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Complexity in Economics and Business 2021

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Research Article | Open Access

Volume 2021 |Article ID 5554501 | https://doi.org/10.1155/2021/5554501

Qiang Wei, Xinyu Gou, Tianyu Deng, Chunguang Bai, "Restrain Price Collusion in Trade-Based Supply Chain Finance", Complexity, vol. 2021, Article ID 5554501, 23 pages, 2021. https://doi.org/10.1155/2021/5554501

Restrain Price Collusion in Trade-Based Supply Chain Finance

Academic Editor: Baogui Xin
Received24 Feb 2021
Accepted06 May 2021
Published08 Jun 2021

Abstract

Collusion can increase the transaction value among supply chain members to obtain higher loans from supply chain finance (SCF) service provider, which will bring some serious risks for SCF. However, it is difficult to be identified and restrain the SCF service provider due to its stability and hiddenness. Different SCF transaction structures will affect the profits of supply chain members from collusion. This paper develops various game models for collusion and not collusion for different SCF transaction structures and investigates the impact of SCF transaction structures on the boundary conditions of collusion. Through comparative analysis, the findings of models are as follows: (1) in a two-echelon supply chain, the supplier and retailer are more likely to conduct collusion under the sequential game than under the simultaneous game; (2) collusion in the two-echelon supply chain can obtain higher loans than that in the three-echelon supply chain, so it has more serious hidden danger; (3) in the two-echelon supply chain, collusion is easier to form than in the three-echelon SCF supply chain that has spontaneous endogenous constraints. We also develop two types of mechanisms to restrain collusion behavior from profit sharing and incomplete information perspectives. Finally, we summarize the theoretical implications and analyze the management implications through a case study.

1. Introduction

Collusion refers to the behavior that some firms reach a secret agreement on the price or volume of the products or services they provided and use the agreed price to replace the market price, so as to obtain more profits [1, 2]. Once collusion is implemented, it will inevitably lead to the loss of the profits of consumers and other firms, that is, they will pay higher prices for products and services. Although governments have enacted antitrust laws (such as the antitrust law of China in 2007) to limit the formation of cartels and other collusions in determining market price, collusion is still frequently appeared in the market [1, 3]. One reason is that it is very difficult to obtain concrete evidence to prove collusion behavior between firms [4]. Another reason is that firms of collusion can achieve extra profits, such as high financial loans.

The rapid development of supply chain finance (SCF) has effectively solved the problem of the capital shortage of supply chain firms and promoted the development of real economic and financial services [5]. Although the SCF system has set up many mechanisms to prevent various financial risks, collusion brings great risks to SCF service provider because of its hiddenness. For example, more than 20 steel traders increased the price and amount of transactions through collusion in China to obtain higher financial loans based on the transaction value and were sued by the bank to the court (see [6]). The amount of cash and the number of companies involved are unprecedented. For another example, on April 2, 2020, Luckin Coffee Inc. (NASDAQ: LK) announced that the COO and several other executives engaged in certain misconduct, including fabricating certain transactions amounting to roughly RMB 2.2 billion, resulting in the stock plunging by 80% in one day [7]. Then, SCF service providers, such as banks, funds, and trusts, generally worry that there is no effective way to identify and prevent collusion in the financial industry. Collusion against the real trading bottom line has become a stumbling block for SCF [8]. As far as we know, there is no research on collusion in the field of SCF.

The collusion agreement is not always unbreakable and stable. When the profit of collusion is less than that of noncollusion, the collusion agreement will be broken. SCF service providers can effectively control the profit of collusion and noncollusion through the discount factor of loans. Then, we will investigate the discount factor of loans to determine the boundary condition of collusion.

