Interactive Impacts of Overconfidence and Competitive Preference on Closed-Loop Supply Chain Performance

Abstract

As sustainable development becomes an important goal for all industries, the study of closed-loop supply chains has gradually become a priority. Most of the previous studies on closed-loop supply chains are based on simple and single market conditions, which cannot analyze the real situation well. In this paper, two common behavioral preferences in the market, overconfidence and competitive preference, are incorporated into the study of closed-loop supply chains to investigate how the overconfidence of retailers and the competitive preference of manufacturers jointly affect the decisions and interests of both parties in closed-loop supply chains under different dominant models. It is concluded that in terms of pricing, while the wholesale price increases in the competitive preference, the reselling price in fact decreases when the retailer’s overconfidence level is of a middle level; in terms of recycling, the pursuit of high profits by monopolistic manufacturers is not conducive to recycling quantity in the secondary supply chain with recycling; in terms of profits, in a manufacturer-led model, the profits of all sides in the closed-loop supply chain, including the manufacturer itself, sometimes diminish as the manufacturer’s competitive preference behavior becomes more intense.

1. Introduction

With the continuous development and improvement of global technology and economic level, sustainable development has become the world consensus. The emergence of green trade barriers has made green, low-carbon, and recycling a common agenda in the business strategies of enterprises in all countries. Under such a background, the research on green closed-loop supply chains has become a hot issue in economics. A closed-loop supply chain refers to a complete supply chain cycle that includes both the traditional positive process from raw material purchase to final sales and the reverse process from product recycling to reuse. In a closed-loop supply chain, the manufacturer takes the initiative to recycle the used or waste products and takes them as raw materials to participate in the new production process, so as to reduce production costs and accelerate the product life cycle, and for purposes conducive to the manufacturer’s profit creation [1]. Compared with the traditional supply chain, the unique feature of recycling–remanufacturing can greatly improve the efficiency of resources and bring great benefits to the enterprise itself. Meanwhile, the wide adoption of closed-loop supply chains in different industries saves resources and reduces pollution in society. Nowadays, many enterprises have started to incorporate the recycling of used products into their business, especially in the electronic technology industry, such as the production of smartphones, computers, and other smart terminals [2]. For instance, Apple first announced the concept of product recycling in 2013. Recently, this environmentally friendly company released details about the increasing usage of recycled content across its products; e.g., 59% of their aluminum material came from recycled sources (readers are referred to the report “Apple expands the use of recycled materials across its products” from https://www.wbcsd.org/Overview/News-Insights/Member-spotlight/Apple-expands-the-use-of-recycled-materials-across-its-products, accessed on 8 November 2022).

In the traditional supply chain, the interactions among stakeholders can be affected by many cognitive biases, as has been demonstrated in many papers [3]. A typical example can be found in Li and Ye’s research [4], where they explored how retailers’ cognitive biases affect the decision-making and performance of manufacturers and retailers in a supply chain. In the closed-loop supply chain, the additional process of recycling further complicates the impacts of cognitive bias. Among the many types of bias, overconfidence and competitive preferences are regarded as the major factors in decision-making [5].

Overconfidence is a common cognitive bias in the decision-making process, where the decision-makers exert overestimation on their judgment and prediction ability on the factors relevant to the performance [6]. Think of the case of Kodak’s bankruptcy. Due to the overconfidence of its CEO in the roll film industry chain, the company mistakenly believed the digital imaging technology would not impact the industry, thus missing the chance for transformation (the relevant report titled “Film’s out for Kodak: A Lesson in overconfidence” can be found from https://blogs.ubc.ca/matthewrafael/2017/04/02/films-out-for-kodak-a-lesson-in-overconfidence/, accessed on 8 November 2022).

Similarly, competitive preference, as a common cognitive bias, often affects the decision-making process of stakeholders. Decision-makers with competitive preferences always compare their profits with others and prefer more benefits than others [7]. The competitive preferences are found in this paper. The experiment in their work shows that people express willingness to lower another person’s payoff. As a matter of fact, the decision-makers in the supply chain may want to witness other firms’ profit decline, especially in the competitive setting.

Previous studies have mostly focused on one behavioral factor of one side of the supply chain. The research on the topic of multiple behavioral factors in the supply chain’s performance, nonetheless, is limited. In this paper, we incorporate both overconfidence and competitive preference into a typical closed-loop supply chain with one manufacturer and one retailer. In our setting, the manufacturers exhibit competitive preferences, and the retailers exhibit overconfidence. Following the previous literature, we consider the game in different dominant modes (e.g., centralized and decentralized decision-making; the diverse leading party) and solve the profit maximization problem through backward induction and optimization.

Our main results are summarized as follows. We find that no matter which type of decentralized decision-making mode is held, the profit of both the manufacturer and the retailer decrease with the competitive preference, making the closed-loop supply chain performance worse off. Additionally, the relationship between a product’s retail price and the level of competitive preference is affected by the range of the retailer’s overconfidence (measured by the overconfidence parameter). Meanwhile, the recycling volume of waste products in the closed-loop supply chain under the non-leader model is greater than that under the manufacture-lead model, and both of them are less than the recycling volume under the centralized model. In the two decentralized models, when the levels of these two cognitive biases are constant, the quantity of recycling worn-out products under the non-leader model is always larger than that under the manufacturer-led model. We believe that our results can partially explain the real practice in the closed-loop supply chain where both the manufacturer and the retailer are biased.

The rest of this paper is organized as follows. First, in Section 2, we review relevant literature on closed-loop supply chains and bounded rationality and highlight our contribution. Next, in Section 3, we set up our models and derive the equilibrium under different settings. Subsequently, in Section 4, we compare our results in different scenarios and demonstrate some interesting results. In Section 5, we summarize our results and propose directions for future research.

