Research on Price Discrimination Behavior Governance of E-Commerce Platforms—A Bayesian Game Model Based on the Right to Data Portability

Abstract

The behavior of e-commerce platforms using big data algorithms to implement “big data killing” is not only rejected by regular customers, but also creates many difficulties for supervision by relevant government departments. In order to study how to curb the price discrimination behavior of e-commerce platforms in the case of taking regular customers as the leaders, this paper introduces the right to data portability and considers two types of regular customers with high price sensitivity and low price sensitivity. Then, we build a Bayesian game model between e-commerce platforms and regular customers on the basis of the established general game model. Our experiments show that when the reuse value coefficient of personal data is high, the e-commerce platform will choose a uniform pricing strategy, which indicates that the right to data portability can curb the price discrimination behavior of the e-commerce platform to a certain extent. Moreover, when the proportion of high-sensitivity consumers among regular customers increases, e-commerce platforms will be prompted to choose the uniform pricing strategy, which indicates that consumers can curb price discrimination behaviour on e-commerce platforms by increasing their sensitivity for price change.

1. Introduction

The generation of big data has created a positive development environment for e-commerce platforms (in brief, E-CP). In particular, personalization of products and services is widely recognised as one of the key outcomes of big data analysis [1,2]. For example, online live streaming of e-commerce platforms provides audiences with a personalized experience, while directly or indirectly influencing impulsive purchases through pleasure and arousal [3]. Regular customers (in brief, RC) obtain convenience through the diverse choices offered by E-CP. Meanwhile, E-CP also use algorithms to gather information about RC to then offer them different prices based on browsing and purchasing information on the platform. Amazon, the largest online e-commerce company in the US, has been reported for “big data killing” to RC. Similar situations are common in other industries, such as online car platforms and airlines [4,5]. Generally speaking, “big data killing” is a terminology that has emerged in the process of the rapid development of big data, which is essentially a kind of price discrimination. It means that some companies use big data analysis to offer different product pricing or service quality to different consumers based on their personal information and consumption habits [6,7].

The essence of price discrimination is that the e-commerce platform seeks to obtain greater profit. E-CP adopt different pricing strategies for different customers by collecting and analyzing customers’ personal information, device types, purchasing habits and other data. Typically, most customers prefer to shop on platforms they have spent money on before because they are used to shopping on familiar e-commerce platforms or are more satisfied with their previous shopping experience. In the transaction process, due to the information asymmetry between RC and E-CP [8], a number of regular customers will pay a higher price than new customers. The main reason why E-CP can adopt a price discrimination strategy for RC is that they use big data algorithms to analyze regular customers’ spending information from past transactions and can predict the maximum price accepted by RC. Wu et al. [9] found that the price discrimination behavior of E-CP can lead to feelings of betrayal among RC using ANOVA and other algorithms. Wang et al. [10] constructed a semantic recognition framework to analyze the data set of social media review texts and found that $61\%$ of RC resisted price discrimination under big data algorithms. Steinberg [11] argued that the mistake of E-CP implementing price discriminatory behaviour towards RC is that they undermine the right of RC to benefit fairly from markets.

In summary, the phenomenon of price discrimination arising from the rapid development of big data is an urgent problem for RC to protect their rights and interests. A large number of studies have investigated the issue of price discrimination, but most of them are confined to analysing the reason why E-CP adopt a price discrimination strategy and consideration of government departments’ regulation of E-CP. Actually, it is quite difficult for government departments to supervise this phenomenon [12]. If RC can exercise the right of data portability after mastering their own data information, then they will be the main means of curbing price discrimination behavior of E-CP. In the General Data Protection Regulation, the European Union has proposed the right to data portability [6,13]. It has two meanings. Firstly, data subjects can acquire personal information from a data controller, i.e., the data subject is able to download personal data stored on the platform. Secondly, the data subject is able to share individual data on other Internet platforms, i.e., the data subject has the right to transfer the downloaded private personal data to other platforms when he/she wants to switch E-CP. In the context of the digital platform economy, the right to transplant personal data on a continuous and real-time basis is necessary to truly empower consumers [14]. In addition, data portability is recognized as a function that must be provided by cloud services [15]. The customers analyzed in this paper are those who have made at least one purchase on an e-commerce platform, and such customers are called regular customers. In daily transactions, if RC discover the price discrimination behaviour of an e-commerce platform, they may choose to exercise their right of data portability and disclose the price discrimination behaviour of the E-CP, which will cause the E-CP to suffer a certain amount of sales reduction and loss of reputation [16,17]. In the context of the Internet, a bad review can influence the purchasing decision of millions of potential consumers [18]. In particular, negative or unpleasant experiences posted by influencers on social software can have an even greater impact on e-commerce companies [19]. Hence, E-CP will reformulate their pricing strategies in order to promote consumers’ purchasing willingness [20]. So the right to data portability can impact the pricing strategy of e-commerce platforms.

In this paper, the primary goal is building a Bayesian game model between E-CP and RC based on the right of data portability and analysing the factors affecting the strategies of two players when E-CP have incomplete information about the type of RC. To better analyze the research goals of this paper, we mainly solve the following problems:

(1)

What is the payoff matrix in the game model after introducing the right to data portability?

(2)

What Bayesian Nash equilibrium can be formed by RC and E-CP, and what are the conditions for the formation?