Transaction structure plays an important role in all kinds of supply chain financial loans. Previous research on SCF focuses on the design of SCF transaction structures to prevent various risks [9, 10]. However, the impact of SCF transaction structures on the boundary condition of collusion is unclear. This paper focuses on two types of trade-based SCF transaction structures. The first is the hierarchical transaction structures, which are often divided into two-echelon supply chain and three-echelon supply chain [11]. The second is the relation structures, which are often divided into master-slave relation and equivalent relation [12]. The objective of this paper is to investigate the boundary conditions of collusion between the supply chain members in different trade-based SCF transaction structures. We mainly address the following issues:(1)What are the boundary conditions (discount factor) (according to collusion theory in microeconomics, the boundary condition is when the discount factor is greater than a threshold, the collusion can be conducted and will be stable; otherwise, the collusion cannot be conducted and will be unstable (similar to [13]) of price collusion in these different trade-based SCF transaction structures?(2)Which trade-based SCF transaction structure has a spontaneous endogenous constraint on collusion that is called self-restraint (not easy to collusion)? Which trade-based SCF transaction structure has hidden, unidentifiable collusion that is called hidden vulnerability (easy to collusion)?(3)How to develop a mechanism to restrain price collusion in trade-based SCF transaction structure with hidden vulnerability from the profit sharing and incomplete information perspectives?

To answer these questions, we develop different game models for different trade-based SCF transaction structures to identify the boundary condition of collusion. We then compare and analyze the results of these boundary conditions to confirm the advantages and disadvantages of different trade-based SCF transaction structures on restraining price collusion. We look forward to providing reference values for the design of trade-based SCF transaction structure. SCFWG also points out that financial institutions are risk-averse and lack resources to evaluate numerous and varied trade-based SCF structures. In current SCF market conditions where loan quality has become a key issue, this study can provide new solutions for trade-based SCF service providers in preventing collusion and making loan decisions.

This study contributes to the operation management literature studies in the following respects. First, as far as we know, this study is the first focus on the impact of trade-based SCF transaction structures on collusion in the supply chain. Few studies have integrated collusion [14] and SCF [15] to design an effective trade-based SCF transaction structure to prevent collusion from the perspective of supply chain financial risk. Second, we also investigate the impact of the different relation structures on the collusion, such as master-slave relationship and equivalent relationship. Finally, we develop two mechanisms to restrain price collusion from profit sharing and incomplete information perspectives.

The rest of this paper is organized as follows. Section 2 reviews relevant research streams. Section 3 describes the problems. Section 4 discusses the collusion in the two-echelon supply chain, and Section 5 discusses that in the three-echelon supply chain. Section 6 conducts a comparative analysis, and Section 7 tries to extend the research, for example, profit sharing and incomplete information. Section 8 further discusses the theoretical and managerial implications. Finally, Section 9 highlights the main conclusions, limitations, and future research directions.

2. Literature Review

To provide research background and highlight our contributions, we mainly review two related research fields: (1) collusion in the field of economy and management and (2) SCF transaction structure.

2.1. Collusion in Economics and Management

Collusion is a kind of risk behavior in the economic field, which widely exists in insurance, financing, and other financial fields [16]. According to existing research, many different types of collusion exist, and they can be divided into two major categories, namely, management collusion and business collusion. Management collusion mainly refers to the collusion between the company’s stakeholders, managers, and employees [17]. On the contrary, business collusion is complex and diverse, such as the market collusion, production collusion, and price collusion [18].

In recent years, some scholars have paid attention to collusion research in the field of operation management [11, 19, 20]. Piccolo and Reisinger. [21] analyze the impact of exclusive territories on manufacturers’ incentives to sustain tacit collusion between competing supply chains. Melkonyan et al. [22] develop a formal account of virtual bargaining and demonstrate that it leads to collusion in Bertrand, but not in Cournot, competition. Zheng et al. [23] establish an infinitely repeated game to examine the interaction between the manufacturer’s channel strategy and the downstream retailers’ collusion behavior. Bian et al. [13] find that upstream collusion in a two-echelon supply chain is easier to sustain under Cournot competition than Bertrand competition, and it is least likely to be sustained under mixed Bertrand–Cournot competition. Miklós-Thal and Tucker [14] build a game-theoretic model to examine how better demand forecasting resulting from algorithms, machine learning, and artificial intelligence affects the sustainability of collusion in an industry. Wang et al. [24] built three two-tier game models: Stackelberg-collusion model, Stackelberg-Nash model, and Stackelberg-Stackelberg model, to consider the retailers’ potential collusive behavior and the upstream manufacturer’s interactive decisions.