2. Literature Review

Our research intersects with two broad streams of literature: closed-loop supply chain management and bounded rationality.

2.1. Closed-Loop Supply Chain Management

Research on closed-loop supply chain management has broadly focused on the following aspects: game structure and supply chain performance [8].

Most of the existing research results mainly focus on the closed-loop supply chain led by manufacturers. Along with the birth of new business models, new research results on closed-loop supply chains led by retailers have also started to emerge, such as Zhang et al. [9], Gao et al. [10], and Yao et al. [11]. However, the above research results have ignored the influence of government power structure on closed-loop supply chains. At present, the power structure of the supply chain is showing a trend of diversification. There are mainly three power structures which are dominated respectively by large manufacturers such as Apple and Lenovo, by retail stores such as Metro and Gome, and by both manufacturers and retail stores with equal power. Some studies pointed out that the power structure of enterprises will affect the decision-making process and performance level of the closed-loop supply chain. A closed-loop supply chain consisting of a single manufacturer, two major competing retailers, and a third-party processor is studied by Yi [12] in-depth under different subjective capabilities, and it is concluded that the retailer-dominated model prevails. Wang et al. [13] explored the pricing and synergy of a closed-loop supply chain consisting of a manufacturer and a retailer under three-channel power structures and examined the differentiated prices for newly produced and reprocessed goods. It was noted that differentiated pricing diminishes the impact of resource recovery power on positive suppliers, homogenizes reprocessed products with new product development in the distribution channel, and can better explain the impact of channel power on closed-loop supply chains. In the closed-loop supply chain of resource recovery in manufacturing firms, the negative impact of channel control composition on the decision-making process and the performance of the closed-loop supply chain is mainly studied in depth by Li et al. [14]. Gong [15] explored the optimal combination of the closed-loop supply chain-dominant model and recycling method and found that a combination of producer-dominant and retailer recycling methods works best.

The performance of closed-loop supply chains is always the priority concern in the literature. In 2007, Telegraphi [16] considered the difference in the reusability and lifecycle of product parts due to the different consumption levels of the parts and showed that balancing the production cost, recycling rate, lifecycle, and durability of parts could lead to cost savings. Later, Roland et al. [17] found that stable demand can facilitate the development of reverse capacity in the supply chain process, i.e., reverse capacity in a closed-loop supply chain can replace previous large-scale capacity investments, lowering the threshold for supply chain operations and improving supply chain performance. Zhu Chen et al. [18] analyzed the profitability and operational efficiency of manufacturers and sellers under different conditions, using production equipment, production staff, and other constraints as variables that can make manufacturers’ capacity levels vary. The performance of closed-loop supply chains can also be affected by differences in corporate strategies, as confirmed by Gao Wenjun et al. [19]. Considering the characteristics of circular economies and closed-loop supply chains, E. Manavalan and K. Javakrishna [20] formulated the conceptual framework model from five important perspectives of supply chain management, namely, Business, Technology, Sustainable Development, Collaboration, and Management Strategy to measure the performance of the supply chain. The research of Kechagias et al. took a maritime company as a case to analyze a set of audit methods for the company’s cyber risk and performance [21]. In order to simplify the analysis, this paper takes the profits of both sides of the closed-loop supply chain and the recycling quantity of worn-out products in the supply chain as the criteria for evaluating performance.

2.2. Bounded Rationality

The topic of this paper has also seen much interest in the operation and management (OM) literature as it sits at the intersection of operations and psychology. Different from the bounded rationality issue arising from the consumer side, we consider two pivotal cognitive issues from the supply chain: overconfidence and competitive preference.

Overconfidence is a common cognitive bias in which decision-makers often overestimate their own judgment. This preference is widespread in behavioral operations management. Ren et al. [22] introduced overconfidence into the supply chain to study overconfident decision news suppliers and then demonstrated that overconfidence was significantly associated with order bias in an experimental study by introducing a debiasing technique. Kirshner et al. [23] concluded that overconfidence usually leads to lower profits, increased inventory, and higher prices. Doyle et al. [24] evaluated how overconfidence affects the decision-making of grassroots employees in a complex supply chain system. Liu et al. [25] investigated the dual factors that influence the preference for overconfidence and the changing demand for decision-making and utility. They further developed a two-stage service sourcing model in a logistics service supply chain and illustrated that dynamic pricing mechanisms eliminate the negative effects of overconfidence. Li [26] clearly illustrated that overconfidence bias can reduce the impact of double marginalization. In addition, Xu et al. [27] analyzed the effect of retailer overconfidence on optimal pricing by ordering volume reduction for each sector in a double oligopoly supply chain. However, most existing papers focused only on the impact of overconfidence as a single behavioral preference on decision-making and revenue, while this paper extends the single behavioral preference to dual behavioral preferences in a supply chain system.

Human societies are not completely rational in the distribution of benefits, but there are situations of social preferences such as equality, competition, and mutual benefit. Additionally, such social preferences also have far-reaching effects on the decisions of interested parties. Among them, competitive preference is an important social preference, which means that decision-makers not only focus on an individual’s maximum income but also compare their own gains with those of other decision-makers.

Indeed, the current research focus in this area is on equity concerns. The concern for equity is an important social preference, which means that decision-makers should pay attention not only to the maximum income of individuals but also to whether the distribution of channel income or prices is fair. Cui et al. [28] introduced the equity concern principle into a traditional binary supply chain consisting of a producer and a retailer and examine how it affects channel coordination in that supply chain. Caliskan et al. [29] further extended Cui’s model to a nonlinear demand environment. Nie et al. [30] explored the question of whether different contracts can coordinate supply chain performance when retailing exhibits dual equity. Wang et al. [31] introduced the issue of manufacturer fairness in an e-commerce supply chain model. Pan et al. [32] explored the impact of equity concerns on the decision-making of a supply chain consisting of a dominant retailer and two manufacturers.