(3)

How do the right to data portability, the type of customer and the parameters in the model affect the strategy of E-CP?

In order to solve the above problems, we develop a Bayesian game model composed of RC and E-CP and give the payoff matrix. Then, we obtain the Bayesian Nash equilibrium under different conditions by solving and analyzing the game model. Finally, through numerical simulation of the model, we further research the influence of the parameters in the model on the price discrimination behavior of E-CP.

The rest of the paper is presented as follows: In Section 2, the paper reviews some associated literature about the phenomenon of price discrimination. In Section 3, we establish a general game model between E-CP and RC. In Section 4, the Bayesian game model between E-CP and RC is established and the Bayesian Nash equilibrium is solved. In Section 5, some numerical simulations of the models in Section 3 and Section 4 are obtained. In Section 6, we analyze the theoretical results and the simulation results of these models. In Section 7, we present some relevant recommendations based on the previous analysis.

2. Literature Review

Two research branches are relevant to this paper. One concerns the influence of factors on the price discrimination behavior of E-CP. The other concerns the governance and supervision of E-CP.

Scholars have studied the influence factors of the price discrimination behavior of E-CP. Zhang et al. [21] studied the effects of third-degree price discrimination on welfare under an asymmetric price game between firms in a duopoly market. Their research explained the reasons why firms choose price discrimination against customers. Bonatti and Cisternas [22] studied the role of aggregating regular customers’ purchase data as scores of their willingness to pay, and found that enterprises attach great importance to regular customers’ scores and set prices according to regular customers’ scores. Moreover, the price set by the enterprise is related to the amount of information disclosed by RC. Colombo [23] added regular customers’ behavior and characteristics to create a price discrimination model in which the company learns about the price sensitivity of RC. His research showed that the type of consumer and the level of consumer heterogeneity were factors that affected the price discrimination behaviour of E-CP. Mahmood [24] used experiments to analyze customer heterogeneity and randomness of preferences and found that customer heterogeneity makes E-CP inclined to choose a price discrimination strategy, and randomness of preferences makes E-CP inclined to choose a uniform pricing strategy. E-commerce companies have been working to mitigate the impact of negative evaluations on consumers [25], and consumers’ evaluations affect the behavioral decisions of E-CP.

After the issue of price discrimination was identified, the supervision of E-CP also became an important part of scholars’ research. Favaretto et al. [26], whose research suggested that the principal factors in price discrimination are personal bias and shortcomings in the law, recommended the application of data protection legislation. Wang [27] proposed that anti-monopoly regulators should use tools such as dynamic price regulation to assess the new business models of e-commerce companies more accurately. Bar-Gill [28] argued that when sellers use a price discrimination strategy, regulators need to determine the potential of personalized laws and use the law to address sellers’ behavior.

The online transaction market under big data algorithms has an obvious game character. In 1978, Peter Taylor and Jonker proposed the replication dynamic equation [29]. Then John Maynard Smith summarized the results of the development in the field and laid the theoretical foundation for evolutionary game theory [30]. Many scholars have analyzed the price discrimination behaviour of e-commerce platforms using evolutionary game theory. Lei et al. [31] built an evolutionary game model of co-regulation by government and RC and discovered that government’s punishment intensity can curb the price discrimination behavior of e-commerce companies. Wu et al. [32] developed an evolutionary game model based on psychological accounts and prospect theory; their results demonstrated that the probability of E-CP choosing a price discrimination strategy decreases as the government increases penalties. Xiao [7] established an evolutionary game among government regulators, E-CP, e-commerce companies and RC, and discussed the way government departments regulate E-CP and e-commerce companies. His results showed that government regulation could significantly curb the phenomenon of E-CP adopting price discrimination for RC.

However, in practice, it is very hard for governments to regulate the behavior of E-CP. RC are usually in a passive position in their interactions with E-CP, due to the lack of control over their own data. When RC have left a record of browsing and shopping on the e-commerce platform, the e-commerce platform may predict the maximum price that RC can accept, and the e-commerce platform may further decide whether or not to adopt a price discrimination strategy for RC. If RC have the right to data portability, they can choose to download their personal data and transfer it to other platforms and be well-served on new platforms as well, so they are no longer limited to the same familiar platform. At the same time, E-CP will face the problem of losing RC by implementing a price discrimination strategy, so E-CP will consider whether to continue to adopt a price discrimination strategy for RC.

In real life scenarios, some RC are more sensitive to the price of commodities, and they will compare the price of commodities with other consumers when they browse commodities. We call these consumers high price-sensitive consumers. There are some RC who do not compare prices with others, and we call these consumers low price-sensitive customers. E-CP do not know the type of each regular customer when setting prices for their regular customer, so we also consider a Bayesian game in the article—E-CP have incomplete information about RC. Based on the above literature review and the problems to be solved in this paper, we propose the following hypothesis:

Hypothesis 1. 

Regular customers can exercise the right to data portability.

Based on the above hypothesis, we introduce the right to data portability and establish a Bayesian game model between E-CP and RC by considering two types of RC with high price sensitivity and low price sensitivity. The main points of our paper are as follows:

(1)

Most studies consider the government to be the dominant player in regulating e-commerce platforms, but they neglect the fact that, relying only on the government, the effectiveness of regulation is limited. In order to make RC become the leader to restrain the price discrimination behavior of E-CP, this paper introduces the right to data portability, and analyzes the role of the right to data portability. It also provides some new ideas for analyzing the price discrimination behavior of E-CP.

