest and compete in the ticketing market of public transportation.
Taking partial derivatives in with respect to different parameters, we can draw the following two conclusions.
Conclusion 10 .
Conclusion 11 .
Corollary 1 Based on Conclusion , it is suggested that, with regard to online shopping market, the pricing for the third party-transaction platform increases with the impact factors due to the presence of competitors.
To discuss and , we have predefined that and . Figure 4 shows the relationships between pricing and the impact factor under different market demand conditions.
Figure 4 Relation diagram of the price and the impact factor in the third-party payment platform different market demand conditions |
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Reassessing our discussion from the prospective of Alipay, the pricing for TenPay in the online shopping market is directly proportional to the Alipay's impact factor. Subsequently, this will contribute to the increasing price of Alipay in the online shopping market. The demand of online shopping market has a significant impact on the pricing for Alipay. That is, the greater the market demand is, the higher the pricing for Alipay in the online shopping market will be. Given the differences in cost, trends that are similar to those showed in Figure 4 can be obtained when the demand of the online shopping market is fixed. This is to emphasize that the growing unit cost of the online shopping market will result in the high price of Alipay. And with same reasoning, comparable results can be obtained for TenPay.
Corollary 2 To explore Conclusion , we have predefined that . Figure 5 illustrates the relationships between and under different market demand conditions.
Figure 5 Relation diagram of the price and the impact factor in the third-party payment platform different market demand conditions |
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It is observed that the price for the third-party transaction platform in the online shopping market shares a linear relationship with its impact factor . The price rises in the presence of the increasing . Although the elevated demand of the online shopping market raises the price, it does not exhibit any observable impact on the rate of price's increase. However, on the contrary, the increase of cost in the online shopping market does contribute to the increasing rate of the price. But, in the context of small impact factors, the price difference is said to be marginal.
Corollary 3 Based on Conclusion , equilibrium results for the ticketing market of public transportation can be obtained as
Assuming that the online shopping market and the ticketing market of public transportation do not affect each other mutually, then we have
Substituting into the matrices and yields the equilibrium result of the price in Conclusion .
Conclusion 12
Corollary 4 When , the equilibrium result is
By treating online shopping market and ticketing market of public transportation as two separate events, Corollary is a combination that demonstrates the equilibrium results for the price game concerning the third-party transaction platform. This is obtained from Conclusion and Corollary .
To further analyze our data, we have made the following hypotheses:
Let the demand of the online shopping market be ;
Let the demand of ticketing market of public transportation be ;
Let the cost of the online shopping market be ;
Let the cost of ticketing market of public transportation be ;
Let the impact factors for different markets be
As demonstrated by Figure 3, we have made two observations: ) the total sales of online shopping market are three times larger than that of the ticketing market of public transportation, and ) the unit cost of the online shopping market is larger than that of the ticketing market of public transportation. By evaluating the relationships of market share, we have confirmed that, in connection with impact factor, the online shopping market is bigger than the ticketing market of public transportation. From the prospective of third-party transaction platform, it is believed that the two markets under discussion (i.e., online shopping and public transportation ticketing) have a strong internal influence for pricing that is of direct nature. This is to stress that the competition within the two markets will exhibit the impact factor of smaller scale for the third-party transaction platform. However, with regard to the objective existence of multiple competitors, the impact factor of the online shopping market is bigger than that of the ticketing market of public transportation. Therefore, the assumptions aforementioned are theorized in accordance with the reality of the third-party transaction market in China. Upon expanding Conclusion , we have substituted these assumption data into Equation to obtain the following equilibrium results
By further substituting into the profit functions, we have obtained the total profits for Alipay and TenPay
By considering Conclusion , if we excluded the mutual influence for the online shopping market and the ticketing market of public transportation from the preconditions, we have calculated the following equilibrium results
Corollary 5 By exploring Equations and , we have applied the game theory concerning the third-party transaction platform for the online shopping market and the ticketing market of public transportation. What is more, if we simultaneously denied the joint role of multidimensional game for strategies in both the online shopping market and the ticketing market of public transportation, it is our view that, given the consideration for a single game, the profit made by a third-party platform in the single game as calculated by Equation is less than the profit made by the same third-party platform in the multidimensional game as calculated by Equation . This is to show that a single-game based strategy is not optimal for any third-party transaction platforms. On the contrary, in order to maximize the commercial returns, the third-party transaction companies should take into account that the optimization of strategy is characterized by comprehensive calculations that incorporate diverse range of market segments.
6 Conclusions
) Given the context of evaluating HHI and CRn index, we confirm that the Chinese third-party transaction market has formed an oligopolistic competition structure. By statistically analyzing the market share for the three dominating enterprises: Alipay, TenPay and UnionPay, we conclude that, annually, China's third-party transaction market structure is observed to be Oligopoly type Ⅰ through the exploration of the CRn index. Upon characterizing the integral structure of the third-party transaction market through HHI index, we observe that China's market structure is transforming from High oligopoly degree type Ⅰ to High oligopoly degree type Ⅱ. This partially illustrates that the oligopoly is experiencing a gradual decline in the third-party transaction market given the presence of increasing competitions. But the overall structure of China's third-party transaction market is of oligopolistic competition.
) By applying the traditional Cournot model and Stackelberg model for oligopolistic competition, we contextualize these two oligopolistic models for Alipay, TenPay and UnionPay. We establish 1) a "one superpower and multi powers" Stackelberg dynamic game model of perfect information for the online shopping market, and 2) a "multi powers" Cournot static game model of perfect information for the telecom payment market.
) Through the multi-oligopoly Stackelberg dynamic game model of perfect information, it is concluded that the elevation in the investment of enterprise resources by a third-party transaction platform in the online shopping market will contribute to the high totality of profits. Given the increase of enterprise resources, the profit growth rate of the third-party transaction enterprises in the online shopping market is equipped with a significant acceleration. Therefore, by inputting the vast resources in online shopping market, the leading enterprise will eventually form a monopoly situation given free development. If we made the assumptions that the profits earned by all third-party platforms are the same, then the investment of enterprise resources is inversely proportional to market shares. It is recommended that there exists a need for national supervision that in long term will promote a healthy environment for competition through policy-making.
) The Cournot static game model for multi-player oligopoly in perfect information is defined by oligopolistic competition. So the results obtained by Cournot static game model are similar to those from the Stackelberg's dynamic game model. However, for the Cournot static game model, the third party transaction enterprises are studied in the telecom payment market. Given the free development of the telecom payment market, Alipay, TenPay and UnionPay will form a "big-three" domination. Consequently, it is the role of governmental agencies to exert a supervisory force on the market to prevent collusive monopoly strategies for Alipay, TenPay and UnionPay, thus encouraging a healthy environment for competition in the telecom payment market.
) In the context of multiple markets, we elucidate the relationships between impact factors through the multidimensional game model of the third-party transaction platform. By experimenting numerical simulation, we verify the influence of different impact factors on the pricing strategy employed by the third-party transaction platform. In addition, the numerical results show that the profit of simple game is less than that of the multidimensional game, and therefore, the equilibrium strategy in multidimensional market game is the global optimal strategy.
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