# Decision and Coordination of Cross-Border E-Commerce Supply Chain: Based on Four Modes of Cooperation

Authors: Wei Yan; Huijun Zhou; Hui Li
Journal: Scientific Programming
 (2021)

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## Abstract

Due to the explosive growth trend of cross-border e-commerce, a series of problems such as high transportation costs and insufficient publicity are to be solved urgently by researching on supply chain from both decision-making and coordination perspectives. Under the four-incomplete cooperative Stackelberg decision-making modes of cross-border e-commerce supply chain members, the transportation cost of overseas suppliers and the promotion strategy of domestic retailers determine the profit of the supply chain together and further influence the choice of the optimal decision-making plan. Furthermore, the Shapley value method and full cooperative income incremental sharing mechanism are used to redistribute the profits under different cooperation modes, and it is expected to provide scientific decision-making reference for domestic cross-border e-commerce enterprises to rationally choose cooperative relationships.


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## Body

## 1. Introduction

With the increasing popularity of Internet technology and the improvement in payment system and the influence of new coronavirus (COVID-19), more and more consumers are buying imported goods through cross-border e-commerce platforms. Therefore, the import cross-border e-commerce shows an explosive growth trend. According to the data released by China E-Commerce Research Center (100%) EC, the transaction volume of Chinaʼs import cross-border e-commerce market in 2019 is 2.47 trillion yuan, an increase of nearly 30% over 2018, and it is expected to reach 29.66 trillion yuan in 2020.The vigorous development of cross-border e-commerce has not only greatly enriched the product supply in the domestic market but also exposed a series of problems in the supply chain management of cross-border e-commerce in China [1]. On the one hand, the high transportation cost of cross-border e-commerce (accounting for about 20%∼30% of the total cost) not only increases the purchase cost of consumers but also reduces the profits of middlemen; on the other hand, due to the insufficient publicity of cross-border e-commerce, the single channel of commodity promotion, it is difficult for retailers to avoid the third-party e-commerce platform, which increases the intermediate links and weakens the profits of domestic cross-border e-commerce enterprises ability [2].Therefore, in order to solve the vicious competition cycle caused by the non-cooperative game between overseas e-commerce and domestic retailers, it is urgent to study the influence of changes in transportation costs and propaganda strategy on the pricing strategy and member profit distribution of cross-border e-commerce supply chain. In this paper, we focus on the following question: first, in the decentralized and centralized scenario, how do the members in the cross-border e-commerce supply chain make decisions; second, how do the influences of transport cost and advertising cost on the decisions; finally, which can coordination mechanism effectively balance the stakeholders to make the total performance maximization.From the existing literature, the research related to the above contents mainly focuses on the following two aspects:(1)
Influence of advertising strategy on supply chain decision-makingBased on the supply chain of manufacturers and retailers, study the problems of price promotion and advertising strategy of manufacturers [3]; considering the problem that advertising investment restricts market demand, discuss the optimal decision-making and coordination mechanism under the mode of concentration and dispersion of single- and double-channel supply chain [4]; by using the consumer demand function, explore the cooperative advertising and supply chain coordination of pricing [5]; from the perspective of the dynamic influence of advertising on market demand, discuss the issues of manufacturerʼs advertisement competition and manufacturer-retailer channel price competition [6]; on the basis of the influence of innovation and advertising on the demand of commodity market, probe into the optimal decision-making of supply chain members under cooperative and non-cooperative mechanisms [7].(2)
Influence of transport costs on supply chain decision-makingTo reduce transport costs and divide the cross-border e-commerce costs into management cost, logistics cost, and sale cost [8]; different supply chain logistics cost-sharing strategies are applied to explore the influence on supply chain profit through the study of the impact of tariffs, transport costs on global value chains, find that the rise of trade costs such as tariffs will increase the investment of enterprises and the purchase price of raw materials [9]; based on the game model of cross-border supply chain led by retailers, introduce the index of tariff and international transportation cost to analyze the influence of tariff change in commodity pricing and member profit of cross-border supply chain [10]; the optimized countermeasure is applied to how to use overseas warehouse to realize the timeliness of cross-border logistics in order to reduce transportation cost; consider that logistics cost has an important impact on cross-border e-commerce imports and then make a deep study on the cost optimization of cross-border e-commerce logistics [11, 12].(3)
Influence of coordination contract on supply chain decision-makingThrough the supply chain contract to coordinate the decision-making behavior among the members, the profit can be optimized. Under the uncertain environment, Peng et al. [13] proposed a unidirectional option contract and bidirectional option contract to coordinate supply chain members and analyze their different impacts on members. Xu et al. [14] introduced the revenue sharing and cost sharing into designing an improved contract to coordinate the participates effectively. Designed the decision model for the nongreen and green products pricing to ensure the supply chainʼs participants achieve Pareto improvement. Dai et al. [15] designed the delivery-time-dependent quantity flexibility contract and late-rebate contract to balance the stakeholders under the uncertain demand. Liu et al. [16] discussed whether an option contract coordinated the members effectively when express delivery was provided from retailer.Through the analysis of the above literature, it is found that the research methods of supply chain are rich and mature, which provide a specific reference for this paper from the technical point of view. However, most of the research results on supply chain publicity and transportation costs are concentrated in the traditional production enterprises. There are few studies on the influence of publicity strategy and transportation cost on cross-border e-commerce pricing strategy. There is little research on the influence of supplier retailer cooperation mode on supply chain pricing at home and abroad.Based on this, from the perspective of cross-border e-commerce supply chain pricing and publicity strategies under different cooperation modes, this paper discusses the coordination of cross-border e-commerce supply chain pricing strategy and member profit distribution, as well as how cross-border e-commerce enterprises cope with the impact of changes. In terms of transportation cost and publicity level, this paper makes optimization decisions for cross-border e-commerce supply chain members to optimize cross-border e-commerce supply chain e-commerce supply chain memberʼs profit. Cross-border e-commerce supply chain provides a scientific reference for the rapid and healthy development of Chinaʼs e-commerce industry.


## 2. Model Hypothesis

Hypothesis 1.
Domestic retailers use a variety of promotional tools to enable consumers to buy their goods, and according to [17], the demand function is not only affected by retail price but also by propaganda strategy, so suppose the demand function dp,θ2=a−p+λθ2, in which “a” for the potential market demand, “p” for the retail prices per unit product of domestic retailers, “λ” for consumer sensitivity to retailer propaganda λ>0, and “θ2” for the domestic retailerʼs propaganda strategy.Hypothesis 2.
According to [18], wholesale price for unit products of overseas suppliers is w, and the transportation cost per unit product is a linear relationship of monotone decreasing with the volume of transport, so cd=c−ρdp,θ2, in which “ρ” is for marginal transport cost factor for unit product ρ>0 and “c” is fixed transport costs per unit product (i.e., fixed transport costs per unit product regardless of economies of scale).Hypothesis 3.
Domestic retailers promote the extra cost of product propaganda. Assume the publicity costs of domestic retailersCθ2=K2θ22/2, in which K2 indicates the scale of domestic retailer propaganda activity.Hypothesis 4.
If only the cost of transportation of products from overseas suppliers to domestic suppliers is considered, the cost of transportation from domestic retailers to consumers is ignored.Hypothesis 5.
Overseas suppliers and domestic retailers are completely rational persons, and the decision information of both sides is completely symmetrical.


## 3. Construction of Cross-Border E-Commerce Supply Chain Decision Model

In view of the space limitation, this paper mainly studies the decision-making problem under the two-level cross-border supply chain cooperation mode composed of a single overseas supplier and a single domestic retailer; that is, the overseas supplier sells the goods to the domestic retailer and bears the transportation cost. Clearly, the overseas supplier and the domestic retailer form a kind of Stackelberg cooperation relationship, and the overseas supplier is the decision-maker, while the domestic retailer is the decision follower.By constructing decision-making models of non-cooperation, semi-cooperation (including two kinds of one-way cooperation modes of retailers sharing transportation cost and supplier sharing propaganda cost), and full cooperation between overseas suppliers and domestic retailers, it can clarify the influence of pricing and propaganda strategy on profit of cross-border e-commerce supply chain and provide scientific decision reference for rational selection of cooperative relationship.Furthermore, the introduction of Shapley value method and the incremental benefit sharing mechanism for full cooperation is beneficial to the rational redistribution of profits of overseas suppliers and domestic retailers under different cooperation modes.