Collusion price, which differs from false price, is a collusion agreement that increases the real price consumers pay for a product and then obtains high loans from SCF service providers through the increased transaction value. Collusion also differs from the supply chain integration which realizes the maximization of supply chain benefits by positive practices, such as improving production efficiency, increasing product quality, reducing production costs, or other means [25, 26]. However, collusion realizes the maximization of supply chain benefits by negative practices, such as increasing product price and limiting production. Then, it not only damages the benefits of consumers but also reduces the benefits of financial institutions. Supply chain integration denotes Pareto optimization, whereas collusion is the opposite [27]. Supply chain members easily make short-sighted successful decisions in collusion, thus shaking the development foundation of strategic and stable supply chain.

Collusion can increase the transaction value among supply chain members to obtain higher loans from supply chain finance (SCF) service provider, which will bring some serious risks for SCF. As collusion is very common in supply chain transactions, identifying and preventing this kind of behavior is difficult by means of policy. However, the research of price collusion in supply chain finance has not been effectively analyzed, especially in order to obtain high loans.

2.2. Supply Chain Finance and Transaction Structure

SCF has evolved from the original trade finance, which plays an increasingly important role in solving the financing problems of SMEs [28]. Therefore, most of the existing literature mainly studies how to design an SCF solution that can not only meet the requirements of financial institutions but also effectively solve the financing problem of SMEs, such as bill discount business [29], inventory and receivables finance [30], purchase order finance [9], supply chain inventory finance [10] and trade credit [31].

Trade finance is a very important form of SCF. Lee and Rhee [32] explain trade finance from a supplier perspective and use it as a tool for supply chain coordination. Seifert et al. [33] summarize the relevant literature of trade finance from the aspects of motivation, order quantity decision, credit period decision, and settlement period decision. They hold that trade finance can increase the number of economic orders and serve as the coordination mechanism of the supply chain. Supply chain structure and SCF have a very close relationship. Lee et al. [34] study how trade finance responds to various kinds of competition in the supply chain and the impact of trade finance on firm performance. Peura et al. [35] study whether trade finance is beneficial to suppliers in the horizontal supply chain structure.

Only when more than 20 SCF cases were heard [6] that scholars began to realize the seriousness of the SCF risk. However, at that time, few studies are about the risk management of SCF. Zhao et al. [20] use the external big dataset to establish a forecasting model from the perspective of risk management, and they predict the failures of SCF customers aiming to reduce the risk of financial institutions. They find that cooperation between logistics service providers and financial service providers seems to be a feasible method to solve the financing problem through the case analysis of Swiss Post Logistics in Hofmann’s study. Martin and Hofmann [36] conduct a survey of 62 companies from Switzerland and 10 expert interviews to analyze the reasons financial service providers participate in the integrated management of the supply chain processes.

The study of SCF has three limitations though. First, collusion risk in SCF is not well studied. In recent years, the transition from the traditional rational economic man hypothesis to the behavioral economic man hypothesis has become increasingly obvious. Behavioral operation management (BOM) and behavioral finance have become new research hotspots. Therefore, SCF risk management research, as a cross-research issue of operation management and finance (OM-finance), must consider this important research foundation change. This trend has been exacerbated by the outbreak of collusion among steel traders. Second, the SCF structure has positive significance for financial loans, but the impact on collusion risk is unclear. Particularly important is the research on SCF risk management based on the behavior of all parties in the SCF transaction structure. Third, what mechanisms can prevent collusion has not been studied in detail. Song et al. [37] indicate that information sharing in supply chain and other related attributes of SMEs’ supply chain network are the key factors that affect the credit quality of SMEs and influence the financing of SMEs.

3. Problem Description

The motivation of collusion among supply chain members is to obtain higher long profits in this paper. If the profits of collusion are high enough, supply chain members will continue to collusion. If the profits of collusion is not higher than the profits of noncollusion, then one member may form cheat behavior in collusion to obtain short-term profit of itself, thus destroying collusion agreement and returning to normal market price trading. Therefore, we need to compare the profits of collusion with the profits of cheat behavior and normal market transaction. When the profits of collusion are higher, supply chain members will choose price collusion. When the profits of price collusion are lower, supply chain members will generate cheat behavior to destroy the current collusion. As financial loans will span multiple stages of sales and production, we need to consider the profits of multiple stages and the discount value of profits. Clearly, the discount factor is the most important factor affecting the profits of collusion and noncollusion. We investigate the discount factor to determine the boundary conditions of collusion. We solve the model according to this idea.