(2)

This paper considers the type of RC and analyzes how the type of RC affects the strategy of E-CP through a Bayesian game model.

3. A General Game Model of Price Discrimination with the Introduction of a Right to Data Portability

Based on game theory, this paper proposes two game models to solve the problem of price discrimination. In this section, first, we describe the behavior strategies of E-CP and RC. Second, we define the parameters of the general game model. Then, we define the payoff functions of E-CP and RC. Finally, we solve the Nash equilibrium of the general game model.

3.1. Strategy Description

According to the definition of data portability, individuals can only transfer “data about themselves provided by data subjects” from E-CP. This data category is limited to two categories. One category is individual information offered by the data subject, including personal user records, search histories, etc. The value of personal data is $V_1(V_1>0)$. The other category is derived data obtained by E-CP using big data algorithms, which can be used to predict business opportunities. Derived data is valuable to E-CP, and its value is $V_2(V_2>0)$.

Customers who have purchased goods or services on a particular e-commerce platform are called regular customers of the e-commerce platform, and customers who have never purchased goods or services are called new customers. E-CP use regular customers’ private information to determine whether a customer is a regular customer or a new customer. Facing RC, E-CP can take advantage of the characteristics of opaque information and charge RC higher prices than new customers through big data algorithms. However, E-CP may face the consequences of the RC transferring personal data to the new platform, at which point the e-commerce platform will no longer have access to the derived data. Therefore, when E-CP are faced with customers who are RC, E-CP have two alternative strategies: price discrimination (denoted $DP$) and uniform pricing (denoted $UP$).

In addition, to protect their rights and interests, RC have an option to exercise their right to data portability and to obtain a copy of their personal data from the original E-CP, and can then transfer their personal data to the new platform. However, RC face certain transfer costs when exercising the right to data portability, so the behavior strategies of RC include exercising the right to data portability (denoted E) and not exercising the right to data portability (denoted $N-E$).

3.2. Definition of the Parameters

The following symbols are used in this article:

$P_d$: The price of goods when E-CP choose the price discrimination strategy, $P_d>0$;

$P_u$: The price of goods when E-CP choose the uniform pricing strategy, $P_d>P_u>0$;

$V_c$: The regular customers’ assessment of the value of goods, $V_c>0$;

C: The cost to RC of exercising their right to data portability when transferring individual data to new platforms, including the cost of obtaining personal data and the time cost of searching for the new platform, etc., $C>0$;

$\alpha$: The retention value factor of personal data, where personal data is not deleted on the original e-commerce platform when a regular customer exercises the right to data portability, and, therefore, personal data has retention value on the original platform; $\alpha$ represents the degree of retention value of individual data, $0\le \alpha \le 1$;

$\kappa$: The reuse value factor of personal data, where personal data can be used on the new platform when the consumer exercises the right to data portability, and, therefore, personal data has reuse value on the new platform; $\kappa$ represents the degree of reuse value of individual data, $0\le \kappa \le 1$;

g: Probability that a regular customer discovers that E-CP have implemented price discrimination strategy against him/her, $0\le g\le 1$;

M: When RC find that E-CP have selected a price discrimination strategy for them, they will publicize the behavior of E-CP. In turn, the reputation of the E-CP will undergo loss M, $M>0$;

N: When RC find that the E-CP have selected a price discrimination strategy for them, the mental damage they will suffer is N, $N>0$;

e: Used as a subscript to denote the E-CP;

c: Used as a subscript to denote the RC.

3.3. Constructing the Payoff Function Matrix

Table 1. Payoff matrix.

		Regular Customer
		$\mathit{E}$	$\mathit{N}-\mathit{E}$
E-commerce platform	$DP$	$\alpha V_1-V_2-gM,\kappa V_1-C-gN$	$P_d+V_2-gM,V_c-P_d-gN$
	$UP$	$\alpha V_1-V_2,\kappa V_1-C$	$P_u+V_2,V_c-P_u$

gives the payoff functions for each possible combination of the strategies chosen by the two participants. In each combination, the first value represents the payoff of E-CP, and the second value represents the payoff of RC.

When E-CP adopt the strategy $DP$ and RC adopt the strategy E, RC will transfer a copy of the personal data to the new platform. E-CP own the retention value $\alpha V_1$ of regular customers’ personal data, while losing the value $V_2$ generated by derived data. In addition, when RC find that E-CP adopt a strategy $DP$ against them, the loss to the platforms will be $gM$. Therefore, the total net payoff of E-CP is $\alpha V_1-V_2-gM$. If RC transfer individual data to a new platform, RC will gain the value of the transfer of individual data, which is $\kappa V_1$. At the same time, RC bear the transfer cost C and the emotional toll $gN$ of discovering that they have been “big data killing”. Therefore, the total net benefit of RC is $\kappa V_1-C-gN$.

When E-CP adopt the strategy $UP$ and RC adopt the strategy E, RC will transfer the copy of personal data to the new platform. At this point, the net benefit of E-CP is $\alpha V_1-V_2$ and the net benefit of RC is $\kappa V_1-C$.

When E-CP adopt the strategy $DP$ and RC adopt the strategy $N-E$, the price paid by RC is $P_d$. E-CP obtain the value $V_2$ of the derived data, and, at the same time, bear the loss $gM$ caused by RC who find they been subject to“big data killing”. At this point, the net benefit of E-CP is $P_d+V_2-gM$ and the net benefit of RC is $V_c-P_d-gN$.