### 3.1. Decision-Making in the Non-Cooperative Model of Suppliers and Retailers (N)

Under this model, overseas suppliers usually set wholesale priceswN first, and then, domestic retailers determine retail prices PN and publicity strategies θ2N.Thus, the profits of overseas suppliers and domestic retailers under the non-cooperation mode are as follows:(1)πmN=w−ca−p+λθ2+ρa−p+λθ22,πrN=p−wa−p+λθ2−12K2θ22.Proposition 1.
Under the non-cooperation structure of overseas suppliers and domestic retailers, the optimal decision of cross-border e-commerce supply chain is(2)wN∗=2a+c−aρK2−a+cλ222−ρK2−λ2,(3)PN∗=c+3a−2aρK2−a+cλ222−ρK2−λ2,(4)θ2N∗=a−cλ22−ρK2−λ2.Proof.
The reverse induction method is used to solve the problem.
Firstly, determine the Hessian matrix for the domestic retailer profit functionπrN:(5)Hp,θ2=∂2πrN∂PN2∂2πrN∂PN∂θ2N∂2πrN∂θ2N∂PN∂2πrN∂θ2N2=−2λλ−K2.
It is not difficult to see from the above Hessian matrix:∂2πrN/∂PN2=−2<0 and H=2K2−λ2>0; πrN is a strictly joint concave function about PN and cθ2N, and there is an optimal solution to maximize profits.
Secondly, first-order partial derivative conditions are as follows:pN¯=a+wK2−wλ2/2K2−λ2 and θ2N¯=a−wλ/2K2−λ2 substituted into formula (1), and the second-order derivative function of profit function of overseas suppliers can be obtained as ∂2πmN/∂wN2=−2K22−ρK2−λ2/2K2−λ22<0.
It can be seen thatπmN is a strict concave function about wN, and there is an optimal solution to maximize profit, and thus, the first-order partial derivative condition is wN∗=2a1−ρ+cK2−a+cλ2/22−ρK2−λ2; decisions available to domestic retailers are PN∗=c+3a−2aρK2−a+cλ2/22−ρK2−λ2 and θ2N∗=a−cλ/22−ρK2−λ2. Now, the commodity market demand and the profits of the members of the cross-border e-commerce supply chain are(6)dN∗=a−cK222−ρK2−λ2,(7)πmN∗=a−c2K242−ρK2−λ2,(8)πrN∗=a−c22K2−λ2K282−ρK2−λ22.
From the above equilibrium results, we can see that the pricing of cross-border e-commerce supply chain is inversely proportional to the unit transportation cost, while the propaganda strategy of domestic retailers and the profits of supply chain members are all proportional to the unit transportation cost; that is,∂wN∗/∂ρ<0, ∂pN∗/∂ρ<0, ∂θ2N∗/∂ρ<0, ∂πmN∗/∂ρ<0, ∂πrN∗/∂ρ<0.


### 3.2. Decision-Making under the One-Way Cooperation Mode for Retailers Sharing Suppliersʼ Transportation Costs (M)

Based on their own profit maximization under this mode, domestic retailers will share the transportation costs of overseas suppliers in proportion ofθm0≤θm≤1.Obviously, whenθm=0, domestic retailers are unwilling to share the transportation costs of overseas suppliers, and when θm=1, domestic retailers are willing to share the full transportation costs of overseas suppliers.Under establishedθm, overseas suppliers usually set wholesale prices wM, and then, domestic retailers determine retail price PM and publicity strategy θ2M.Therefore, the profits of overseas suppliers and domestic retailers under this cooperation model are(9)πmM=w−1−θmc−ρa−p+λθ2a−p+λθ2,πrM=p−w−θmc−ρa−p+λθ2a−p+λθ2−12K2θ22.Proposition 2.
Under the one-way cooperation mode of domestic retailers sharing the transportation cost of overseas suppliers, the optimal decision of cross-border e-commerce supply chain is as follows:(10)θmM∗=1,(11)wM∗=a−c2,(12)pM∗=c+a3−4ρK2−a+cλ2221−ρK2−λ2,(13)θ2M∗=a−cλ221−ρK2−λ2.Proof.
The reverse induction method is used to solve the problem.
Firstly, determine Hessian matrix for the domestic retailer profit functionπrM:(14)Hp,θ2=∂2πrM∂PM2∂2πrM∂PM∂θ2M∂2πrM∂θ2M∂PM∂2πrM∂θ2M2=−21−ρθmλ1−ρθmλ1−ρθm−K2+2λ2ρθm.
It is not difficult to see from the above Hessian matrix:∂2πrM/∂PM2=−21−ρθm<0 and H=2K21−ρθm−λ2>0; πrM is a strictly joint concave function about PM and θ2M, and there is an optimal solution to maximize profits.
Secondly, first-order partial derivative conditions are as follows:pM¯=K2a+w+c−2aρθm−λ2w+cθm/2K21−ρθm−λ2 and θ2M¯=λa−w−cθm/2K21−ρθm−λ2 substituted into formula (2), and the second-order derivative function of profit function of overseas suppliers can be obtained as ∂2πmM/∂wM2=−2K2K22−ρ1+θm−λ2/2K21−ρθm−λ22<0.
It can be seen thatπmM is a strict concave function about wM, and there is an optimal solution to maximize profit; thus, the first-order partial derivative condition is wMθm=2K2a1−ρ+c1−2θm+ρθm2−λ2a+c−2cθm/2K22−ρ1+θm−λ2, and decisions available to domestic retailers are pMθm and θ2Mθm. The profits of domestic retailers are πrMθm=a−c2K22K21−ρθm−λ2/8K22−ρ1+θm−λ22.
Moreover, according to∂2πrMθm/∂θm2<0, πrM is a strict concave function about θm, which has the optimal solution to maximize the profit of domestic retailers, so substituting the first-order partial derivative condition θmM∗=1 into formula wMθm, pMθm, and θ2Mθm, the optimal decisions of overseas suppliers and domestic retailers are wM∗, pM∗, and θ2M∗.
Finally, it can be concluded that the market demand of commodities and the profits of each member of cross-border e-commerce supply chain are as follows:(15)dM∗=a−cK2221−ρK2−λ2,πmM∗=a−c2K2421−ρK2−λ2,πrM∗=a−c2K2821−ρK2−λ2.
It can be seen that, in the semi-cooperative mode of retailers sharing the transportation costs with suppliers, domestic retailers are generally willing to share the total transportation costs of overseas suppliers in order to maximize their profits. Also, the cost of transportation will eventually be passed on to consumers by domestic retailers.


### 3.3. Decision-Making under the One-Way Cooperation Model for Suppliers Sharing Retailersʼ Publicity Costs (R)

Based on their own profit maximization under this mode, most of the overseas suppliers in this model will share the publicity cost with domestic retailers in proportion ofθr0≤θr≤1.Obviously, whenθr=0, overseas suppliers are unwilling to share the promotional costs of domestic retailers; when θr=1, overseas suppliers are willing to share the full promotional costs of domestic retailers. Under established condition θr, overseas suppliers usually set wholesale prices wR first, and then, domestic retailers determine retail prices PR and publicity strategies θ2R.Therefore, the profits of overseas suppliers and domestic retailers under this cooperation model are(16)πmR=w−ca−p+λθ2+ρa−p+λθ22−12θrK2θ22,πrR=p−wa−p+λθ2−121−θrK2θ22.Proposition 3.
Under the one-way cooperation mode of overseas suppliers sharing the propaganda cost of domestic retailers, the optimal decision of cross-border e-commerce supply chain is as follows:(17)θrR∗=13,(18)wR∗=8a+c−aρK2−3a+2cλ282−ρK2−9λ2,(19)pR∗=4c+a3−2ρK2−3a+2cλ282−ρK2−9λ2,(20)θ2R∗=6a−cλ82−ρK2−9λ2.Proof.
Proof. The reverse induction method is used to solve the problem.
Firstly, determine theπrR Hessian matrix for the domestic retailer profit function:(21)Hp,θ2=∂2πrR∂PR2∂2πrR∂PR∂θ2R∂2πrR∂θ2R∂PR∂2πrR∂θ2R2=−21−ρθmλ1−ρθmλ1−ρθm−K2+2λ2ρθm.
It is not difficult to see from the above Hessian matrix,∂2πrR/∂PR2=−21−ρθm<0 and H=2K21−ρθm−λ2>0; πrR is a strictly joint concave function about PR and θ2R, and there is an optimal solution to maximize profits; thus, the first-order partial derivation condition is pR¯=a+wK21−θr−wλ2/2K21−θr−λ2 and θ2R¯=a−wλ/2K21−θr−λ2. Substituting pR¯ and θ2R¯ into formula (2), the second-order derivative function of profit function of overseas suppliers can be obtained. When 0<ρ<4K21−θr2−λ22−3θr/2K21−θr2, ∂2πmR/∂wR2=−K222−ρK21−θr2−λ22−3θr/2K21−θr−λ22<0.
It can be seen thatπmM is the strict concave function about wM, and there is an optimal solution to maximize profits. Therefore, the first-order partial derivative condition is wRθr=2a+c−aρK21−θr2−λ2a+c−2a+cθr/22−ρK21−θr2−λ22−3θr, decisions of domestic retailers are pRθr and θ2Rθr, and profits from overseas suppliers at this time are πmRθr=a−c2K21−θr2/222−ρK21−θr2−λ22−3θr.
According to∂2πmRθr/∂θr2<0, πrR is the strict concave function about θr, and there is an optimal solution to maximize the profits of overseas suppliers, so the first-order partial derivative condition is θrR∗=1/3.
SubstitutingθrR∗ into formula wRθr, pRθr, and θ2Rθr, respectively, optimal decision-making available for overseas suppliers and domestic retailers can be obtained as wR∗, pR∗, and θ2R∗.
Finally, the market demand for commodities and the profits of members of cross-border e-commerce supply chains are(22)dR∗=4a−cK282−ρK2−9λ2,πmR∗=2a−c2K282−ρK2−9λ2,πrR∗=4a−c2K24K2−3λ282−ρK2−9λ22.
In the semi-cooperative mode of supplier sharing retailerʼs propaganda cost, foreign suppliers are mostly willing to share 1/3 propaganda cost of domestic retailers in order to maximize their profits.