In reality, stakeholders in the supply chain often have not only a behavioral preference for fairness but also often exhibit a behavioral preference for competition, which is simple and consistent with rational human psychology. Considering this phenomenon, two cognitive biases, overconfidence and competitive preferences, are incorporated into the analysis of closed-loop supply chains to find their interactive impacts on supply chain performance.

2.3. Contributions

The aforementioned articles have contributed to the study of closed-loop supply chains, but most of them have not considered that firms could exhibit limited rationality in their decision-making, such as overconfidence or competitive preferences. These behavioral preferences usually change their pricing decisions and inevitably impact their performance in the supply chain. To the best of our knowledge, we are the first ones to consider the joint effect of two behavior biases in the closed-loop supply chain. Our results provide many plausible explanations for the reality.

3. Model Setup

This paper investigates a closed-loop supply chain with an upstream manufacturer and a downstream retailer selling products to end-consumers. In this case, the retailer acts as the starting point for recycling by collecting used products from consumers; the manufacturer buys used products from the retailer as raw materials for reproduction. In this process, the manufacturer needs to make decisions about its wholesale price and recycling price (from the retailer), while the retailer needs to make decisions about its retailing price, recycling price, and effort to sell. In this paper, we hypothesize that manufacturers in closed-loop supply chains exhibit competitive preferences and retailers exhibit overconfidence. Following [33], we incorporate the linear demand function where the demand is sensitive to both price and sales efforts. Namely, the market demand in the supply chain $D_0$ is defined by

$$D_0=A-\beta p+k_{0}e$$

(1)

where A is the potential market size, $\beta$ is the coefficient of price elasticity, $k_0$ is the output coefficient of the retailer’s sales effort, and e is the retailer effort level. In order to investigate the impact of retailers’ overconfident behavior, we assume that $e>0$. In general, we assume that the transaction between the manufacturer and the retailer is symmetric, i.e., the manufacturer’s productivity is able to meet the retailer’s ordering demand and allows the retailer to increase its sales through higher sales efforts (e.g., advertising, gift giving, etc.). According to Karray [34], we assume a quadric cost function of the retailer’s sales effort, i.e., $c\left(e\right)=\frac{1}{2}\gamma e^2$, where $\gamma \in \left(0,1\right]$ is the coefficient of sales effort cost.

In a typical closed-loop supply chain, the recycling volume in the market is usually defined by [35]

$$G=l+h{b}_r$$

(2)

where l is the basic recycling volume determined by the level of environmental awareness of consumers, $h$ is the coefficient of price elasticity of recycling, and $b_r$ is the retailer’s price for recycling one unit of waste product. To simplify the problem, it is assumed throughout this paper that all recycled waste products are remanufactured and the recycling rate is 1. Therefore, the profits of the manufacturer, the retailer, and the supply chain as a whole system are defined as

$${\pi }_m=(w-c_m)D_0+(\delta -b_m)G$$

(3)

$${\pi }_r=(p-w-c_r)D_0+(b_m-b_r)G-\frac{1}{2}\gamma e^2$$

(4)

$${\pi }_s={\pi }_m+{\pi }_r=(p-c_m-c_r)D_0+(\delta -b_r)G-\frac{1}{2}\gamma e^2$$

(5)

where w is the wholesaling price, $c_m/c_r$ is the marginal cost of the manufacturer/retailer, $\delta$ is the production cost saving from recycling, and ${\pi }_m$/${\pi }_r$/${\pi }_s$ is the profit of the manufacture/retailer/whole system.

The retailer’s overconfidence preference is defined by Chen et al. [36] as an overestimation of sales effort and market demand. Thus, a retailer’s perceived market demand when overconfidence is incorporated is as follows

$$D=A-\beta p+(k_0+\alpha )e=A-\beta p+ke$$

(6)

In the above equation, let $k=k_0+\alpha$. This demand function form provides an accurate measurement of the effect of overconfidence on the quantity demanded. Clearly, the overconfidence parameter α is positively correlated with the quantity demanded.

The competitive preference behavior of manufacturers is considered, and the competitive preference utility function is introduced in Gary et al. [7], where

$$U_B({\pi }_A,{\pi }_B)=\{\begin{array}{l}{\pi }_B+\rho ({\pi }_A-{\pi }_B),{\pi }_B\ge {\pi }_A\\ {\pi }_B+\sigma ({\pi }_A-{\pi }_B),{\pi }_B\le {\pi }_A\end{array}$$

(7)

With different parameter combinations of $\rho$ and $\sigma$, Equation (7) can be employed to represent different social allocation preferences. We concentrate on the case $\sigma \le \rho \le 0$, where it represents the competitive preference behavior. Decision-makers with competitive preference behavior compare gains and always want more gains than the other party, and their utility increases with the rise of gains above the other party.

In particular, when $\sigma =\rho$ is set, the decision-makers with competitive preferences are equally sensitive to being behind and ahead of each other in terms of returns. At this point, Equation (6) should be simplified to

$$U_B({\pi }_A,{\pi }_B)={\pi }_B-\mu ({\pi }_A-{\pi }_B)$$

(8)

where the parameter $\mu \ge 0$ describes the degree of a manufacturer’s competitive preference. Specifically for the problem studied in this paper, the utility function of a manufacturer with competitive preference behavior can be obtained as

$$U_m({\pi }_r,{\pi }_m)={\pi }_m-\mu ({\pi }_r-{\pi }_m)$$

(9)

All parameters used in this paper are summarized in

Table 1. Notation List.