To systematically reveal the impact of SCF transaction structures on the boundary conditions of collusion behavior, we mainly study two kinds of trade-based SCF transaction structures: hierarchical and relation transaction structures. The hierarchical transaction structures are often divided into a two-echelon supply chain with one supplier and one retailer (see Figure 1) and a three-echelon supply chain with one supplier, one distributor, and one retailer (see Figure 2). The relation transaction structures are often divided into master-slave relation and equivalent relation.

In the two-echelon supply chain, the retailer signs a purchase contract (p, q) with the supplier. represents the unit price of the order product, whereas the represents the quantity of the order product. First, the retailer signs the financial loan contract with SCF service provider and releases the purchase order to the supplier according to the purchase contract, which is the trade flow. Second, the retailer makes a certain proportion of loans to SCF service provider based on the value of order product between the supplier and the retailer. Third, the retailer should pay the percentage () of payments to the supplier according to the financial loan contract (see the cash flow in Figure 1). Based on the trade flow, the cash flow paid by the retailer, and confirmation information from the supplier, the SCF service provider will pay the corresponding payments to the supplier. Once the supplier receives all the payments , they will arrange to ship the order products to the retailer, which is the logistics (see Figure 1). Obviously, to get higher finance loans from the SCF service provider, the supply chain members are prone to collusion, which leads to the false increase in the transaction value of order product between the supplier and retailer.

Although only one kind of collusion exists in the two-echelon supply chain, three different types of collusion among different members exist in the three-echelon supply chain (see Figure 2). We develop various game models to identify the boundary conditions of collusion in the two-echelon supply chain and three-echelon supply chain. We also study the different boundary conditions of collusion among the master-slave relation and equivalent relation in each hierarchical transaction structure. The notation and description of various game models are defined in Table 1.


NotationDescription

In the two-echelon supply chain, is supplier and retailer. In the three-echelon supply chain, is supplier, distributor, and retailer
The marginal price (revenue) of
Potential demand of the market
The actual demand of the market
The profits of

In the two-echelon supply chain with supplier and retailer
The marginal price (revenue) of under sequential Stackelberg model
The actual demand of the market under sequential Stackelberg model
The profits of under sequential Stackelberg model
The marginal price (revenue) of under sequential collusion model
The actual demand of the market under sequential collusion model
The profits of under sequential collusion model
The marginal price (revenue) of under sequential cheat model
The actual demand of the market under sequential cheat model
The profits of under sequential cheat model
The marginal price (revenue) of under simultaneous Cournot model
The actual demand of the market under simultaneous Cournot model
The profits of under simultaneous Cournot model
The marginal price (revenue) of under simultaneous collusion model
The actual demand of the market under simultaneous collusion model
The profits of under simultaneous collusion model
The marginal price (revenue) of under simultaneous cheat model
The actual demand of the market under simultaneous cheat model
The profits of under simultaneous cheat model

In the three-echelon supply chain with supplier, distributor, and retailer
The marginal price (revenue) of under Benchmark_Stackelberg model
The actual demand of the market under Benchmark_Stackelberg model
The profits of under Benchmark_Stackelberg model
The marginal price (revenue) of under S_D_Collusion model
The actual demand of the market under S_D_Collusion model
The profits of under S_D_Collusion model
The marginal price (revenue) of under S_D_Cheat model
The actual demand of the market under S_D_Cheat model
The profits of under S_D_Cheat model
The marginal price (revenue) of under D_R_Collusion model
The actual demand of the market under D_R_Collusion model
The profits of under D_R_Collusion model
The marginal price (revenue) of under D_R_Cheat model
The actual demand of the market under D_R_Cheat model
The profits of under D_R_Cheat model
The marginal price (revenue) of under S_R_Collusion model
The actual demand of the market under S_R_Collusion model
The profits of under S_R_Collusion model
The marginal price (revenue) of under S_R_Cheat model
The actual demand of the market under S_R_Cheat model
The profits of under S_R_Cheat model
The profits of under the simultaneous game
The critical discount factor under the sequential game
The critical discount factor under the simultaneous game
The critical discount factor under the S_D_Collusion game
The critical discount factor under the D_R_Collusion game
The critical discount factor under the S_R_Collusion game
Profit sharing factor between the supplier and retailer
The probability of cheating of the supplier and retailer
Probability of collusion