### 3.4. Decision-Making under the Two-Way Cooperation Mode in Which Retailers Share Transportation Costs and Suppliers Share Publicity Costs (MR)

The domestic retailers in this mode share the transportation costs of overseas suppliers in proportion ofθm0≤θm≤1 based on their own profit maximization considerations, and the overseas suppliers share the propaganda costs of domestic retailers in proportion of θr0≤θr≤1 based on their own profit maximization considerations.Under established conditionθm and θr, overseas suppliers will first determine wholesale prices, and then, domestic retailers determine retail prices PMR and publicity strategies θ2MR.Under this condition, the profit of overseas suppliers and domestic retailers under the cooperation mode is(23)πmMR∗=w−1−θmc−ρa−p+λθ2a−p+λθ2−12θrK2θ22,πrMR∗=p−w−θmc−ρa−p+λθ2a−p+λθ2−121−θrK2θ22.Proposition 4.
Under the two-way cooperation mode between overseas suppliers and domestic retailers, the optimal decision of cross-border e-commerce supply chain is(24)θmMR∗=1−3λ28ρK2,(25)θrMR∗=13,(26)wMR∗=4a−cρK2+3cλ28ρK2,(27)pMR∗=2c+a3−4ρK2−3cλ281−ρK2−3λ2,(28)θ2MR∗=3a−cλ81−ρK2−3λ2.Proof.
The reverse induction method is used to solve the problem.
Firstly, determine theπrMR Hessian matrix for the domestic retailer profit function:(29)Hp,θ2=∂2πrMR∂PMR2∂2πrMR∂PMR∂θ2MR∂2πrMR∂θ2MR∂PMR∂2πrMR∂θ2MR2=−21−ρθmλ1−ρθmλ1−ρθm−K2+2λ2ρθm.
It is not difficult to see from the above Hessian matrix:∂2πrMR/∂PMR2=−21−ρθm<0 and H=2K21−ρθm1−θr−λ2>0. Thus, πrR is a strictly joint concave function about PR and θ2R, and there is an optimal solution to maximize profits.
Secondly, first-order partial derivation conditions are as follows:(30)pMR¯=K2a+w+c−2aρθm1−θr−λ2w+cθm2K21−ρθm1−θr−λ2,θ2MR¯=λa−w−cθm2K21−ρθm1−θr−λ2.
SubstitutingpMR¯ and θ2MR¯ into formula (7), the second-order derivative of the profit function of overseas suppliers can be obtained.
When0<ρ<4K21−θr2−λ22−3θr/2K21+θm1−θr2,(31)∂2πmR∂wR2=−K22K22−ρ1+θm1−θr2−λ22−3θr2K21−ρθm1−θr−λ22<0.
It can be seen thatπmMR is the strict concave function about wMR, and there is an optimal solution to maximize profits. Therefore, the first-order partial derivative condition is wMRθm,θr=2K2a1−ρ+c1−2θm+ρθm21−θr2−λ2a+c−cθm2−3θr−2a+cθr/2K22−ρ1+θm1−θr2−λ22−3θr, so decision-making by domestic retailers is pMRθm,θr and θ2MRθm,θr.
At this point, the profits of the cross-border e-commerce supply chain are(32)πmMRθm,θr=a−c2K21−θr222K22−ρ1+θm1−θr2−λ22−3θr,πrMRθm,θr=a−c2K22K21−ρθm1−θr−λ21−θr322K22−ρ1+θm1−θr2−λ22−3θr2.
According to∂πrMRθm,θr/∂θm=0 and ∂πmMRθm,θr/∂θr=0, the optimal proportion of overseas suppliers and domestic retailers sharing each otherʼs corresponding costs, under this cooperation mode, is θmMR∗=1−3λ2/8ρK2θrMR∗=1/3.
SubstitutingθmMR∗ and θrMR∗ into wMRθm,θr, pMRθm,θr, and θ2MRθm,θr, respectively, optimal decisions for overseas suppliers and domestic retailers can be obtained as wMR∗, pMR∗, and θ2MR∗.
Finally, it can be determined that the commodity market demand and the profits of the members of the cross-border e-commerce supply chain are as follows:(33)dMR∗=2a−cK281−ρK2−3λ2,πmMR∗=a−c2K281−ρK2−3λ2,πrMR∗=a−c2K2281−ρK2−3λ2.
Under the two-way cooperation mode between overseas suppliers and domestic retailers, retailers are no longer willing to share the total transportation costs of suppliers, but suppliers are still willing to share one-third of the promotional costs of retailers.


## 3.1. Decision-Making in the Non-Cooperative Model of Suppliers and Retailers (N)

Under this model, overseas suppliers usually set wholesale priceswN first, and then, domestic retailers determine retail prices PN and publicity strategies θ2N.Thus, the profits of overseas suppliers and domestic retailers under the non-cooperation mode are as follows:(1)πmN=w−ca−p+λθ2+ρa−p+λθ22,πrN=p−wa−p+λθ2−12K2θ22.Proposition 1.
Under the non-cooperation structure of overseas suppliers and domestic retailers, the optimal decision of cross-border e-commerce supply chain is(2)wN∗=2a+c−aρK2−a+cλ222−ρK2−λ2,(3)PN∗=c+3a−2aρK2−a+cλ222−ρK2−λ2,(4)θ2N∗=a−cλ22−ρK2−λ2.Proof.
The reverse induction method is used to solve the problem.
Firstly, determine the Hessian matrix for the domestic retailer profit functionπrN:(5)Hp,θ2=∂2πrN∂PN2∂2πrN∂PN∂θ2N∂2πrN∂θ2N∂PN∂2πrN∂θ2N2=−2λλ−K2.
It is not difficult to see from the above Hessian matrix:∂2πrN/∂PN2=−2<0 and H=2K2−λ2>0; πrN is a strictly joint concave function about PN and cθ2N, and there is an optimal solution to maximize profits.
Secondly, first-order partial derivative conditions are as follows:pN¯=a+wK2−wλ2/2K2−λ2 and θ2N¯=a−wλ/2K2−λ2 substituted into formula (1), and the second-order derivative function of profit function of overseas suppliers can be obtained as ∂2πmN/∂wN2=−2K22−ρK2−λ2/2K2−λ22<0.
It can be seen thatπmN is a strict concave function about wN, and there is an optimal solution to maximize profit, and thus, the first-order partial derivative condition is wN∗=2a1−ρ+cK2−a+cλ2/22−ρK2−λ2; decisions available to domestic retailers are PN∗=c+3a−2aρK2−a+cλ2/22−ρK2−λ2 and θ2N∗=a−cλ/22−ρK2−λ2. Now, the commodity market demand and the profits of the members of the cross-border e-commerce supply chain are(6)dN∗=a−cK222−ρK2−λ2,(7)πmN∗=a−c2K242−ρK2−λ2,(8)πrN∗=a−c22K2−λ2K282−ρK2−λ22.
From the above equilibrium results, we can see that the pricing of cross-border e-commerce supply chain is inversely proportional to the unit transportation cost, while the propaganda strategy of domestic retailers and the profits of supply chain members are all proportional to the unit transportation cost; that is,∂wN∗/∂ρ<0, ∂pN∗/∂ρ<0, ∂θ2N∗/∂ρ<0, ∂πmN∗/∂ρ<0, ∂πrN∗/∂ρ<0.