Notation	Definition
A$\ge 0$	Potential demand size in the market
$\beta \ge 1$	Price elasticity coefficient
p	Retailing price
w	Wholesaling price
e	Retailers’ sales effort level
$k_0\ge 1$	Output coefficient of the retailer’s sales effort
c(e)	Cost of sales effort for retailers
$\gamma \in \left(0,1\right]$	Cost of sales effort factor
$c_i,i\in \left\{m,r\right\}$	The manufacturer’s/retailer’s marginal cost
$c_m^{\prime }$	The marginal production cost of the manufacturer
$\alpha \in \left(0,1\right]$	Retailer’s overconfidence parameter
$D_0$	Demand in the absence of overconfidence
D	Demand in the presence of overconfidence
l	Basic recycling volume in the market
h	Price elasticity of recycling of waste and scrap products
$b_i,i\in \left\{m,,r\right\}$	The manufacturer’s/retailer’s recycling price
G	Total number of waste products recycled in the market
$\delta$	Production cost saving from recycling
$\mu \ge 0$	Manufacturer’s competitive preference coefficient
${\pi }_i,i\in \left\{m,r,s\right\}$	Indicates profit of manufacture/retailer/system
$U_m$	Indicates utility of manufacturer

.

4. Analysis

In this section, we consider three typical dominant models: the centralized decision-making model (C) and two decentralized decision-making models, i.e., the non-leader model ($\overline{N}$) and the manufacturer-led model ($\overline{M}$).

4.1. Centralized Decision-Making Model (C)

In order to better analyze the decision-making and performance under the decentralized decision-making model, the model under the centralized decision-making model with the objective of maximizing system profit is first developed. In this case, both the manufacturer and the retailer exhibit infinite rationality, i.e., no behavioral preferences, and jointly decide the retail price of the product, the recycling price of the used product, and the degree of the sales effort. The game structure of the C-game is shown in Figure 1.

The optimization of the C-game is constructed as follows

$$\underset{p,b_r,e}{max}{\pi }_s^C=(p-c_m-c_r)D_0+(\delta -b_r)G-\frac{1}{2}\gamma e^2$$

(10)

Solving the optimization problem, we show the equilibrium of the C-game in Proposition 1. All proofs are delegated to the Appendix A.

Proposition 1. 

In the C-game, the centralized decision-maker should charge

$$\{\begin{array}{l}{p}^{C^{*}}=\frac{A\gamma +(\beta \gamma -k_0{}^2)(c_r+c_m)}{2\beta \gamma -k_0{}^2}\\ e^{C^{*}}=\frac{A{k}_0-\beta (c_r+c_m)k_0}{2\beta \gamma -k_0{}^2}\\ b_r{}^{C^{*}}=\frac{\delta h-l}{2h}\end{array}$$

(11)

generating the integrated profit as

$${\pi }_S^{C^{*}}=\frac{\gamma {[A-\beta (c_r+c_m)k_0]}^2}{2\beta \gamma -k_0{}^2}+\frac{{(\delta h+l)}^2}{4h}$$

(12)

4.2. Non-Leader Model ($\overline{N}$)

In the non-leader model, neither the manufacturer nor the retailer can dominate the market. In this model, the manufacturer and the retailer move simultaneously, and the manufacturer tends to maximize its utility while the retailer tends to maximize its profit. Specifically, the manufacturer decides its wholesale price $w$ and the recovery transfers price $b_m$. Meanwhile, the retailer decides the selling price $p$, recycling price $b_r$, and the level of sales effort $e$. The game structure of $\overline{N}$-game is shown in Figure 2. All proofs are delegated to the Appendix A.

The equilibrium is derived through backward induction and is shown in Proposition 2. It is worth noticing that in Equation (13), for simplicity, we denote $F_1=(3+4\mu ){\beta }^2{\gamma }^2+(1+\mu )\beta \gamma k_{0}k-2(1+\mu )\beta \gamma k^2$ and $F_2=A[(1+2\mu )\beta \gamma -(1+\mu )\alpha k]+(1+\mu )(2\beta \gamma -k^2)\beta \gamma c_m+c_r[(1+\mu )\alpha \beta \gamma k-(1+2\mu ){\beta }^2{\gamma }^2]$.

Proposition 2. 

In the $\overline{N}$-game, the manufacturer charges

$$\{\begin{array}{l}{w}^{{\overline{N}}^{*}}=\frac{F_2}{F_1}\\ b_m{}^{{\overline{N}}^{*}}=\frac{2(1+\mu )h\delta -(1+2\mu )l}{(3+4\mu )h}\end{array}$$

(13)

the retailer charges

$$\{\begin{array}{l}{p}^{{\overline{N}}^{*}}=\frac{A{F}_1\gamma +(\beta \gamma -k^2)(c_r{F}_1+F_2)}{(2\beta \gamma -k^2)F_1}\\ e^{{\overline{N}}^{*}}=\frac{k[A{F}_1-\beta (c_r{F}_1+F_2)]}{(2\beta \gamma -k^2)F_1}\\ b_r{}^{{\overline{N}}^{*}}=\frac{(1+\mu )h\delta -(2+3\mu )l}{(3+4\mu )h}\end{array}$$

(14)

resulting in the profits and utility of stakeholders as

$${\pi }_r{}^{{\overline{N}}^{*}}=\frac{\gamma {[A{F}_1-\beta (c_r{F}_1+F_2)]}^2}{2(2\beta \gamma -k^2)F_1{}^2}+\frac{{(1+\mu )}^2{(\delta h+l)}^2}{{(3+4\mu )}^{2}h}$$