In the two-echelon supply chain, sequential Stackelberg model represents the benchmark model under the sequential game, sequential collusion model represents the collusion model under the sequential game, sequential cheat model represents the cheat model under the sequential game, simultaneous Cournot model represents the benchmark model under the simultaneous game, simultaneous collusion model represents the collusion model under the simultaneous game, and simultaneous cheat model represents the cheat model under the simultaneous game. In the three-echelon supply chain, Benchmark_Stackelberg model represents the benchmark model (i.e., Stackelberg game), S_D_Collusion model represents the collusion model between the supplier and distributor, S_D_Cheat model represents the cheat model between the supplier and distributor, D_R_Collusion model represents the collusion model between the distributor and retailer, D_R_Cheat model represents the cheat model between the distributor and retailer, S_R_Collusion model represents the collusion model between the supplier and retailer, and S_R_Cheat model represents the cheat model between the supplier and retailer.

4. Collusion in the Two-Echelon Supply Chain

In this section, we study collusion in the two-echelon supply chain with one supplier and one retailer. Following Loch and Wu [38], we suppose that the market demand is a simple linear demand function, assuming that , where and are the marginal revenue (price) of supplier and retailer, respectively. The price game of the vertical two-echelon supply chain is a sequential game process, the supplier (first mover) firstly determines its marginal price (equivalent to the wholesale price minus the cost ), and then the retailer (second mover) decides its marginal price (equivalent to the retail price minus the wholesale price ). Then, the two marginal prices jointly determine the final market price of the product (for ease of calculation, the product cost c is ignored as 0). The profit of supplier or retailer is given as follows:

4.1. Collusion under Sequential Game

According to collusion theory (CT), we first analyze collusion between supplier and retailer in the two-echelon supply chain under the sequential game. The sequential game is similar to Stackelberg game in which the supplier and retailer quote in turn.

4.1.1. Sequential Stackelberg Model

When the supplier and retailer play sequential game, the solution of reverse selection is as follows.

First, the maximization profit of the retailer is

Therefore, the optimal reaction curve of retailer to supplier’s price quotation is

Substituting the above reaction curve into the supplier decision function to solve the optimal price quotation, we have

Then, we obtain the optimal marginal price of the supplier and the retailer , the optimal demand , and the maximum profit of the supplier and retailer .

4.1.2. Sequential Collusion Model

According to CT, when the supplier and retailer collude price to maximize profits, their decision objective of collusion becomes

This analysis model is similar to microeconomics [2], assuming that supplier and retailer equally allocate all profits come from collusion. This paper also gives a more comprehensive analysis in Section 7, considering the random profit sharing of price collusion.

Through the above solution, we have the optimal marginal price of the supplier and the retailer under the price collusion, the optimal demand , and the maximum profit of the supplier and retailer .

4.1.3. Sequential Cheat Model

In the sequential game, the supplier has the first-mover advantage over the retailer. However, this advantage becomes a disadvantage in collusion. When the supplier and retailer quote price one after another, the retailer is most likely to cheat in price collusion to maximize its profits at a given supplier price, thus damaging the profits of supplier. We analyze the cheat behavior in collusion as follows.

According to the collusion agreement, the supplier first quotes based on the goal of maximizing the profit of collusion. However, owing to the inferiority of the first mover, the retailer may produce cheat behavior to maximize its own profits. Therefore, the decision function of the retailer will become the following form:

Then, we solve the following:

We get the optimal marginal price of retailer when cheat behavior in collusion , the demand , and the maximized profit of supplier and retailer . That is, for a single-period game, the profit of cheat behavior is higher than the profit of collusion for retailer, and there is economic temptation of cheat behavior. The profit of retailer for cheat behavior is.

4.1.4. Boundary Condition of Sequential Game

Once producing cheat behavior, the retailer and supplier will stop collusion and resume market price cooperation. Therefore, we compare the profits of collusion and the profits of cheat behavior and maker cooperation for the retailer to determine the boundary conditions of price collusion. At this point, according to CT in microeconomics [2], the decision-making process of the regulatory measures for the cheat behavior in collusion is as follows:where refers the discount factor of the profit.

Seeing that , then

According to the hypothesis of punishment strategy, when the discount factor satisfies the above conditions, the collusion is stable and cannot be disintegrated.