## 3.2. Decision-Making under the One-Way Cooperation Mode for Retailers Sharing Suppliersʼ Transportation Costs (M)

Based on their own profit maximization under this mode, domestic retailers will share the transportation costs of overseas suppliers in proportion ofθm0≤θm≤1.Obviously, whenθm=0, domestic retailers are unwilling to share the transportation costs of overseas suppliers, and when θm=1, domestic retailers are willing to share the full transportation costs of overseas suppliers.Under establishedθm, overseas suppliers usually set wholesale prices wM, and then, domestic retailers determine retail price PM and publicity strategy θ2M.Therefore, the profits of overseas suppliers and domestic retailers under this cooperation model are(9)πmM=w−1−θmc−ρa−p+λθ2a−p+λθ2,πrM=p−w−θmc−ρa−p+λθ2a−p+λθ2−12K2θ22.Proposition 2.
Under the one-way cooperation mode of domestic retailers sharing the transportation cost of overseas suppliers, the optimal decision of cross-border e-commerce supply chain is as follows:(10)θmM∗=1,(11)wM∗=a−c2,(12)pM∗=c+a3−4ρK2−a+cλ2221−ρK2−λ2,(13)θ2M∗=a−cλ221−ρK2−λ2.Proof.
The reverse induction method is used to solve the problem.
Firstly, determine Hessian matrix for the domestic retailer profit functionπrM:(14)Hp,θ2=∂2πrM∂PM2∂2πrM∂PM∂θ2M∂2πrM∂θ2M∂PM∂2πrM∂θ2M2=−21−ρθmλ1−ρθmλ1−ρθm−K2+2λ2ρθm.
It is not difficult to see from the above Hessian matrix:∂2πrM/∂PM2=−21−ρθm<0 and H=2K21−ρθm−λ2>0; πrM is a strictly joint concave function about PM and θ2M, and there is an optimal solution to maximize profits.
Secondly, first-order partial derivative conditions are as follows:pM¯=K2a+w+c−2aρθm−λ2w+cθm/2K21−ρθm−λ2 and θ2M¯=λa−w−cθm/2K21−ρθm−λ2 substituted into formula (2), and the second-order derivative function of profit function of overseas suppliers can be obtained as ∂2πmM/∂wM2=−2K2K22−ρ1+θm−λ2/2K21−ρθm−λ22<0.
It can be seen thatπmM is a strict concave function about wM, and there is an optimal solution to maximize profit; thus, the first-order partial derivative condition is wMθm=2K2a1−ρ+c1−2θm+ρθm2−λ2a+c−2cθm/2K22−ρ1+θm−λ2, and decisions available to domestic retailers are pMθm and θ2Mθm. The profits of domestic retailers are πrMθm=a−c2K22K21−ρθm−λ2/8K22−ρ1+θm−λ22.
Moreover, according to∂2πrMθm/∂θm2<0, πrM is a strict concave function about θm, which has the optimal solution to maximize the profit of domestic retailers, so substituting the first-order partial derivative condition θmM∗=1 into formula wMθm, pMθm, and θ2Mθm, the optimal decisions of overseas suppliers and domestic retailers are wM∗, pM∗, and θ2M∗.
Finally, it can be concluded that the market demand of commodities and the profits of each member of cross-border e-commerce supply chain are as follows:(15)dM∗=a−cK2221−ρK2−λ2,πmM∗=a−c2K2421−ρK2−λ2,πrM∗=a−c2K2821−ρK2−λ2.
It can be seen that, in the semi-cooperative mode of retailers sharing the transportation costs with suppliers, domestic retailers are generally willing to share the total transportation costs of overseas suppliers in order to maximize their profits. Also, the cost of transportation will eventually be passed on to consumers by domestic retailers.


## 3.3. Decision-Making under the One-Way Cooperation Model for Suppliers Sharing Retailersʼ Publicity Costs (R)

Based on their own profit maximization under this mode, most of the overseas suppliers in this model will share the publicity cost with domestic retailers in proportion ofθr0≤θr≤1.Obviously, whenθr=0, overseas suppliers are unwilling to share the promotional costs of domestic retailers; when θr=1, overseas suppliers are willing to share the full promotional costs of domestic retailers. Under established condition θr, overseas suppliers usually set wholesale prices wR first, and then, domestic retailers determine retail prices PR and publicity strategies θ2R.Therefore, the profits of overseas suppliers and domestic retailers under this cooperation model are(16)πmR=w−ca−p+λθ2+ρa−p+λθ22−12θrK2θ22,πrR=p−wa−p+λθ2−121−θrK2θ22.Proposition 3.
Under the one-way cooperation mode of overseas suppliers sharing the propaganda cost of domestic retailers, the optimal decision of cross-border e-commerce supply chain is as follows:(17)θrR∗=13,(18)wR∗=8a+c−aρK2−3a+2cλ282−ρK2−9λ2,(19)pR∗=4c+a3−2ρK2−3a+2cλ282−ρK2−9λ2,(20)θ2R∗=6a−cλ82−ρK2−9λ2.Proof.
Proof. The reverse induction method is used to solve the problem.
Firstly, determine theπrR Hessian matrix for the domestic retailer profit function:(21)Hp,θ2=∂2πrR∂PR2∂2πrR∂PR∂θ2R∂2πrR∂θ2R∂PR∂2πrR∂θ2R2=−21−ρθmλ1−ρθmλ1−ρθm−K2+2λ2ρθm.
It is not difficult to see from the above Hessian matrix,∂2πrR/∂PR2=−21−ρθm<0 and H=2K21−ρθm−λ2>0; πrR is a strictly joint concave function about PR and θ2R, and there is an optimal solution to maximize profits; thus, the first-order partial derivation condition is pR¯=a+wK21−θr−wλ2/2K21−θr−λ2 and θ2R¯=a−wλ/2K21−θr−λ2. Substituting pR¯ and θ2R¯ into formula (2), the second-order derivative function of profit function of overseas suppliers can be obtained. When 0<ρ<4K21−θr2−λ22−3θr/2K21−θr2, ∂2πmR/∂wR2=−K222−ρK21−θr2−λ22−3θr/2K21−θr−λ22<0.
It can be seen thatπmM is the strict concave function about wM, and there is an optimal solution to maximize profits. Therefore, the first-order partial derivative condition is wRθr=2a+c−aρK21−θr2−λ2a+c−2a+cθr/22−ρK21−θr2−λ22−3θr, decisions of domestic retailers are pRθr and θ2Rθr, and profits from overseas suppliers at this time are πmRθr=a−c2K21−θr2/222−ρK21−θr2−λ22−3θr.
According to∂2πmRθr/∂θr2<0, πrR is the strict concave function about θr, and there is an optimal solution to maximize the profits of overseas suppliers, so the first-order partial derivative condition is θrR∗=1/3.
SubstitutingθrR∗ into formula wRθr, pRθr, and θ2Rθr, respectively, optimal decision-making available for overseas suppliers and domestic retailers can be obtained as wR∗, pR∗, and θ2R∗.
Finally, the market demand for commodities and the profits of members of cross-border e-commerce supply chains are(22)dR∗=4a−cK282−ρK2−9λ2,πmR∗=2a−c2K282−ρK2−9λ2,πrR∗=4a−c2K24K2−3λ282−ρK2−9λ22.
In the semi-cooperative mode of supplier sharing retailerʼs propaganda cost, foreign suppliers are mostly willing to share 1/3 propaganda cost of domestic retailers in order to maximize their profits.


## 3.4. Decision-Making under the Two-Way Cooperation Mode in Which Retailers Share Transportation Costs and Suppliers Share Publicity Costs (MR)