(15)

$${\pi }_m{}^{{\overline{N}}^{*}}=\frac{(\beta \gamma -\alpha k)(F_2-c_m{F}_1)[A{F}_1-\beta (c_r{F}_1+F_2)]}{(2\beta \gamma -k^2)F_1{}^2}+\frac{(1+\mu )(1+2\mu ){(\delta h+l)}^2}{{(3+4\mu )}^{2}h}$$

(16)

$$\begin{array}{c}{U}_m{}^{{\overline{N}}^{*}}=\frac{2(1+\mu )(\beta \gamma -\alpha k)(F_2-c_m{F}_1)+\gamma [A{F}_1-\beta (c_r{F}_1+F_2)]}{(2\beta \gamma -k^2)F_1{}^2}\\ [A{F}_1-\beta (c_r{F}_1+F_2)]+\frac{{(1+\mu )}^3{(\delta h+l)}^2}{{(3+4\mu )}^{2}h}\end{array}$$

(17)

$$\begin{array}{c}{\pi }_S{}^{{\overline{N}}^{*}}=\frac{2(\beta \gamma -\alpha k)(F_2-c_m{F}_1)+\gamma [A{F}_1-\beta (c_r{F}_1+F_2)]}{2(2\beta \gamma -k^2)F_1{}^2}\\ [A{F}_1-\beta (c_r{F}_1+F_2)]+\frac{(1+\mu )(2+3\mu ){(\delta h+l)}^2}{{(3+4\mu )}^{2}h}\end{array}$$

(18)

Before proceeding, we show the impacts of cognitive bias on the equilibrium solution in Corollary 1.

Corollary 1. 

In the non-leader ($\overline{N}$) model, we have

A.

The optimal wholesale price of the manufacturer increases in the competitive preference if, and only if, the retailer’s overconfidence level is of a high or low level, i.e.,

$$\frac{\partial w^{{\overline{N}}^{*}}}{\partial \mu }=\{\begin{array}{cc}>0& \alpha \in \left(0,{\alpha }_L\right)\\ >0& \alpha \in \left({\alpha }_H,1\right]\end{array}$$

B.

The optimal selling price of the retailer increases in the competitive preference if, and only if, the retailer’s overconfidence level is of a high or low level and decreases otherwise, i.e.,

$$\frac{\partial p^{{\overline{N}}^{*}}}{\partial \mu }=\{\begin{array}{cc}>0& \alpha \in \left(0,{\alpha }_M\right){{\displaystyle \cup }}^{}\left({\alpha }_H,1\right]\\ <0& \alpha \in \left(\sqrt{\beta \gamma }-k_0,{\alpha }_L\right]\end{array}$$

C.

The optimal sales effort of the retailer increases in the competitive preference with a high retailer’s overconfidence level and decreases otherwise, i.e.,

$$\frac{\partial e^{{\overline{N}}^{*}}}{\partial \mu }=\{\begin{array}{cc}<0& \alpha \in \left(0,{\alpha }_L\right)\\ >0& \alpha \in \left({\alpha }_H,1\right]\end{array}$$

where ${\alpha }_L=min\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{2\beta \gamma }-k_0\right),{\alpha }_H=max\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{2\beta \gamma }-k_0\right),$ $and{\alpha }_M=min\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{\beta \gamma }-k_0\right)$.

All proofs are delegated to the Appendix B. The reason behind Corollary 1(A) is that, when the manufacturer’s competitive preferences increase, it tends to extract more profit from the downward retailer, and it is willing to raise wholesale price, while the overconfidence of the retailer makes it overestimate the market demand and willing to accept higher wholesale prices from the manufacturer. The interactive impacts of these two cognitive biases makes it possible to raise the wholesale prices to increase the utility of the manufacturer itself.

The reason behind Corollary 1(B) is that when $\alpha \in \left(0,{\alpha }_M\right)$, the manufacturer will raise the wholesale price; meanwhile, the retailer will not put too much effort into the sale because of its low level of overconfidence. As a result, the retailer could raise the retailing price to achieve a higher profit; when $\alpha \in \left(\sqrt{\beta \gamma }-k_0,{\alpha }_L\right]$, the retailer has paid a considerable cost of sales effort and has not yet predicted the market demand beyond a certain point, so the retail price will be reduced in order to obtain more profit; when $\alpha \in \left({\alpha }_H,1\right]$, the retailer is overly optimistic about the market demand and will therefore increase retail prices in line with higher wholesale prices in order to make higher profits.

The reason behind Corollary 1(C) is that, when $\alpha \in \left(0,{\alpha }_L\right)$, the retailer tends to believe that even increased sales efforts will not lead to a considerable rise in demand. At this point, as the manufacturer’s competitive preference rises, the retailer chooses to reduce the cost of the sales effort in order to achieve higher expected profits; when $\alpha \in \left({\alpha }_H,1\right]$, the retailer is overly optimistic about the rise in the market demand due to their sales effort. At this point, as the manufacturer’s competitive preference rises, the retailer chooses to increase its sales effort in order to achieve higher expected profits.

To demonstrate the results vividly, we conduct numerical studies to show how prices, profits, and utility change with two behavioral preferences. The relevant parameters are assigned as $A=100$, $\gamma =1$, $c_m=6$, $c_r=8$, $\beta =5$, $k_0=2$, $l=10$, $h=20$, and $\delta =3$.

First, we observe how the decisions of both sides in the closed-loop supply chain change with the behavioral preferences of both parties under the two market models. According to the study of Pan et al. [31], we set $\alpha \in \left[0,1\right]$ and $\mu =\left\{0,1,2\right\}$ to describe the competitive preference of the manufacturer and the overconfidence of the retailer.