Proposition 1. In a two-echelon supply chain under the sequential game, the profits of retailer in collusion, cheating, and sequential game satisfy .(1)When the discount factor satisfies , the supplier and retailer are likely to collude to get higher loans from the SCF service provider in the two-echelon trade-based SCF transaction structure.(2)When the discount factor satisfies , the two-echelon trade-based SCF transaction structure has the ability to actively restrain price collusion, that is, self-restraint, which can effectively avoid the price collusion behavior.

Proof. It follows directly from the above analysis and is thus omitted.

4.2. Collusion under Simultaneous Game

The simultaneous game is similar to Cournot game in which the supplier and retailer quote at the same time.

4.2.1. Simultaneous Cournot Model

When the supplier and retailer play simultaneous game, they first consider the reaction curve of each other to their own pricing decision and then make the optimal pricing decision in the way of reverse selection. After repeated games, the equilibrium strategy of the simultaneous game will be fixed at the intersection of the response curve of supplier and retailer to each other’s pricing decision. First, the profit maximization of the supplier and retailer respectively is as follows:

Therefore, under the simultaneous game, the optimal reaction curves of the supplier to retailer’s quoted price and the retailer to supplier’s quoted price are as follows:

Based on the homologous structures of the above two reaction functions, the optimal pricing for the simultaneous game equilibrium can be easily found by substituting the first reaction curve into the second one. Then, we get the optimal marginal price of the supplier and the retailer , the optimal demand , and the maximum profit of the supplier and retailer .

4.2.2. Simultaneous Collusion Model

According to CT, when the supplier and retailer collude price to maximize profits, their price collusion decision objectives are as follows:

This analysis method is similar to microeconomics, assuming that supplier and retailer equally distribute all profits of price collusion.

Through the above solution, we have the optimal marginal price of the supplier and the retailer under the price collusion, the optimal demand , and the maximum profit of the supplier and retailer .

4.2.3. Simultaneous Cheat Model

Based on the analysis of the optimal pricing decision under the price collusion and simultaneous games, the possible cheat behaviors of the supplier and retailer are analyzed. As the leader of two-level supply chain, the original advantages of supplier become disadvantages when cheat occurs under the sequential game. Under the premise of the sequential game, it is almost impossible for the supplier to cheat because its cheating behavior can be discovered by the retailer in “one time” game, but the cheat behavior of the retailer can be found at least twice in the game process. Then, supplier thinks the retailer may be cheating. When the hypothesis becomes a simultaneous game, the supplier and retailer may cheat because there is no sequential relationship between their pricing behaviors. Next, we analyze the cheat behaviors of the supplier and retailer.

According to the collusion agreement, the supplier first quotes on the basis of the decision of maximizing the profit of price collusion. However, the supplier realizes that the retailer may take cheating to damage his own interests. After the supplier completes his own pricing, the decision making of the retailer’s cheat behavior is based on the new profit function to decide its new quotation .

Then, we solve the following:

We have the optimal marginal price of retailer when cheating in price collusion , the demand , and the maximum profit . The profit of cheating for retailer is higher than the profit of price collusion for the single-period game, and there is the economic temptation of cheat. The cheat profit of retailer is .

4.2.4. Boundary Condition of Simultaneous Game

According to CT, the idea of preventing price collusion parties from cheat is to make the present value of price collusion profits higher than the present value of cheat and simultaneous game profits. Both the supplier and retailer are likely to cheat under the simultaneous game, so taking the larger critical discount factor as the constraint condition is necessary to regulate the occurrence of cheat in price collusion.

The “threat” of punishment at this time is that if the supplier or the retailer cheats in the price collusion, they will enter the simultaneous game forever, so, which shows that

Because the supplier and retailer are homogeneous in the simultaneous game, the following is easy to know:

Therefore, , and the critical discount factor in the simultaneous game is .

Proposition 2. In a two-echelon supply chain under the simultaneous game, the profits of retailer in price collusion, cheating, and simultaneous game satisfy .(1)When the discount factor satisfies , the supplier and retailer are likely to collude price to get higher loans from the SCF service provider in the two-echelon trade-based SCF transaction structure.(2)When the discount factor satisfies , the two-echelon trade-based SCF transaction structure has the ability to actively restrain price collusion, that is, self-restraint, which can effectively avoid the price collusion behavior.