When E-CP adopt the strategy $UP$ and RC adopt the strategy $N-E$, the price paid by RC is $P_u$. At this point, the net benefit of E-CP is $P_u+V_2$ and the net benefit of RC is $V_c-P_u$.

3.4. Solving the Nash Equilibrium of the General Game Model

In order to calculate the Nash equilibrium of the general game model, we have to identify the optimal response of each participant to the strategy selected by the other participants. The definitions of optimal response and the Nash equilibrium are given as follows:

Definition 1. 

(Optimal response): $x_{-i}=(\cdots ,x_j,\cdots )(j\ne i)$ is a given combination of strategies other than the player i. Strategy $x_i^{*}$ is said to be an optimal response of player i to strategy combination $x_{-i}=(\cdots ,x_j,\cdots )(j\ne i)$ if none of the payoffs obtained by player i by choosing another strategy $x_i^{\prime }$ are higher than the payoff obtained by choosing strategy $x_i^{*}$. That is, for each strategy of player i, the following equation holds: $u_i(x_i^{*},x_{-i})\ge u_i(x_i^{\prime },x_{-i})$.

Definition 2. 

(Nash equilibrium): Strategy combination $x^{*}=(\cdots ,x_i^{*}\cdots )$ is said to be a Nash equilibrium if, for each player $i\in I$, strategy $x_i^{*}$ is the optimal response to the combination of strategies $x_{-i}^{*}=(\cdots ,x_j^{*}\cdots )(j\ne i)$ for the other players.

The Nash equilibrum is a stable state of a system involving the interaction of different participants, in which no participant can gain a greater profit by a unilateral change of strategy if the strategies of the others remain.

3.4.1. Solving the Pure-Strategy Nash Equilibrium

For E-CP, firstly, we need to determine the optimal responses when they face two possible strategies of RC. When RC choose the strategy E, the benefit of E-CP selecting the strategy $UP$ is higher than the benefit when choosing the strategy $DP$; that is, the strategy $UP$ is the optimal response of E-CP to the strategy E. When RC choose the strategy $N-E$, the payoff to the E-CP of choosing the strategy $DP$ is $P_d+V_2-gM$, and the payoff to E-CP of selecting the strategy $UP$ is $P_u+V_2$. If $P_d+V_2-gM>P_u+V_2$, which is equivalent to $g<\frac{P_d-P_u}{M}$, the strategy $DP$ is the optimal response to the strategy $N-E$. If $g>\frac{P_d-P_u}{M}$, the strategy $UP$ is the optimal response to the strategy $N-E$. If $g=\frac{P_d-P_u}{M}$, both strategies $UP$ and $DP$ are optimal responses to the strategy $N-E$, depending on the definition of the optimal response.

For RC, if E-CP select the strategy $DP$, the payoff of RC selecting the strategy E is $\kappa V_1-C-gN$ and the payoff of RC selecting the strategy $N-E$ is $V_c-P_d-gN$. If $\kappa V_1-C-gN>V_c-P_d-gN$, which is equivalent to $\kappa >\frac{V_c+C-P_d}{V_1}$, the strategy E is the optimal response to the strategy $DP$. If $\kappa <\frac{V_c+C-P_d}{V_1}$, the strategy $N-E$ is the optimal response to the strategy $DP$. If $\kappa =\frac{V_c+C-P_d}{V_1}$, both strategies E and $N-E$ are optimal responses to the strategy $DP$. If E-CP select the strategy $UP$, the benefit of RC who choose the strategy E is $\kappa V_1-C$, and the benefit of RC who choose the strategy $N-E$ is $V_c-P_u$. If $\kappa V_1-C>V_c-P_u$, which is equivalent to $\kappa >\frac{V_c+C-P_u}{V_1}$, the strategy E is the optimal response to the strategy $UP$. If $\kappa <\frac{V_c+C-P_u}{V_1}$, the strategy $N-E$ is the optimal response to the strategy $UP$. If $\kappa =\frac{V_c+C-P_u}{V_1}$, both strategies E and $N-E$ are the optimal response to the strategy $UP$.

Based on the above optimal responses of the two participants, the pure-strategy Nash equilibrium of the general game model is shown in

Table 2. Pure-strategy Nash equilibrium for the general game model.

Conditions	Pure-Strategy Nash Equilibrium
$\kappa \le \frac{V_c+C-P_d}{V_1},g\le \frac{P_d-P_u}{M}$	(price discrimination, Non-exercise of data portability rights)
$\kappa \le \frac{V_c+C-P_u}{V_1},g\ge \frac{P_d-P_u}{M}$	(uniform pricing, Non-exercise of data portability rights)
$\kappa \ge \frac{V_c+C-P_u}{V_1}$	(uniform pricing, Exercise of data portability rights)

.

3.4.2. Solving the Mix-Strategy Nash Equilibrium

If $\frac{V_c+C-P_d}{V_1}<\kappa <\frac{V_c+C-P_u}{V_1}$ and $g<\frac{P_d-P_u}{M}$, we can recognize that there is no pure-strategy Nash equilibrium in this game model. The reason is that when one player chooses the optimal response to the strategy chosen by the other player, the other player can change the current strategy, and the previous player also chooses to change the strategy, in which case a cycle is formed. Therefore, E-CP and RC should choose their strategies randomly and not always choose the same ones.