The domestic retailers in this mode share the transportation costs of overseas suppliers in proportion ofθm0≤θm≤1 based on their own profit maximization considerations, and the overseas suppliers share the propaganda costs of domestic retailers in proportion of θr0≤θr≤1 based on their own profit maximization considerations.Under established conditionθm and θr, overseas suppliers will first determine wholesale prices, and then, domestic retailers determine retail prices PMR and publicity strategies θ2MR.Under this condition, the profit of overseas suppliers and domestic retailers under the cooperation mode is(23)πmMR∗=w−1−θmc−ρa−p+λθ2a−p+λθ2−12θrK2θ22,πrMR∗=p−w−θmc−ρa−p+λθ2a−p+λθ2−121−θrK2θ22.Proposition 4.
Under the two-way cooperation mode between overseas suppliers and domestic retailers, the optimal decision of cross-border e-commerce supply chain is(24)θmMR∗=1−3λ28ρK2,(25)θrMR∗=13,(26)wMR∗=4a−cρK2+3cλ28ρK2,(27)pMR∗=2c+a3−4ρK2−3cλ281−ρK2−3λ2,(28)θ2MR∗=3a−cλ81−ρK2−3λ2.Proof.
The reverse induction method is used to solve the problem.
Firstly, determine theπrMR Hessian matrix for the domestic retailer profit function:(29)Hp,θ2=∂2πrMR∂PMR2∂2πrMR∂PMR∂θ2MR∂2πrMR∂θ2MR∂PMR∂2πrMR∂θ2MR2=−21−ρθmλ1−ρθmλ1−ρθm−K2+2λ2ρθm.
It is not difficult to see from the above Hessian matrix:∂2πrMR/∂PMR2=−21−ρθm<0 and H=2K21−ρθm1−θr−λ2>0. Thus, πrR is a strictly joint concave function about PR and θ2R, and there is an optimal solution to maximize profits.
Secondly, first-order partial derivation conditions are as follows:(30)pMR¯=K2a+w+c−2aρθm1−θr−λ2w+cθm2K21−ρθm1−θr−λ2,θ2MR¯=λa−w−cθm2K21−ρθm1−θr−λ2.
SubstitutingpMR¯ and θ2MR¯ into formula (7), the second-order derivative of the profit function of overseas suppliers can be obtained.
When0<ρ<4K21−θr2−λ22−3θr/2K21+θm1−θr2,(31)∂2πmR∂wR2=−K22K22−ρ1+θm1−θr2−λ22−3θr2K21−ρθm1−θr−λ22<0.
It can be seen thatπmMR is the strict concave function about wMR, and there is an optimal solution to maximize profits. Therefore, the first-order partial derivative condition is wMRθm,θr=2K2a1−ρ+c1−2θm+ρθm21−θr2−λ2a+c−cθm2−3θr−2a+cθr/2K22−ρ1+θm1−θr2−λ22−3θr, so decision-making by domestic retailers is pMRθm,θr and θ2MRθm,θr.
At this point, the profits of the cross-border e-commerce supply chain are(32)πmMRθm,θr=a−c2K21−θr222K22−ρ1+θm1−θr2−λ22−3θr,πrMRθm,θr=a−c2K22K21−ρθm1−θr−λ21−θr322K22−ρ1+θm1−θr2−λ22−3θr2.
According to∂πrMRθm,θr/∂θm=0 and ∂πmMRθm,θr/∂θr=0, the optimal proportion of overseas suppliers and domestic retailers sharing each otherʼs corresponding costs, under this cooperation mode, is θmMR∗=1−3λ2/8ρK2θrMR∗=1/3.
SubstitutingθmMR∗ and θrMR∗ into wMRθm,θr, pMRθm,θr, and θ2MRθm,θr, respectively, optimal decisions for overseas suppliers and domestic retailers can be obtained as wMR∗, pMR∗, and θ2MR∗.
Finally, it can be determined that the commodity market demand and the profits of the members of the cross-border e-commerce supply chain are as follows:(33)dMR∗=2a−cK281−ρK2−3λ2,πmMR∗=a−c2K281−ρK2−3λ2,πrMR∗=a−c2K2281−ρK2−3λ2.
Under the two-way cooperation mode between overseas suppliers and domestic retailers, retailers are no longer willing to share the total transportation costs of suppliers, but suppliers are still willing to share one-third of the promotional costs of retailers.


## 4. Comparative Analysis

Proposition 5.
Under the specific unit transportation cost, the pricing decisions of different cooperation modes satisfy the following:(34)wR∗>wN∗>wMR∗>wM∗,pR∗>pN∗>pMR∗>pM∗.Proof.
According to the above proposition, comparing the optimal solutions under the four different cooperation modes, the following relationships can be found:(35)wR∗−wN∗=a−cλ26−4ρK2−3λ222−ρK2−λ282−ρK2−9λ2>0,wN∗−wMR∗=4ρ4c−c+aρK22−cλ26+5ρK2+3cλ48ρK22−ρK2−λ2>0,wMR∗−wM∗=3cλ28ρK2>0,pR∗−pN∗=a−cλ27−4ρK2−3λ222−ρK2−λ282−ρK2−9λ2>0,pN∗−pMR∗=a−c4ρK22−λ25+2ρK2+3λ422−ρK2−λ281−ρK2−3λ2>0,pMR∗−pM∗=a−cλ25−4ρK2−3λ2221−ρK2−λ281−ρK2−3λ2>0.
It is found from Proposition5 that, when overseas suppliers share part of the publicity costs of domestic retailers, the premise of raising or lowering wholesale prices is that domestic retailers are willing to share all or part of their transportation costs. Also, the retail price ranking of domestic retailers is consistent with the wholesale price ranking of overseas suppliers. More importantly, in the pricing decision of cross-border e-commerce supply chain, the cost of upstream enterprises will be transferred directly to downstream enterprises and eventually apportioned to each consumer.Proposition 6.
Under the specific unit transportation cost, the propaganda strategy of different cooperation modes satisfies the following:
When0<ρ<8K2−3λ2/16K2, θ2MR>θ2R>θ2M>θ2N.
When8K2−3λ2/16K2<ρ<1, θ2MR>θ2M>θ2R>θ2N.Proof.
According to the above proposition, comparing the optimal solutions under the four different cooperation modes, the following relationships can be found:(36)θ2MR∗−θ2R∗=3a−cλ8ρK2−3λ282−ρK2−9λ281−ρK2−3λ2>0,θ2MR∗−θ2M∗=a−cλ41−ρK2−3λ2221−ρK2−λ281−ρK2−3λ2>0,θ2R∗−θ2M∗=a−cλ81−2ρK2−3λ2282−ρK2−9λ221−ρK2−λ2.
When0<ρ<8K2−3λ2/16K2a−cλ81−2ρK2−3λ2/282−ρK2−9λ221−ρK2−λ2>0, i.e., θ2R∗>θ2M∗.
When8K2−3λ2/16K2<ρ<1, a−cλ81−2ρK2−3λ2/282−ρK2−9λ221−ρK2−λ2<0, i.e., θ2R∗<θ2M∗; θ2R∗−θ2N∗=a−cλ42−ρK2−3λ2/22−ρK2−λ282−ρK2−9λ2>0, and θ2M∗−θ2N∗=a−cλρK2/22−ρK2−λ221−ρK2−λ2>0.
It is found from Proposition6 that the two-way cooperation mode between overseas suppliers and domestic retailers can most effectively enhance the product publicity strategy of domestic retailers. However, for the two one-way cooperation modes, with the increase in unit transportation cost, the initial one-way cooperation of the supplier sharing the retailerʼs propaganda cost will become the one-way cooperation of the retailer sharing the supplierʼs transportation cost.Proposition 7.
Under the specific unit transportation cost, the profits of cross-border e-commerce supply chain members of different cooperation modes satisfy, respectively, the following:(37)πmM∗>πmMR∗>πmR∗>πmN∗,πrM>πrMR>πrN>πrR.Proof.
According to the above proposition, comparing the profits of cross-border e-commerce supply chain members under four different cooperation modes, we can get the following relationship:(38)πmM∗−πmMR∗=a−c2λ2K2421−ρK2−λ281−ρK2−3λ2>0,πmMR∗−πmR∗=a−c2K28ρK2−3λ282−ρK2−9λ281−ρK2−3λ2>0,πmR∗−πmN∗=a−c2λ2K242−ρK2−λ282−ρK2−9λ2>0,πrM∗−πrMR∗=a−c2λ2K2821−ρK2−λ281−ρK2−3λ2>0,πrMR∗−πrN∗=a−c2K24ρ2K22−2λ2K2+λ482−ρK2−λ2281−ρK2−3λ2>0,πrN∗−πrR∗=a−c2λ2K2322−3ρ+ρ2K22−2λ231−24ρK2+15λ482−ρK2−λ2282−ρK2−9λ22>0.
It is found from Proposition7 that both overseas suppliers and domestic retailers will choose the one-way cooperation mode of retailers sharing the transportation costs of suppliers and the two-way cooperation mode to improve their profits, and the former is more effective than the latter.


## 5. Coordination Analysis

In cross-border e-commerce, even if overseas suppliers and domestic retailers choose the decision-making mode of semi-cooperation (between non-cooperation and full cooperation), the two parties will still keep some room for profit. Therefore, it is necessary to introduce the Shapley value method and full cooperative decision profit incremental sharing mechanism to coordinate non-cooperation and the three semi-cooperation modes, but before that, it is necessary to analyze the problem of full cooperative decision-making between suppliers and retailers.