Proof. It follows directly from the above analysis and is thus omitted.

5. Price Collusion in the Three-Echelon Supply Chain

Considering that the three-echelon supply chain is composed of one supplier, one distributor, and one retailer, the increase of supply chain levels leads to different forms of price collusion. This section focuses on the following different forms of price collusion under complete information: (1)Price collusion between the supplier and distributor (see Figure 3(a))(2)Price collusion between the distributor and retailer (see Figure 3(b))(3)Price collusion between the supplier and retailer (see Figure 3(c))

The market demand assumption in this section also refers to Loch and Wu [38]. Therefore, the general linear demand can be expressed as

The profit function of each member in the three-echelon supply chain can be expressed as follows:

5.1. Price Collusion under Sequential Game

According to CT, we first analyze price collusion with or without cheat behavior of the supplier, distributor, and retailer in the three-echelon supply chain under the sequential game. The sequential game is similar to Stackelberg game in which the supplier, distributor, and retailer quote in turn.

5.1.1. Benchmark Model: Stackelberg Game

Stackelberg game is a benchmark model for the supplier, distributor, and retailer to quote in turn. According to CT, we first analyze the Stackelberg game in the three-echelon supply chain and then the price collusion and cheating in three different forms of price collusion. When the supplier, distributor, and retailer play Stackelberg game, the solution of reverse selection is as follows. First, the profit maximization of the retailer is

Therefore, the optimal reaction curve of retailer to the supplier’s and distributor’s quotations is as follows:

Substituting the above reaction curve into the decision function of the distributor to solve the optimal quoted price, we have

Then, the optimal reaction curve of the distributor to the supplier’s quotation is

Substituting the above reaction curve into the decision function of the supplier to solve the optimal quoted price, we get

At last, we obtain the optimal marginal price of the supplier , the distributor , and the retailer , the optimal demand , and the maximum profit of the supplier, the distributor, and the retailer .

5.1.2. Price Collusion between the Supplier and Distributor

(1) S_D_Collusion Model. According to CT, when the supplier and distributor collude price in order to maximize profits, the decision objectives of collusion will be

However, to solve the problem of profit maximization, the first step is to determine the optimal price reaction curve of the retailer to the price quotation of the supplier and the distributor based on the reverse selection strategy. We can know that the profit maximization of the retailer is

We easily get this optimal reaction curve as follows:

Substituting the above reaction curve into the decision function of price collusion, we can solve the optimal quoted price as follows:

At last, we obtain the optimal marginal price of the supplier , the distributor , and the retailer , the optimal demand , and the maximum profit of the supplier, the distributor, and the retailer .

(2) S_D_Cheat Model. This model is similar to the previous analysis of the cheating model because the first-mover advantage of the supplier becomes a disadvantage. The distributor is most likely to cheat in the price collusion, thus damaging the profit of supplier. The profit maximization and reaction curve of retailer are as follows:

According to the price collusion agreement, the supplier shall first quote on the basis of the decision of maximizing the profit of price collusion. After the supplier completes his own pricing, the decision making of distributor’s cheating behavior is to decide his new quotation based on the new profit function.

Through the above objective function, we can have the entire optimal marginal price , the optimal demand , and all the optimal profits .

According to the punishment mechanism of CT in microeconomics, the critical discount factor can be solved as follows:

Proposition 3. In a three-echelon supply chain, the distributor’s profits of distributor in price collusion, cheating, and Stackelberg game satisfy .(1)When the discount factor satisfies , the supplier and distributor are likely to collude price to get higher loans from the SCF service provider in the three-echelon trade-based SCF transaction structure.(2)When the discount factor satisfies , the three-echelon trade-based SCF transaction structure has the ability to actively restrain price collusion between the supplier and distributor, that is, self-restraint, which can effectively avoid the price collusion behavior.

Proof. It follows directly from the above analysis and is thus omitted.

5.1.3. Price Collusion between the Distributor and Retailer

(1) D_R_Collusion Model. According to CT, when the distributor and retailer collude price to maximize profits, their collusion decision objectives are

By solving the following partial derivatives, we can get the optimal reaction curve of the distributor and retailer to the supplier’ price quotation.