To calculate the mixed-strategy Nash equilibrium for this game, we have to calculate the probability of each player adopting each strategy. We assume the probability of E-CP selecting the strategy $DP$ is x, and the probability of selecting the strategy $UP$ is $1-x$. The probability of RC choosing the strategy E is y, and the probability of selecting the strategy $N-E$ is $1-y$. In other words, in a mixed-strategy Nash equilibrium, each player receives the same payoff for selecting any of the strategies.

So we have the following equations:

$$\begin{array}{c}\begin{array}{cc}\hfill & x(\kappa V_1-C-gN)+(1-x)(\kappa V_1-C)=x(V_c-P_d-gN)+(1-x)(V_c-P_u)\hfill \\ \hfill & y(\alpha V_1-V_2-gM)+(1-y)(P_d+V_2-gM)=y(\alpha V_1-V_2)+(1-y)(P_u+V_2)\hfill \end{array}\end{array}$$

(1)

The first equation of Equation (1) shows that in a mixed-strategy Nash equilibrium, the E-CP obtain the same benefit from choosing the strategy $DP$ and the strategy $UP$, and the second equation shows that the RC obtain the same benefit from choosing the strategy E and the strategy $N-E$.

This can be solved as follows:

$$\begin{array}{c}\begin{array}{c}\hfill x=\frac{V_c-P_u-\left(\kappa V_1-C\right)}{P_d-P_u},y=\frac{P_d-P_u-gM}{P_d-P_u}\end{array}\end{array}$$

(2)

If $\frac{V_c+C-P_d}{V_1}<\kappa <\frac{V_c+C-P_u}{V_1}$ and $g<\frac{P_d-P_u}{M}$, the mixed-strategy Nash equilibrium of the game is {$x\ast DP$ +$(1-x)\ast UP$, $y\ast E$+$(1-y)\ast N-E$}, where $x=\frac{V_c-P_u-\left(\kappa V_1-C\right)}{P_d-P_u},y=\frac{P_d-P_u-gM}{P_d-P_u}$.

4. The Price Discrimination Bayesian Game Model with the Introduction of Right to Data Portability

In Section 3, the price discrimination problem of E-CP is modelled as a general game. There is an implicit assumption in the game that RC and E-CP are certain that they are playing a game with each other. In real life situations, there are usually two types of RC: high price-sensitive (denoted as H) and low price-sensitive (denoted as L). RC who are highly price-sensitive use Internet information to compare price with other RC. As a result, they have a high probability of discovering that E-CP have selected a price discrimination strategy for them, and then select to exercise the right to data portability. In contrast, regular customers with low price sensitivity do not have this ability. Based on the differences between the realistic scenario and the general game model, this paper builds a Bayesian game model to analyze the problem of price discrimination. The Bayesian game model allows for multiple types of participants and at least one participant in the model has incomplete information about the types of the other participants. In this Section, first, the Bayesian game model between E-CP and RC is constructed, and then the Bayesian Nash equilibrium is solved.

4.1. Constructing the Bayesian Game Model

In the Bayesian game model, it is assumed that there is only one type of E-CP and two types of RC. The first type of RC, which is highly price-sensitive, has two strategies: (1) exercise the right to data portability (denoted as E), and (2) do not exercise the right to data portability (denoted as $N-E$). The second type of RC is the low price-sensitive RC who has only one strategy; namely, they do not exercise the right to data portability. There are two strategies for E-CP: (1) price discrimination (denoted as $DP$), and (2) uniform pricing (denoted as $UP$).

Next, a Bayesian game form is constructed based on the types of E-CP and RC and their strategies, as shown in Figure 1. The node at the top of the tree, which represents “nature”; nature makes a stochastic decision about the type of regular customer. We assume that the probability that “nature” chooses RC who are high price-sensitive is h. With probability $1-h$, “nature” chooses RC who are low price-sensitive. The middle dotted line indicates that E-CP cannot determine which type of RC they are facing. The endpoints of each branch correspond to a tuple, with the first value representing the benefit of RC and the second value representing the benefit of E-CP. In addition, these symbols in the payoff function have the same meaning as those defined in Section 3.

4.2. Solving the Bayesian Nash Equilibrium of the Model

Depending on the type of RC, there are two possible strategies for RC. In the first strategy, RC choose to exercise the right to data portability if the RC are high price-sensitive, and they choose not to exercise data portability if the RC are low price-sensitive. In the second strategy, all RC always choose not to exercise their right to data portability. We denote the first strategy as E, if the RC are high price-sensitive, $N-E$ if the RC are low price-sensitive, and the second strategy, as $N-E$, if the RC are high price-sensitive, and $N-E$ if the RC are low price-sensitive.