### 5.1. Coordination of the Full Cooperation Mode between Overseas Suppliers and Domestic Retailer (C)

In the mode of full cooperation, the members of the supply chain of cross-border e-commerce pay great attention to the maximization of the overall benefit, so they generally make joint decisions on the retail pricePC and propaganda strategy θ2C of the goods at the same time.Therefore, the profit of cross-border e-commerce supply chain under the mode of full cooperation is as follows:(39)πscC=p−ca−p+λθ2+ρa−p+λθ22−12K2θ22.Proposition 8.
Under the mode of full cooperation between overseas suppliers and domestic retailers, the optimal decision of cross-border e-commerce supply chain is(40)pC∗=a+c−2aρK2−cλ221−ρK2−λ2,θ2C∗=a−cλ21−ρK2−λ2.Proof.
Solved by reverse induction.
Firstly, determine Hessian matrix ofπscC for the domestic retailer profit function:(41)Hp,θ2=∂2πscC∂PC2∂2πscC∂PC∂θ2C∂2πscC∂θ2C∂PC∂2πscC∂θ2C2=−21−ρλ1−2ρλ1−2ρ−K2+2λ2ρ.
It is not difficult to see from the above Hessian matrix: when0<ρ<2K2−λ2/2K2, ∂2πrMR/∂PMR2=−21−ρ<0 and H=21−ρK2−λ2>0. Thus, πscC is a strictly joint concave function about PC and θ2C, and there is an optimal solution to maximize profits. So the first-order partial derivation conditions are as follows: pC∗=a+c−2aρK2−cλ2/21−ρK2−λ2 and θ2C∗=a−cλ/21−ρK2−λ2, and the market demand for commodities and the profits of cross-border e-commerce supply chain can be determined as(42)dC∗=a−cK221−ρK2−λ2,πscC∗=a−c2K2221−ρK2−λ2.


### 5.2. Shapley Value Method Coordination (S)

Shapley value method is a method of fair distribution of cooperative income based on the marginal contribution of individuals to the whole.For the non-cooperation mode and 3 semi-cooperation modes between overseas suppliers and domestic retailers, the Shapley value method is used to distribute the overall supply chain profits when the two fully cooperate, and the profits distributed by both sides under different cooperation modes can be obtained:(1)
Non-cooperative coordination between overseas suppliers and domestic retailers (SN)At this point,(43)πmSN∗=12πmN∗+12πscC∗−πrN∗=a−c2K2421−ρK2−λ2+a−c2K221−ρK2−λ2162−ρK2−λ22,πrSN∗=12πrN∗+12πscC∗−πmN∗=a−c2K2421−ρK2−λ2−a−c2K221−ρK2−λ2162−ρK2−λ22.(2)
One-way cooperative coordination of domestic retailers sharing transportation costs for overseas suppliers (SM)At this point,(44)πmSM∗=12πmM∗+12πscC∗−πrM∗=5a−c2K21621−ρK2−λ2,πrSM∗=12πrM∗+12πscC∗−πmM∗=3a−c2K21621−ρK2−λ2.(3)
One-way cooperative coordination of domestic retailers sharing publicity costs for overseas suppliers (SR)At this point,(45)πmSR∗=12πmR∗+12πscC∗−πrR∗=a−c2K2421−ρK2−λ2+a−c2K281−ρK2−3λ282−ρK2−9λ22,πrSR∗=12πrR∗+12πscC∗−πmR∗=a−c2K2421−ρK2−λ2−a−c2K281−ρK2−3λ282−ρK2−9λ22.(4)
Two-way cooperative coordination of domestic retailers sharing transportation costs of overseas suppliers and overseas suppliers sharing promotional costs of domestic retailers (SMR)At this point,(46)πmSMR∗=12πmMR∗+12πscC∗−πrMR∗=a−c2K2421−ρK2−λ2+a−c2K2481−ρK2−3λ2,πrSMR∗=12πrMR∗+12πscC∗−πmMR∗=a−c2K2421−ρK2−λ2−a−c2K2481−ρK2−3λ2.


### 5.3. Benefit-Sharing Coordination for Full Cooperation Decision-Making between Suppliers and Retailers (V)

The profit increment mechanism of the shared system is based on the profit increment of the whole supply chain under the decision of full cooperation, compared with that under the decision of non-cooperation or semi-cooperation. The system income increment is distributed to each member according to the proportion of the supply chain memberʼs input.Therefore, the input of overseas suppliers and domestic retailers is as follows, respectively:(47)Tm=ca−p+λθ2,(48)Tr=wa−p+λθ2+12K2θ22.


#### 5.3.1. Non-Cooperative Coordination between Suppliers and Retailers (VN)

Under this structure, the income increment of supply chain is as follows:(49)ΔπVN=πscC∗−πmN∗+πrN∗=a−c22K2−λ22K282−ρK2−λ2221−ρK2−λ2.Substituting the aforementioned values ofPN∗,θ2N∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(50)θmVN∗=TmNTmN+TrN=4c2−ρK2−λ24c3−ρ+a1−ρK2−a+7cλ2,θrVN∗=TrNTmN+TrN=4a1−ρ+cK2−a+3cλ24c3−ρ+a1−ρK2−a+7cλ2.Thus, the profits of overseas suppliers and domestic retailers after coordination are(51)πmVN∗=a−c2K242−ρK2−λ2+θmVN∗ΔπVN,πrVN∗=a−c22K2−λ2K282−ρK2−λ22+θrVN∗ΔπVN.


#### 5.3.2. Coordination of One-Way Cooperation of Retailers Sharing Suppliers’ Transport Costs (VM)

In this mode, the income increment of supply chain system is as follows:(52)ΔπVM=πscC∗−πmM∗+πrM∗=a−c2K2821−ρK2−λ2.Substituting formulas (12) and (13) PM∗,θ2M∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(53)θmVM∗=TmMTmM+TrM=4c21−ρK2−λ24a+c1−ρK2−a+3cλ2,θrVM∗=TrMTmM+TrM=a−c41−ρK2−λ24a+c1−ρK2−a+3cλ2.Thus, the profits of overseas suppliers and domestic retailers after coordination are as follows:(54)πmVM∗=a−c2K2421−ρK2−λ2+θmVM∗ΔπVM,πrVM∗=a−c2K2821−ρK2−λ2+θrVM∗ΔπVM.


#### 5.3.3. Coordination of One-Way Cooperation of Suppliers Sharing Retailers’ Publicity Costs (VR)

In this mode, the income increment of supply chain system is(55)ΔπVR=πscC∗−πmR∗+πrR∗=a−c2K221λ4−8λ29+ρK2+64K22282−ρK2−9λ2221−ρK2−λ2.Substituting formulas (19) and (20) PR∗,θ2R∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(56)θmVR∗=TmRTmR+TrR=2c82−ρK2−9λ23a−13cλ2+16c3−ρ+a1−ρK2,θrVR∗=TrRTmR+TrR=16a1−ρ+cK2+3a−7cλ23a−13cλ2+16c3−ρ+a1−ρK2.Thus, the profits of overseas suppliers and domestic retailers after coordination are(57)πmVR∗=2a−c2K282−ρK2−9λ2+θmVR∗ΔπVR,πrVR∗=4a−c2K24K2−3λ282−ρK2−9λ22+θrVR∗ΔπVR.


#### 5.3.4. Coordination of Two-Way Cooperation of Retailers Sharing Suppliers’ Transport Costs and Suppliers Sharing Retailersʼ Publicity Costs (VMR)

In this mode, the income increment of supply chain system is(58)ΔπVMR=πscC∗−πmMR∗+πrMR∗=a−c21−ρK2221−ρK2−λ281−ρK2−3λ2.Substituting formulas (27) and (28) PMR∗,θ2MR∗ into (47) and (49), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(59)θmVMR∗=TmMRTmMR+TrMR=8cρK281−ρK2−3λ232a+c1−ρρK22+6λ2c4−9ρ+aρK2−9cλ4,θrVMR∗=TrMRTmMR+TrMR=32a−c1−ρρK22+6λ2c4−5ρ+aρK2−9cλ432a+c1−ρρK22+6λ2c4−9ρ+aρK2−9cλ4.Thus, the profits of overseas suppliers and domestic retailers after coordination are(60)πmVMR∗=a−c2K281−ρK2−3λ2+θmVMR∗ΔπVMR,πrVMR∗=a−c2K2281−ρK2−3λ2+θrVMR∗ΔπVMR.


## 5.1. Coordination of the Full Cooperation Mode between Overseas Suppliers and Domestic Retailer (C)

In the mode of full cooperation, the members of the supply chain of cross-border e-commerce pay great attention to the maximization of the overall benefit, so they generally make joint decisions on the retail pricePC and propaganda strategy θ2C of the goods at the same time.Therefore, the profit of cross-border e-commerce supply chain under the mode of full cooperation is as follows:(39)πscC=p−ca−p+λθ2+ρa−p+λθ22−12K2θ22.Proposition 8.
Under the mode of full cooperation between overseas suppliers and domestic retailers, the optimal decision of cross-border e-commerce supply chain is(40)pC∗=a+c−2aρK2−cλ221−ρK2−λ2,θ2C∗=a−cλ21−ρK2−λ2.Proof.
Solved by reverse induction.
Firstly, determine Hessian matrix ofπscC for the domestic retailer profit function:(41)Hp,θ2=∂2πscC∂PC2∂2πscC∂PC∂θ2C∂2πscC∂θ2C∂PC∂2πscC∂θ2C2=−21−ρλ1−2ρλ1−2ρ−K2+2λ2ρ.
It is not difficult to see from the above Hessian matrix: when0<ρ<2K2−λ2/2K2, ∂2πrMR/∂PMR2=−21−ρ<0 and H=21−ρK2−λ2>0. Thus, πscC is a strictly joint concave function about PC and θ2C, and there is an optimal solution to maximize profits. So the first-order partial derivation conditions are as follows: pC∗=a+c−2aρK2−cλ2/21−ρK2−λ2 and θ2C∗=a−cλ/21−ρK2−λ2, and the market demand for commodities and the profits of cross-border e-commerce supply chain can be determined as(42)dC∗=a−cK221−ρK2−λ2,πscC∗=a−c2K2221−ρK2−λ2.