The reaction curve is

Through the reverse selection strategy, we substitute the above reaction curve into the supplier’s profit maximization, and the solution is as follows:

At last, we obtain the optimal marginal price of the supplier , the distributor , and the retailer , the optimal demand , and the maximum profit .

(2) D_R_Cheat Model. Similar to the analysis of the cheating behavior of the distributor under the price collusion between supplier and distributor, when they collude, the retailer obtains the motivation of cheating in the price collusion. At this time, the optimal marginal price of the supplier and distributor will be similar to that in the D_R_Collusion model, which is . Then, the decision making of retailer cheating behavior is based on the new profit function to determine its new quotation :

Through the above objective function, we get the retailer’s optimal marginal price , the optimal demand , and all the optimal profits .

According to the punishment mechanism of CT in microeconomics, the critical discount factor can be solved as follows:

Proposition 4. In a three-echelon supply chain, the profits of retailer in price collusion, cheating, and Stackelberg game satisfy .(1)When the discount factor satisfies , the distributor and retailer are likely to collude price to get higher loans from the SCF service provider in the three-echelon trade-based SCF transaction structure.(2)When the discount factor satisfies , the three-echelon trade-based SCF transaction structure has the ability to actively restrain price collusion, that is, self-restraint, which can effectively avoid the price collusion behavior.

Proof. It follows directly from the above analysis and is thus omitted.

5.1.4. Price Collusion between the Supplier and Retailer

(1) S_R_Collusion Model. According to CT, when the supplier and retailer collude to maximize profits, their collusion decision objectives are

By solving the following partial derivatives, we can get the optimal reaction curve of the supplier and retailer to the distributor’s price quotation.

The reaction curve is

Through the reverse selection strategy, the above reaction curve is put into the profit maximization of distributor, and the solution is as follows:

At last, we obtain the optimal marginal price of the supplier , the distributor , and the retailer , the optimal demand , and the maximum profit is .

(2) S_R_Cheat Model. Similar to the analysis of the cheating behavior of the distributor under the price collusion between supplier and distributor, when they collude, the retailer obtains the motivation of cheating in the price collusion. At this time, the optimal marginal price of the supplier and distributor will be similar to that in the S_R_Collusion model, which is . Then, the decision making of the retailer’s cheating behavior is to decide its new quotation based on the new profit function:

Through the above objective function, we get the optimal marginal price of retailer, the optimal demand , and all the optimal profit.

According to the punishment mechanism of the CT in the Microeconomics, the critical discount factor can be solved as follows:

Proposition 5. In a three-echelon supply chain, the retailer’s profits of price collusion, cheating, and Stackelberg game satisfy .(1)When the discount factor satisfies, the supplier and retailer are likely to collude price to get higher loans the SCF service provider in the three-echelon trade-based SCF transaction structure.(2)When the discount factor satisfies , the three-echelon trade-based SCF transaction structure has the ability to actively restrain price collusion, that is, self-restraint, which could effectively avoid the price collusion behavior.

Proof. It follows directly from the above analysis and is thus omitted.

5.2. Price Collusion under Simultaneous Game

Simultaneous game is similar to Cournot game in which the supplier, distributor, and retailer quote at the same time. According to CT, we analyze the simultaneous game, price collusion, and cheating behaviors of the supplier, distributor, and retailer in the three-echelon supply chain.

5.2.1. Benchmark Model: Simultaneous Game

Simultaneous game (similar to Cournot game) is a benchmark model for the supplier, distributor, and retailer to quote at the same time. According to CT, we first analyze the simultaneous game in the three-echelon supply chain and then the price collusion and cheating in three different forms of price collusion. When the supplier, distributor, and retailer play simultaneous game, the solution of reverse selection is as follows. First, the profit maximization of the supplier is

Therefore, the optimal reaction curve of supplier to the distributor and retailer’s quotations is as follows:

Following the same principle, we could get and . Then, we solve the above three reaction curves simultaneously, that is,

At last, we have , , and .

5.2.2. All the Collusion and Cheating Scenarios under Simultaneous Game

Similar to Sections 5.1.25.1.4, we need to analyze all the price collusion and cheating behaviors between any two members in the three-echelon supply chain. To easily compare and analyze all the scenarios, we summarize the calculation results in all cases in Table 2.


Supplier and distributorDistributor and retailerSupplier and retailer

Price collusion,, ,
Cheating,