Noting that the expected payoff of E-CP when E-CP select the strategy $DP$ is recorded as $E_e\left(DP\right)$, the expected payoff when they choose the strategy $UP$ is recorded as $E_e\left(UP\right)$. Under the first strategy, if the regular customer is a high price-sensitive consumer, he/she will choose the strategy E, then the gain of the e-commerce platform choosing the strategy $DP$ is $\alpha V_1-V_2-gM$, and the gain of the e-commerce platform choosing the strategy $UP$ is $\alpha V_1-V_2$. If the regular customer is a low price-sensitive consumer, he/she will choose the strategy $N-E$, then the gain of the e-commerce platform choosing the strategy $DP$ is $P_d+V_2-gM$, and the gain of the e-commerce platform choosing the strategy $UP$ is $P_u+V_2$. Thus, under the first strategy, the e-commerce platform’s expected payoff from choosing the strategy $DP$ is shown in Equation (3), and the e-commerce platform’s expected payoff from choosing the strategy $UP$ is shown in Equation (4).

$$\begin{array}{c}\begin{array}{cc}\hfill E_e\left(DP\right)& =h(\alpha V_1-V_2-gM)+(1-h)(P_d+V_2-gM)\hfill \\ \hfill & =(P_d+V_2-gM)+h(\alpha V_1-P_d-2V_2)\hfill \end{array}\end{array}$$

(3)

$$\begin{array}{c}\begin{array}{cc}\hfill E_e\left(UP\right)& =h(\alpha V_1-V_2)+(1-h)(P_u+V_2)\hfill \\ \hfill & =(P_u+V_2)+h(\alpha V_1-P_u-2V_2)\hfill \end{array}\end{array}$$

(4)

If $E_e\left(DP\right)>E_e\left(UP\right)$, which means that the optimal response of E-CP is the strategy $DP$, we can derive that $h<\frac{P_d-P_u-gM}{P_d-P_u}$. At this point, we detect that the strategy E is still the optimal response to the strategy $DP$ when RC are high price-sensitive; that is, the condition $\kappa V_1-C-gN>V_c-P_d-gN$ needs to be satisfied. We can derive that $\kappa >\frac{V_c+C-P_d}{V_1}$. Thus, if $h<\frac{P_d-P_u-gM}{P_d-P_u}$ and $\kappa >\frac{V_c+C-P_d}{V_1}$, the combination of strategies ($DP$, (E if the regular consumer is high price-sensitive, $N-E$ if the regular consumer is low price-sensitive), h) is a Bayesian Nash equilibrium.

If $E_e\left(DP\right)<E_e\left(UP\right)$, which means that the optimal response of the e-commerce platform is the strategy $UP$, we can derive that $h>\frac{P_d-P_u-gM}{P_d-P_u}$. At this point, we detect that the strategy E is still the optimal response to the strategy $UP$ when RC are high price-sensitive; that is, the condition $\kappa V_1-C>V_c-P_u$ needs to be satisfied. We can derive that $\kappa >\frac{V_c+C-P_u}{V_1}$. Thus, if $h>\frac{P_d-P_u-gM}{P_d-P_u}$ and $\kappa >\frac{V_c+C-P_u}{V_1}$, the combination of strategies ($UP$, (E if the regular consumer is high price-sensitive, $N-E$ if the regular consumer is low price-sensitive), h) is a Bayesian Nash equilibrium.

Under the second strategy, if the regular customer is a high price-sensitive consumer, he/she will choose the strategy $N-E$; then, the gain of the e-commerce platform choosing the strategy $DP$ is $P_d+V_2-gM$, and the gain of the e-commerce platform choosing the strategy $UP$ is $P_u+V_2$. If the regular customer is a low price-sensitive consumer, he/she will choose the strategy $N-E$; then, the gain of the e-commerce platform choosing the strategy $DP$ is $P_d+V_2-gM$, and the gain of the e-commerce platform choosing the strategy $UP$ is $P_u+V_2$. Thus, under the second strategy, the e-commerce platform’s expected payoff from choosing the strategy $DP$ is shown in Equation (5), and the e-commerce platform’s expected payoff from choosing the strategy $UP$ is shown in Equation (6).

$$\begin{array}{c}\begin{array}{cc}\hfill E_e\left(DP\right)& =h(P_d+V_2-gM)+(1-h)(P_d+V_2-gM)\hfill \\ \hfill & =P_d+V_2-gM\hfill \end{array}\end{array}$$

(5)

$$\begin{array}{c}\begin{array}{cc}\hfill E_e\left(UP\right)& =h(P_u+V_2)+(1-h)(P_u+V_2)\hfill \\ \hfill & =P_u+V_2\hfill \end{array}\end{array}$$

(6)

If $E_e\left(DP\right)>E_e\left(UP\right)$, which means that the optimal response of the E-CP is the strategy $DP$, we can derive that $g<\frac{P_d-P_u}{M}$. At this point, we detect that the strategy $N-E$ is still the optimal response to the strategy $DP$ when RC are high price-sensitive; that is, the condition $\kappa V_1-C-gN<V_c-P_d-gN$ needs to be satisfied. We can derive $\kappa <\frac{V_c+C-P_d}{V_1}$. Thus, if $g<\frac{P_d-P_u}{M}$ and $\kappa <\frac{V_c+C-P_d}{V_1}$, the combination of strategies ($DP$, ($N-E$ if the regular consumer is high price-c, $N-E$ if the regular consumer is low price-sensitive)) is a Bayesian Nash equilibrium.

If $E_e\left(DP\right)<E_e\left(UP\right)$, which means that the optimal response of E-CP is the strategy $UP$, we can derive that $g>\frac{P_d-P_u}{M}$. At this point, we detect that the strategy $N-E$ is still the optimal response to the strategy $UP$ when RC are high price-sensitive; that is, the condition $\kappa V_1-C<V_c-P_u$ needs to be satisfied. We can derive $\kappa <\frac{V_c+C-P_u}{V_1}$. Thus, if $g>\frac{P_d-P_u}{M}$ and $\kappa <\frac{V_c+C-P_u}{V_1}$, the combination of strategies ($UP$, ($N-E$ if the regular consumer is high price-sensitive, $N-E$ if the regular consumer is low price-sensitive)) is a Bayesian Nash equilibrium.