## 5.2. Shapley Value Method Coordination (S)

Shapley value method is a method of fair distribution of cooperative income based on the marginal contribution of individuals to the whole.For the non-cooperation mode and 3 semi-cooperation modes between overseas suppliers and domestic retailers, the Shapley value method is used to distribute the overall supply chain profits when the two fully cooperate, and the profits distributed by both sides under different cooperation modes can be obtained:(1)
Non-cooperative coordination between overseas suppliers and domestic retailers (SN)At this point,(43)πmSN∗=12πmN∗+12πscC∗−πrN∗=a−c2K2421−ρK2−λ2+a−c2K221−ρK2−λ2162−ρK2−λ22,πrSN∗=12πrN∗+12πscC∗−πmN∗=a−c2K2421−ρK2−λ2−a−c2K221−ρK2−λ2162−ρK2−λ22.(2)
One-way cooperative coordination of domestic retailers sharing transportation costs for overseas suppliers (SM)At this point,(44)πmSM∗=12πmM∗+12πscC∗−πrM∗=5a−c2K21621−ρK2−λ2,πrSM∗=12πrM∗+12πscC∗−πmM∗=3a−c2K21621−ρK2−λ2.(3)
One-way cooperative coordination of domestic retailers sharing publicity costs for overseas suppliers (SR)At this point,(45)πmSR∗=12πmR∗+12πscC∗−πrR∗=a−c2K2421−ρK2−λ2+a−c2K281−ρK2−3λ282−ρK2−9λ22,πrSR∗=12πrR∗+12πscC∗−πmR∗=a−c2K2421−ρK2−λ2−a−c2K281−ρK2−3λ282−ρK2−9λ22.(4)
Two-way cooperative coordination of domestic retailers sharing transportation costs of overseas suppliers and overseas suppliers sharing promotional costs of domestic retailers (SMR)At this point,(46)πmSMR∗=12πmMR∗+12πscC∗−πrMR∗=a−c2K2421−ρK2−λ2+a−c2K2481−ρK2−3λ2,πrSMR∗=12πrMR∗+12πscC∗−πmMR∗=a−c2K2421−ρK2−λ2−a−c2K2481−ρK2−3λ2.


## 5.3. Benefit-Sharing Coordination for Full Cooperation Decision-Making between Suppliers and Retailers (V)

The profit increment mechanism of the shared system is based on the profit increment of the whole supply chain under the decision of full cooperation, compared with that under the decision of non-cooperation or semi-cooperation. The system income increment is distributed to each member according to the proportion of the supply chain memberʼs input.Therefore, the input of overseas suppliers and domestic retailers is as follows, respectively:(47)Tm=ca−p+λθ2,(48)Tr=wa−p+λθ2+12K2θ22.


### 5.3.1. Non-Cooperative Coordination between Suppliers and Retailers (VN)

Under this structure, the income increment of supply chain is as follows:(49)ΔπVN=πscC∗−πmN∗+πrN∗=a−c22K2−λ22K282−ρK2−λ2221−ρK2−λ2.Substituting the aforementioned values ofPN∗,θ2N∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(50)θmVN∗=TmNTmN+TrN=4c2−ρK2−λ24c3−ρ+a1−ρK2−a+7cλ2,θrVN∗=TrNTmN+TrN=4a1−ρ+cK2−a+3cλ24c3−ρ+a1−ρK2−a+7cλ2.Thus, the profits of overseas suppliers and domestic retailers after coordination are(51)πmVN∗=a−c2K242−ρK2−λ2+θmVN∗ΔπVN,πrVN∗=a−c22K2−λ2K282−ρK2−λ22+θrVN∗ΔπVN.


### 5.3.2. Coordination of One-Way Cooperation of Retailers Sharing Suppliers’ Transport Costs (VM)

In this mode, the income increment of supply chain system is as follows:(52)ΔπVM=πscC∗−πmM∗+πrM∗=a−c2K2821−ρK2−λ2.Substituting formulas (12) and (13) PM∗,θ2M∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(53)θmVM∗=TmMTmM+TrM=4c21−ρK2−λ24a+c1−ρK2−a+3cλ2,θrVM∗=TrMTmM+TrM=a−c41−ρK2−λ24a+c1−ρK2−a+3cλ2.Thus, the profits of overseas suppliers and domestic retailers after coordination are as follows:(54)πmVM∗=a−c2K2421−ρK2−λ2+θmVM∗ΔπVM,πrVM∗=a−c2K2821−ρK2−λ2+θrVM∗ΔπVM.


### 5.3.3. Coordination of One-Way Cooperation of Suppliers Sharing Retailers’ Publicity Costs (VR)

In this mode, the income increment of supply chain system is(55)ΔπVR=πscC∗−πmR∗+πrR∗=a−c2K221λ4−8λ29+ρK2+64K22282−ρK2−9λ2221−ρK2−λ2.Substituting formulas (19) and (20) PR∗,θ2R∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(56)θmVR∗=TmRTmR+TrR=2c82−ρK2−9λ23a−13cλ2+16c3−ρ+a1−ρK2,θrVR∗=TrRTmR+TrR=16a1−ρ+cK2+3a−7cλ23a−13cλ2+16c3−ρ+a1−ρK2.Thus, the profits of overseas suppliers and domestic retailers after coordination are(57)πmVR∗=2a−c2K282−ρK2−9λ2+θmVR∗ΔπVR,πrVR∗=4a−c2K24K2−3λ282−ρK2−9λ22+θrVR∗ΔπVR.


### 5.3.4. Coordination of Two-Way Cooperation of Retailers Sharing Suppliers’ Transport Costs and Suppliers Sharing Retailersʼ Publicity Costs (VMR)

In this mode, the income increment of supply chain system is(58)ΔπVMR=πscC∗−πmMR∗+πrMR∗=a−c21−ρK2221−ρK2−λ281−ρK2−3λ2.Substituting formulas (27) and (28) PMR∗,θ2MR∗ into (47) and (49), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(59)θmVMR∗=TmMRTmMR+TrMR=8cρK281−ρK2−3λ232a+c1−ρρK22+6λ2c4−9ρ+aρK2−9cλ4,θrVMR∗=TrMRTmMR+TrMR=32a−c1−ρρK22+6λ2c4−5ρ+aρK2−9cλ432a+c1−ρρK22+6λ2c4−9ρ+aρK2−9cλ4.Thus, the profits of overseas suppliers and domestic retailers after coordination are(60)πmVMR∗=a−c2K281−ρK2−3λ2+θmVMR∗ΔπVMR,πrVMR∗=a−c2K2281−ρK2−3λ2+θrVMR∗ΔπVMR.


## 5.3.1. Non-Cooperative Coordination between Suppliers and Retailers (VN)

Under this structure, the income increment of supply chain is as follows:(49)ΔπVN=πscC∗−πmN∗+πrN∗=a−c22K2−λ22K282−ρK2−λ2221−ρK2−λ2.Substituting the aforementioned values ofPN∗,θ2N∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(50)θmVN∗=TmNTmN+TrN=4c2−ρK2−λ24c3−ρ+a1−ρK2−a+7cλ2,θrVN∗=TrNTmN+TrN=4a1−ρ+cK2−a+3cλ24c3−ρ+a1−ρK2−a+7cλ2.Thus, the profits of overseas suppliers and domestic retailers after coordination are(51)πmVN∗=a−c2K242−ρK2−λ2+θmVN∗ΔπVN,πrVN∗=a−c22K2−λ2K282−ρK2−λ22+θrVN∗ΔπVN.


## 5.3.2. Coordination of One-Way Cooperation of Retailers Sharing Suppliers’ Transport Costs (VM)

In this mode, the income increment of supply chain system is as follows:(52)ΔπVM=πscC∗−πmM∗+πrM∗=a−c2K2821−ρK2−λ2.Substituting formulas (12) and (13) PM∗,θ2M∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(53)θmVM∗=TmMTmM+TrM=4c21−ρK2−λ24a+c1−ρK2−a+3cλ2,θrVM∗=TrMTmM+TrM=a−c41−ρK2−λ24a+c1−ρK2−a+3cλ2.Thus, the profits of overseas suppliers and domestic retailers after coordination are as follows:(54)πmVM∗=a−c2K2421−ρK2−λ2+θmVM∗ΔπVM,πrVM∗=a−c2K2821−ρK2−λ2+θrVM∗ΔπVM.