The curve of the equilibrium solution of the wholesale price in the non-leader model with $\alpha \in \left[0,1\right]$ under three values of $\mu$ are shown in Figure 3. Observing Figure 3, we find that the wholesale price equilibrium solution increases with the increase in the competitive preference coefficient. Since at this point, $min\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{2\beta \gamma }-k_0\right)=\sqrt{10}-2>1$, it follows from the conclusion of Corollary 1(A) above that in this case, the wholesale price $w^{{\overline{N}}^{*}}$ is an increasing function of the competitive preference coefficient $\mu$ when $\alpha \in \left[0,1\right]$. Corollary 1(A) is corroborated by the findings shown in Figure 3. In short, the interactive impact of the two cognitive biases is detrimental to the wholesale price.

The curve of the equilibrium solution of the retail price in the non-leader model with $\alpha \in \left[0,1\right]$ under three values of $\mu$ are shown in Figure 4. Observing Figure 4, we find that at this point, the equilibrium solution of the retail price is first positively proportional to the competitive preference coefficient $\mu$ and then inversely proportional to $\mu$. According to Corollary 1(B), it is known that when $\alpha \in \left(0,{\alpha }_L\right)$, the retail price $p^{{\overline{N}}^{*}}$ is an increasing function of the competitive preference coefficient $\mu$. Substituting the values of each parameter, it can be obtained that when $\alpha \in \left[0,\sqrt{5}-2\right]$, $p^{{\overline{N}}^{*}}$ increases as $\mu$ increases; when $\alpha \in \left(\sqrt{5}-2,1\right)$, $p^{{\overline{N}}^{*}}$ decreases with the increase in $\mu$. Corollary 1(B) is corroborated by the findings shown in Figure 4. This interesting finding is not quite the same as previous supply chain decision-making under single cognitive bias [23]. That is, when a retailer’s overconfidence is within a particular range, the overconfidence it holds would weaken the detrimental effect of the manufacturer’s competitive preferences on retail prices.

The curve of the equilibrium solution of the sales effort level in the non-leader model with $\alpha \in \left[0,1\right]$ under three values of $\mu$ is shown in Figure 5. Observation of Figure 5 reveals that at this point, the equilibrium solution for sales effort decreases as the competitive preference coefficient $\mu$ increases since at this point, ${\alpha }_L=min\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{2\beta \gamma }-k_0\right)=\sqrt{10}-2>1$. It follows from the conclusion of Corollary 1(C) above that in this case, the retailer’s sales effort $e^{{\overline{N}}^{*}}$ is a decreasing function of the competitive preference coefficient $\mu$ when $\alpha \in \left[0,1\right]$. The conclusion of Corollary 1(C) is corroborated in Figure 5. This means that, at this point, the interactive impact of the two cognitive biases makes the retailer choose to reduce its sales efforts. The reason is, when $\alpha \in \left(0,{\alpha }_L\right)$, the retailer tends to believe that even increased sales efforts will not lead to a considerable rise in demand. At this point, as the manufacturer’s competitive preference rises, the retailer chooses to reduce the cost of the sales effort in order to achieve higher expected profits.

4.3. Manufacturer-Led Model ($\overline{M}$)

The manufacturer-led model refers to the case where the manufacturer with competitive preferences dominates the market. In this case, the manufacturer first maximizes its utility and decides its wholesale price $w$ and recycling transfer price $b_m$. The retailer then maximizes its profit based on the manufacturer’s decision and decides its selling price $p$ and recycling price $b_r$ and sales effort $e$. The retailer then maximizes its profit based on the manufacturer’s decision and decides its selling price, recycling price, and sales effort. The game structure of $\overline{M}$-game is shown in Figure 6. All proofs are delegated to the Appendix A.

Following the same paradigm, the equilibrium results of $\overline{M}$-game are shown in Proposition 3. Note that we further denote let $F_3=2{\beta }^2\gamma -2\alpha \beta k-2\mu \alpha \beta k+3\mu {\beta }^2\gamma$, and $F_4=[A-\beta (c_r-c_m)](\beta \gamma -\alpha k-\mu \alpha k)$$+\mu \beta \gamma [2A-\beta (2c_r-c_m)]$.

Proposition 3. 

In the $\overline{M}$-game, the manufacturer charges

$$\{\begin{array}{l}{w}^{{\overline{M}}^{*}}=\frac{F_4}{F_3}\\ b_m{}^{{\overline{M}}^{*}}=\frac{(1+\mu )h\delta -(1+2\mu )l}{(2+3\mu )h}\end{array}$$

(19)

the retailer charges

$$\{\begin{array}{l}{p}^{{\overline{M}}^{*}}=\frac{A{F}_3\gamma +(\beta \gamma -k^2)(c_r{F}_3+F_4)}{(2\beta \gamma -k^2)F_3}\\ e^{{\overline{M}}^{*}}=\frac{k[A{F}_3-\beta (c_r{F}_3+F_4)]}{(2\beta \gamma -k^2)F_3}\\ b_r{}^{{\overline{M}}^{*}}=\frac{(1+\mu )h\delta -(3+5\mu )l}{2(2+3\mu )h}\end{array}$$

(20)

The profits and utility of stakeholders can be given

$${\pi }_r{}^{{\overline{M}}^{*}}=\frac{\gamma {[A{F}_3-\beta (c_r{F}_3+F_4)]}^2}{2(2\beta \gamma -k^2)F_3{}^2}+\frac{{(1+\mu )}^2{(\delta h+l)}^2}{4{(2+3\mu )}^{2}h}$$