5. Simulation

In this section, we use Python to numerically simulate the game model established above. First, we simulate the general game model, in which E-CP have complete information about RC. Then, we simulate the Bayesian game model. E-CP no longer have complete information about RC in the Bayesian game model. The variables needed in this paper are $V_1$, $V_2$, $P_d$, $P_u$, $V_c$, C, $\alpha$, $\kappa$, g, M, N. Some parameters are described as follows: $V_1=20$, $V_2=2.4$, $P_d=44$, $P_u=40$, $V_c=48$, $C=4$, $\alpha =0.3$, $M=6$, $N=4$.

5.1. Simulation of the General Game Model

In the general game model, the aim of the simulation in this paper is to observe how the reuse value coefficient $\kappa$ of personal data and the detection rate g of RC affect the payoffs of RC and E-CP. We vary $\kappa$ from 0.0 to 1.0 and g takes values of 0.1, 0.3, 0.5 and greater than 0.667, while keeping other parameters constant to calculate the payoffs of E-CP and RC.

Figure 2 shows that the regular consumer’ payoff decreases as g increases when $\kappa <0.4$ and $g<0.667$, which corresponds to the first pure-strategy Nash equilibrium. When $0.4<\kappa <0.6$ and $g<0.667$, the regular consumer’s payoff increases with increase in $\kappa$ and decreases with increasing g, which corresponds to the mixed-strategy Nash equilibrium. When $0<\kappa <0.6$ and $g>0.667$, the regular consumer’s payoff remains constant, which corresponds to the second pure-strategy Nash equilibrium. When $\kappa >0.6$, the regular consumer’s payoff increases with increasing $\kappa$, which corresponds to the third pure-strategy Nash equilibrium.

Figure 3 illustrates that, when $\kappa <0.4$ and $g<0.667$, which corresponds to the first pure strategic Nash equilibrium, the payoff of E-CP at this point decreases with increasing g. When $0.4<\kappa <0.6$ and $g<0.667$, the e-commerce platform’s payoff decreases with increasing $\kappa$ and decreases with increasing g, which corresponds to a mixed-strategy Nash equilibrium. When $0<\kappa <0.6$ and $g>0.667$, the e-commerce platform’s payoff remains constant, which corresponds to the second pure-strategy Nash equilibrium. When $\kappa >0.6$, the e-commerce platform’s payoff remains constant, which corresponds to the third pure-strategy Nash equilibrium.

5.2. Simulation of the Bayesian Game Model

In the next part of this section, we extend the simulation of the general game model to the Bayesian game model. The major distinction between the Bayesian game and the general game is that E-CP no longer have complete information about RC, and “nature” is introduced into the game. “Nature” makes a random decision about the type of RC. Therefore, it is necessary to consider the effect of changes in h on the payoffs of RC and E-CP when simulating the Bayesian game model.

5.2.1. Simulation of the Bayesian Game Model When RC Choose the First Strategy

Firstly, we analyze the Bayesian Nash equilibrium when RC adopt the first strategy. When RC choose the first strategy, the payoffs of RC and E-CP are dependent on the type of RC. Therefore, the purpose of the simulation is to observe how the type of RC and the detection rate of RC affect the expected payoffs of RC and E-CP. We vary h from 0.0 to 1.0 and g takes values of 0.1, 0.3, 0.6 and values greater than 0.667, and $\kappa =0.7$, while keeping other parameters constant to calculate the payoffs of the E-CP and RC.

Figure 4 shows that regular consumers’ expected payoffs increase with increasing h. When $h>\frac{P_d-P_u-gM}{P_d-P_u}$, E-CP select unified pricing. When $h<\frac{P_d-P_u-gM}{P_d-P_u}$, E-CP select price discrimination. The expected payoffs of RC decrease with increase in the detection rate g when the detection rate $g<0.667$. When $g>0.667$, g does not influence the payoff of RC.

Figure 5 shows that the e-commerce platform’s expected payoff reduces with increasing h. When $g<0.667$, the expected payoff of E-CP reduces with increase in the detection rate g. When $g>0.667$, g has no effect on the payoff of E-CP.

5.2.2. Simulation of Bayesian Game Model When RC Choose the Second Strategy

When RC choose the second strategy, the expected payoff of both RC and E-CP are independent of the type of RC. We vary g from 0.0 to 1.0 and the value of $\kappa$ is 0.3, while keeping other parameters constant to calculate the payoffs of E-CP and RC.

Figure 6 shows that the impact of the detection rate on the regular consumer’s payoff is consistent no matter whether E-CP choose price discrimination or uniform pricing. When the detection rate g is low, the regular consumer’s payoff decreases with increase in the detection rate g. When the detection rate g is high, g does not influence the payoff of RC. In addition, the payoff of a regular customer choosing strategy $N-E$ is higher than when he/she chooses the strategy E.

Figure 7 shows that when RC select not to exercise the right to data portability, there are differences in payoff for E-CP choosing price discrimination and unified pricing. If the detection rate is low, E-CP will select price discrimination; E-CP will select unified pricing if the detection rate is high.