## 5.3.3. Coordination of One-Way Cooperation of Suppliers Sharing Retailers’ Publicity Costs (VR)

In this mode, the income increment of supply chain system is(55)ΔπVR=πscC∗−πmR∗+πrR∗=a−c2K221λ4−8λ29+ρK2+64K22282−ρK2−9λ2221−ρK2−λ2.Substituting formulas (19) and (20) PR∗,θ2R∗ into (47) and (48), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(56)θmVR∗=TmRTmR+TrR=2c82−ρK2−9λ23a−13cλ2+16c3−ρ+a1−ρK2,θrVR∗=TrRTmR+TrR=16a1−ρ+cK2+3a−7cλ23a−13cλ2+16c3−ρ+a1−ρK2.Thus, the profits of overseas suppliers and domestic retailers after coordination are(57)πmVR∗=2a−c2K282−ρK2−9λ2+θmVR∗ΔπVR,πrVR∗=4a−c2K24K2−3λ282−ρK2−9λ22+θrVR∗ΔπVR.


## 5.3.4. Coordination of Two-Way Cooperation of Retailers Sharing Suppliers’ Transport Costs and Suppliers Sharing Retailersʼ Publicity Costs (VMR)

In this mode, the income increment of supply chain system is(58)ΔπVMR=πscC∗−πmMR∗+πrMR∗=a−c21−ρK2221−ρK2−λ281−ρK2−3λ2.Substituting formulas (27) and (28) PMR∗,θ2MR∗ into (47) and (49), the proportion of input from overseas suppliers and domestic retailers to the total input of the supply chain is(59)θmVMR∗=TmMRTmMR+TrMR=8cρK281−ρK2−3λ232a+c1−ρρK22+6λ2c4−9ρ+aρK2−9cλ4,θrVMR∗=TrMRTmMR+TrMR=32a−c1−ρρK22+6λ2c4−5ρ+aρK2−9cλ432a+c1−ρρK22+6λ2c4−9ρ+aρK2−9cλ4.Thus, the profits of overseas suppliers and domestic retailers after coordination are(60)πmVMR∗=a−c2K281−ρK2−3λ2+θmVMR∗ΔπVMR,πrVMR∗=a−c2K2281−ρK2−3λ2+θrVMR∗ΔπVMR.


## 6. Example Analysis

In order to further analyze and compare the rationality and effectiveness of decision-making in different cooperation modes, this paper verifies the above proposition by example analysis. Based on the investigated data, the relevant parameters can be set as the scale of domestic retailersʼ publicity activitiesK2=50, potential market demand a=100, fixed transportation costs per unit product c=5, and the sensitivity of consumers to retailersʼ publicity λ=0.6. The value range of marginal transportation cost factor per unit product ρ can be limited to range 0.1,0.7.Substituting the above parameters into the profit algebraic formula of supply chain members of Propositions1–4 and the corresponding algebraic formula after coordination, as ρ increases gradually in the range of values, the profits of the members of cross-border e-commerce will change accordingly. In order to observe the law of concrete change, the results of operations in different cooperative modes can be mapped to graphs to analyze the coordinating effect of the two coordination mechanisms, as shown in Figures 1–4.Figure 1
Impact of unit transport costs on member profits in theN mode.
(a)(b)Figure 2
Impact of unit transport costs on member profits in theM mode.
(a)(b)Figure 3
Impact of unit transport costs on member profits in theR mode.
(a)(b)Figure 4
Impact of unit transport costs on member profits in the MR mode.
(a)(b)It can be seen from Figures1–4 that, under different cooperation modes, the Shapley value method and full cooperation revenue increment sharing coordination mechanism can improve the profits of overseas suppliers and domestic retailers. Firstly, overseas suppliers under different cooperation modes are more willing to choose the Shapley value method for profit redistribution, while domestic retailers are more willing to choose the full cooperation incremental revenue sharing mechanism for profit redistribution; secondly, the larger the unit transportation cost is, the more obvious the profit redistribution is; the impact of these two coordination mechanisms on the profits of cross-border e-commerce supply chain members will be different; Finally, under the two semi-cooperation modes of domestic retailers participating in the sharing of transportation costs of overseas suppliers, the profit coordination effect of full cooperation benefits is increasing, which is generally not important for the sharing mechanism of overseas suppliers. Taking different coordination mechanisms as units, the results can be drawn into tables to analyze the changing trend of profit under different cooperation modes before and after coordination, as shown in Tables 1 and 2.Table 1
Profits of members of different cooperation modes under the Shapley value method mechanism.
ρ0.10.20.30.40.50.60.7πMSN∗1540.771696.061894.102156.762523.913076.454006.16πMSM∗1573.131770.662024.922364.452840.773557.414757.61πMSR∗1541.321696.661894.752157.462524.673077.274007.04πMSMR∗1572.821770.262024.402363.732839.743555.804754.73πRSN∗976.241137.001345.781626.362021.322615.403606.02πRSM∗943.881062.401214.951418.671704.462134.442854.57πRSR∗975.691136.411345.131625.662020.52614.583605.14πRSMR∗944.191062.801215.481419.381705.492136.062857.45Table 2
Profits of members of different cooperative modes under the full cooperation income incremental mechanism.
ρ0.10.20.30.40.50.60.7πMVN∗1255.331342.171446.971578.581754.202011.892453.71πMVM∗1318.331483.851696.901981.392380.482980.893986.34πMVR∗1255.691342.501447.201578.631753.802010.442449.38πMVMR∗1316.961482.221694.821978.532376.462974.623975.16πRVN∗1261.681490.891792.912204.532791.033679.965158.47πRVM∗1198.691349.211542.981801.732164.752710.963625.84πRVR∗1261.321490.561792.672204.492791.433681.415162.8πRVMR∗1200.061350.841545.061804.542168.772717.243637.02It can be seen from Tables1 and 2 that, under different cooperation modes, after the profits of supply chain members are coordinated by the Shapley value method and full cooperation revenue sharing mechanism, when the domestic retailers share the transportation costs of overseas suppliers, the suppliers get the maximum profits, while the domestic retailers get the maximum profits when the overseas suppliers and domestic retailers do not cooperate.


## 7. Conclusion

By constructing a cooperative game model of cross-border e-commerce supply chain composed of a single overseas supplier and a single domestic retailer, this paper explores how the propaganda strategy and transportation cost impact the pricing strategy of cross-border e-commerce. Meanwhile, the Shapley value method and the full cooperative income incremental sharing mechanism are introduced to redistribute the profits of supply chain members under different cooperation modes.By verifying the decision results of different cooperation modes, the following conclusions can be drawn:(1)
If domestic retailers pursue lower wholesale prices, they need to share the transportation costs of overseas suppliers and attract more consumers at lower retail prices. Therefore, retailers sharing transport risks with overseas suppliers can significantly reduce the cost of cross-border e-commerce to expand customer groups to enhance product sales and ultimately achieve an increase in profitability.(2)
The whole cross-border e-commerce supply chain is pursuing the most efficient commodity promotion strategy, and it needs two-way cooperation between overseas suppliers and domestic retailers; that is, domestic retailers share the transportation costs of overseas suppliers and overseas suppliers share the publicity costs of domestic retailers. This indicates that, in the cross-border e-commerce supply chain, domestic retailers share overseas suppliers as a win-win strategy.(3)
When the members of cross-border e-commerce supply chain choose the mode of first coordination and then cooperation, overseas suppliers generally choose retailers to share the total transportation costs of suppliers, while domestic retailers choose the non-cooperation mode; when the members of the cross-border e-commerce supply chain choose the mode of cooperation before coordination, most of the overseas suppliers will choose the Shapley value method to redistribute the profits, while the domestic retailers will choose the full cooperative income incremental sharing mechanism to redistribute the profits.(4)
Overseas suppliers under different cooperation modes are more willing to choose the Shapley value method for profit redistribution, while domestic retailers are more willing to choose the full cooperative income incremental sharing mechanism for profit redistribution. In addition, the greater the unit transportation cost is, the more obvious the effect of the two coordination mechanisms on the profits of the members of the cross-border e-commerce supply chain will be.Although our article has made a lot of contributions around these problems, there are still many places to continue to study. When the demand is uncertain, whether the same result will be obtained and what kind of change will happen when the supply chain structure changes are very interesting research issues.



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*Source: 5561357-2021-05-07.xml*