(21)

$${\pi }_m{}^{{\overline{M}}^{*}}=\frac{(\beta \gamma -\alpha k)(F_4-c_m{F}_3)[A{F}_3-\beta (c_r{F}_3+F_4)]}{(2\beta \gamma -k^2)F_3{}^2}+\frac{(1+\mu )(1+2\mu ){(\delta h+l)}^2}{2{(2+3\mu )}^{2}h}$$

(22)

$$\begin{array}{c}{U}_m{}^{{\overline{M}}^{*}}=\frac{2(1+\mu )(\beta \gamma -\alpha k)(F_4-c_m{F}_3)-\mu \gamma [A{F}_3-\beta (c_r{F}_3+F_4)]}{2(2\beta \gamma -k^2)F_3{}^2}\\ [A{F}_3-\beta (c_r{F}_3+F_4)]+\frac{{(1+\mu )}^2{(\delta h+l)}^2}{4(2+3\mu )h}\end{array}$$

(23)

$$\begin{array}{c}{\pi }_S{}^{{\overline{M}}^{*}}=\frac{2(\beta \gamma -\alpha k)(F_4-c_m{F}_3)+\gamma [A{F}_3-\beta (c_r{F}_3+F_4)]}{2(2\beta \gamma -k^2)F_3{}^2}\\ [A{F}_3-\beta (c_r{F}_3+F_4)]+\frac{(1+\mu )(3+5\mu ){(\delta h+l)}^2}{4{(2+3\mu )}^{2}h}\end{array}$$

(24)

Before proceeding, we show the impacts of cognitive bias on the equilibrium solution in Corollary 2.

Corollary 2. 

In the manufacturer-led ($\overline{M}$) model, we have

A.

The optimal wholesale price of the manufacturer increases in the competitive preference if, and only if, the retailer’s overconfidence level is of a high or low level, i.e.,

$$\frac{\partial w^{{\overline{M}}^{*}}}{\partial \mu }=\{\begin{array}{cc}>0& \alpha \in \left(0,{\alpha }_L\right)\\ >0& \alpha \in \left({\alpha }_H,1\right]\end{array}$$

B.

The optimal selling price of the retailer increases in the competitive preference if, and only if, the retailer’s overconfidence level is of a high or low level and decreases otherwise, i.e.,

$$\frac{\partial p^{{\overline{M}}^{*}}}{\partial \mu }=\{\begin{array}{cc}>0& \alpha \in \left(0,{\alpha }_M\right){{\displaystyle \cup }}^{}\left({\alpha }_H,1\right]\\ <0& \alpha \in \left(\sqrt{\beta \gamma }-k_0,{\alpha }_L\right]\end{array}$$

C.

The optimal sales effort of the retailer increases in the competitive preference with a high retailer overconfidence level and decreases otherwise, i.e.,

$$\frac{\partial e^{{\overline{M}}^{*}}}{\partial \mu }=\{\begin{array}{cc}<0& \alpha \in \left(0,{\alpha }_L\right)\\ >0& \alpha \in \left({\alpha }_H,1\right]\end{array}$$

where ${\alpha }_L=min\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{2\beta \gamma }-k_0\right),{\alpha }_H=max\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{2\beta \gamma }-k_0\right),$ $and{\alpha }_M=min\left(\frac{\sqrt{k_0{}^2+4\beta \gamma }-k_0}{2},\sqrt{\beta \gamma }-k_0\right)$.

All proofs are delegated to the Appendix B. The reason behind Corollary 2(A) is that, when the manufacturer’s competitive preferences increase, they tend to extract more profit from retailers and are willing to raise the wholesale price, while the overconfidence of the retailer makes them overestimate the market demand, and they are willing to accept higher wholesale prices from the manufacturer. The interactive impacts of these two cognitive biases make it possible to raise wholesale prices to increase the utility of the manufacturer itself.

The reason behind Corollary 2(B) is that, when $\alpha \in \left(0,{\alpha }_M\right)$, the manufacturer will raise the wholesale price. Meanwhile, the retailer will not put too much effort into sales because of its low level of overconfidence, so it has the scope to raise retail prices to achieve higher profits; when $\alpha \in \left(\sqrt{\beta \gamma }-k_0,{\alpha }_L\right]$, the retailer has paid a considerable cost of sales effort and has not yet predicted the market demand beyond a certain point, so the retail price will be reduced in order to obtain more profit; when $\alpha \in \left({\alpha }_H,1\right]$, the retailer is overly optimistic about market demand and will therefore increase retail prices in line with higher wholesale prices in order to make higher profits.

The reason behind Corollary 2(C) is that, when $\alpha \in \left(0,{\alpha }_L\right)$, the retailer tends to believe that even increased sales efforts will not lead to a considerable rise in demand. At this point, as the manufacturer’s competitive preference rises, the retailer chooses to reduce the cost of the sales effort in order to achieve higher expected profits; when $\alpha \in \left({\alpha }_H,1\right]$, the retailer is overly optimistic about the rise in the market demand due to their sales effort. At this point, as the manufacturer’s competitive preference rises, the retailer chooses to increase its sales effort in order to achieve higher expected profits.

Similarly, we obtain images of each decision as a function of both sides in the manufacturer-led model ($\overline{M}$).

Observing Figure 7, Figure 8 and Figure 9, it is found that Corollary 2 is corroborated by the findings shown in Figure 7, Figure 8 and Figure 9. The discussion of decision-making in the manufacturer-led model with Figure 7, Figure 8 and Figure 9 is similar to that in the non-leader model above with Figure 3, Figure 4 and Figure 5 and is therefore not repeated here.

4.4. The Comparison between $\overline{N}$-Game and $\overline{M}$-Game

The profit comparison between the two types of games is summarized in Corollary…

Corollary 3. 