6. Discussion

The price discrimination behavior of e-commerce platforms violates the legitimate rights of consumers and has also created a crisis of trust in itself. In previous studies, many scholars used game theory to analyze the discriminatory pricing problem using big data algorithms. In contrast to previous studies on price discrimination based on an evolutionary stable strategy [12,31,33], we introduce the right of data portability and propose a supervision mechanism with the regular customer as the regulatory subject. Based on the assumption that consumers can exercise the right of data portability, this paper establishes a Bayesian game model between regular customers and e-commerce platforms and analyzes the factors affecting the behavioural strategies of both players.

6.1. The Results of Model Analysis

Through the theoretical analysis and numerical simulation of the general game model, the following results can be obtained from the general game model:

(1)

For RC, they will choose not to exercise the right to data portability when the reuse value coefficient of personal data is too low. The payoff will also be higher if the detection rate increases. The reason for this is that when the detection rate is higher, E-CP will shift from a price discrimination strategy to a uniform pricing strategy. When the reuse value coefficient of personal data is low and the detection rate is low, RC will randomly choose a strategy. At this point the payoff of RC increases with increase in the reuse value coefficient of personal data and decreases with increase in the detection rate. When the reuse value factor of personal data is low and the detection rate is high, RC will choose not to exercise their right to data portability. The explanation is that E-CP will select uniform pricing at this point. When the reuse value coefficient of personal data is high, RC will choose to exercise the right to data portability. At this point the regular consumer’s payoff will increase as the reuse value coefficient of personal data increases.

(2)

For E-CP, when the reuse value coefficient of personal data is too low, E-CP will choose a price discrimination strategy if the detection rate is too low, or uniform pricing if the detection rate is high. When the reuse value coefficient of personal data is low and the detection rate is low, E-CP will randomly choose a strategy. When the reuse value coefficient of personal data is low and the detection rate is high, E-CP will choose a uniform pricing strategy. When the reuse value coefficient of personal data is high, the payoff of E-CP is constant. The reason is that, at this point, E-CP will select a uniform pricing strategy and RC will choose to exercise the right to data portability.

Through the theoretical analysis and numerical simulation of the Bayesian game model, we obtain the following results through the Bayesian game model:

(1)

For RC, when they choose the first strategy, the expected payoff of RC will increase as the proportion of high price-sensitive RC among all RC increases. In addition, if the regular consumer’s detection rate is higher, the regular consumer’s expected payoff will be higher. The reason is that E-CP will select a uniform pricing strategy when the detection rate is higher. If RC choose the second strategy, the expected payoff will be higher if the detection rate is higher.

(2)

For E-CP, when RC select the first strategy, if the proportion of high price-sensitive RC among all RC increases, E-CP will select uniform pricing. When RC choose the second strategy, if the regular consumer’s detection rate is higher, the E-CP will select uniform pricing.

6.2. Practical Implications

Based on the results of the analyzes of the general game model and the Bayesian game model, we can obtain the following results:

(1)

If the reuse value coefficient of personal data is high, then it is possible for regular customers to be well-served on a new platform as well. Therefore, e-commerce platforms may lose regular customers if they choose the price discrimination strategy. In order to retain regular customers, e-commerce platforms will choose a uniform pricing strategy, which indicates that the right to data portability is effective in curbing the price discrimination of e-commerce platforms.

(2)

If the reuse value coefficient of personal data is low and the detection rate of regular consumers is high, then e-commerce platforms will choose a uniform pricing strategy, which indicates that the detection rate of regular customers is also a key factor in curbing the price discrimination behaviour of e-commerce platforms.

(3)

If the proportion of high-sensitivity consumers among regular customers is high, then e-commerce platforms will be prompted to choose a uniform pricing strategy, which indicates that consumers can curb e-commerce platforms’ differential pricing behaviours by increasing their sensitivity to price change.

6.3. Limitations and Future Research

Although we have analyzed the price discrimination behaviour of e-commerce platforms by introducing the right to data portability, we can still improve the model in future research. In the Bayesian game model, we only consider that the reason for regular customers to exercise the right to data portability is that the e-commerce platform adopts a price discrimination strategy against them. Regular customers choose to exercise their right to data portability, perhaps because they are dissatisfied with the merchandise. In future research, we will consider the above issues.

7. Conclusions

In this paper, we introduce the right to data portability, focusing on the phenomenon of price discrimination, and establish a general game model and a Bayesian game model between regular consumers and e-commerce platforms. We analyze the impact of the right to data portability, the types of regular consumers and the detection rate of regular consumers on the behavior of e-commerce platforms. According to the above analysis, the following recommendations are given:

Firstly, the right to data portability can curb price discrimination on e-commerce platforms to a certain extent. However, how consumers use data portability to protect their legitimate rights and interests is a problem that needs to be solved. Therefore, the law needs to improve the power rules and formulate more behavioral norms for data controllers to ensure that consumers can exercise their right to data portability.

Secondly, the law must improve the relevant definitions of individual data and unify the data storage format and download format to increase the reuse value of individual information, and urge e-commerce platforms to choose uniform pricing strategies.

Thirdly, in order to increase their probability of identifying price discrimination on e-commerce platforms, regular consumers should use internet information to compare price with other regular consumers, so as to curb the phenomenon of price discrimination on the e-commerce platform by their own actions.