When the manufacturer has competitive preference behavior and the retailer is overconfident,

A.

For the retailer, the profits under the non-leader ($\overline{N}$) model ${\pi }_r^{{\overline{N}}^{*}}$are larger than the profits under the manufacturer-led ($\overline{M}$) model ${\pi }_r^{{\overline{M}}^{*}}$.

B.

For manufacturers, the profits under the manufacturer-led ($\overline{M}$) model ${\pi }_m^{{\overline{M}}^{*}}$is larger than the profits under the non-leader ($\overline{N}$) model ${\pi }_m^{{\overline{N}}^{*}}$.

C.

The amount of waste products recycled under the manufacturer-led ($\overline{M}$) model $G^{{\overline{M}}^{*}}$is smaller than that under the non-leader ($\overline{N}$) model $G^{{\overline{N}}^{*}}$, and further smaller than that in the centralized decision model $G^{C^{*}}$.

D.

The amount of used product recycled in the non-leader ($\overline{N}$) model $G^{{\overline{N}}^{*}}$and the amount of used product recycled in the manufacturer-led ($\overline{M}$) model $G^{{\overline{M}}^{*}}$are both inversely proportional to the competitive preference coefficient $\mu$.

All proofs are delegated to the Appendix B. The reason behind Corollary 3(A) and (B) is that, when a manufacturer with a competitive preference dominates the supply chain, it tends to use its channel power to extract more profit from the retailer. At this point, the retailer’s profit will decrease, and the manufacturer’s profit will increase.

Next, we compare the profits of the manufacturer and the retailer in the two decentralized decision-making models. At this point, assume that $\alpha =1$, $\mu \in \left[0,5\right]$.

Figure 10 and Figure 11 visualize the difference between the retailer’s and manufacturer’s profits under the two dominant modes. Looking at the function images, it is found that at this point, the retailer’s profit under the non-leader model is greater than the profit under the manufacturer-led model, while the manufacturer’s profit under the non-leader model is less than the profit under the manufacturer-led model. The conclusion of Corollary 3(A) and Corollary 3(B) is corroborated by the findings shown in Figure 10 and Figure 11. Additionally, the conclusion is intuitive since, when a manufacturer with a competitive preference dominates the supply chain, it tends to use its channel power to extract more profit from the retailer.

Figure 12 shows an image of the market’s recycling volume $G$ as a function of the coefficient of competitive preference $\mu$ for the two decentralized decision-making models. It is easy to find that the amount of used product recycled in the non-leader model is always higher than that in the manufacturer-led model, which confirms the conclusion of Corollary 3(C). It can also be found that the amounts of used products recycled $G$ under both decentralized decision-making models is a decreasing function of the competitive preference coefficient $\mu$, which corroborates the conclusion of Corollary 3(D), indicating that the stronger the manufacturer’s competitive preference is, the more unfavorable the product recycling is. The reason is, as a manufacturer’s channel power and competitive preference increase, it will have greater willingness and ability to seize the profits of the retailer, which will lead to a lower marginal return for the retailer for recycling, thereby reducing the amount of recycling.

5. Conclusions

This paper incorporates two behavioral preferences, overconfidence and competitive preference, into the study of closed-loop supply chains. A series of Stackelberg models with multiple dominant models is proposed. The proposed models explore how the behavioral preferences chain jointly affects the decisions of both sides, such as pricing, profits, utility, and social benefits, under different dominant modes. Numerical examples are provided to illustrate the proposed models.

Firstly, in terms of profit generation. We find that regardless of which decentralized decision-making model it takes, manufacturers with competitive preferences will capture the profits of retailers due to their behavioral preferences. Moreover, in a manufacturer-led model, the profits of all sides in the closed-loop supply chain, including the manufacturer itself, sometimes diminish as the manufacturer’s competitive preference behavior becomes more intense. This conclusion may seem unconventional and different from existing research [32], but there are two reasons that can be suggested. One, in a closed-loop supply chain, the manufacturer’s profits are more closely linked to those of the retailer than in a traditional supply chain because of the reverse process it contains, and at this point, the manufacturer may be willing to reduce some of its own profits in order to increase the difference between its profits and those of the retailer; two, when the retailer’s confidence in the demand for the product is within a certain range, the retailer will choose to reduce its sales effort to minimize its own costs when the manufacturer seizes its profits, thereby reducing the manufacturer’s profits.

Secondly, in terms of pricing. We find that wholesale price always increases as manufacturers’ competitive preferences increase, but that retail price sometimes decreases as competitive preferences increase. We consider that the reason behind this is that the retailer’s overconfidence can influence its judgment of market demand, so that in some cases when the manufacturer raises wholesale prices due to its competitive preference, the retailer will reduce its retail prices based on its own judgment of demand in order to maximize expected profits.

Thirdly, in terms of recycling quantity, we find that the decentralized decision-making mode is detrimental to recycling when comparing it to the centralized decision-making mode, where the manufacturer-led model has the least recycling quantity. Moreover, the recycling quantity under the non-leader ($\overline{N}$) model $G^{{\overline{N}}^{*}}$ and the recycling quantity under the manufacturer-led ($\overline{M}$) model $G^{{\overline{M}}^{*}}$ are both inversely proportional to the competitive preference coefficient $\mu$. It results in a conclusion that the pursuit of high profits by monopolistic manufacturers is not conducive to recycling quantity in the secondary supply chain with recycling.

One limitation of this paper is that market demand is certain. As we know, changes in market environments and customer preferences may cause a variety of changes in market demand. Thus, we will build relevant models to study the effect of uncertainty and fuzziness based on different behavioral preferences, such as the uncertain demand function.