# Cooperative Advertising in Dual Channel Supply Chain System with Different Contracting Schemes

Authors: Qi Tan; Fengmin Yao; Tao Li; Bin Liu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This paper deals with the efficacy of revenue-sharing and cost-sharing contracts in a dual-exclusive channel, in which each manufacturer announces a cooperative advertising policy, such as cost-sharing contract, revenue-sharing contract, or neither of them, to its retailer. Under such cooperative advertising schemes, two models are developed—one in which each manufacturer determines the sharing rate endogenously or exogenously under the Stackelberg game approach and the other in which each manufacturer and its exclusive retailer cooperatively determine the sharing rate under the Nash bargaining approach. Some counterintuitive findings suggest that the advertising coordination mechanism critically depends on parameters, such as the basic demand share and product substitution. Most notably, the higher sharing rate can lead the retailer’s performance to be worse, especially when the competition becomes fierce. Furthermore, the cost-sharing contract is more beneficial to the cooperative advertising mechanism than the revenue-sharing contract.


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## Body

## 1. Introduction

The beverage industry features a highly competitive nature including price and advertising competitions, especially the soft drink market is almost a duopoly market. The average advertising expenditures by Coca-Cola or Pepsi are about $4 billion each year from 2015 to 2020 [1]. In the fast food industry, it is natural to see products of Coca or Pepsi alongside a burger on restaurant billboards. This case is a typical cooperative program, in which Coke or Pepsi often offer some incentive schemes to their partners who advertise to boost their sales. Cost-sharing (CS) has often been implemented in the form of cooperative advertising. In reality, most manufacturers set the cost-sharing rate arbitrarily and without detailed analysis to 50% or 100% [2]. However, according to Dutta et al. [3]; they pointed out that participation rates are higher only when there are fewer competitors. Bergen and John [4] demonstrate that the competition between channels has a significant impact on the participation rates. A question arises, is a higher cost-sharing rate always beneficial to the retailers? Meantime, a taste experiment sponsored by Pepsi Cola shows that consumers prefer Pepsi Cola over Coca-Cola if they are only guided by taste. Interestingly, the market share of Coca-Cola in the soft drink market accounts for 42.5%, which is larger than Pepsi’s [5]. The other question arises, how do market shares between two competing firms influence the efficiency of advertising? Furthermore, are there some other forms of cooperative advertising schemes that can be used to coordinate the supply chain?The cost-sharing contract is very prevalent in cooperative advertising, such as Aust and Buscher [6]; Aust and Buscher [7]; Huang et al. [8]; Szmerekovsky and Zhang [9]; SeyedEsfahani et al. [10]; Xie and Ai [11]; Xie and Neyret [12]; Zhao et al. [13]. The literature listed above is limited by the assumption that the cost-sharing rate is an endogenous variable in the single channel and show that the cost-sharing contract can coordinate the entire supply chain. This is because they adopt a centralized decision-making approach to characterize the cooperative advertising efficiency, in which they assume a unique decision maker announces both the manufacturer and the retailer advertising levels. It is obvious that the coordination can be achieved under such cooperative advertising assumption. However, the hypothesis of a centralized control is not realistic in marketing practices when supply chain members are independent economic entities [14]. Notably, we find that the coordination mechanism proposed by the aforementioned literature does not work well by comparing the scenarios with and with cost sharing. Moreover, Zhang et al. [15] use a very general function to demonstrate that cost-sharing is not an effective coordination mechanism when the cost-sharing rate is assumed to be endogenous. Additionally, all of the above-cited literature are limited to a cooperative advertising scheme in a single channel. Different from the above literature, Li et al. [16] examine the efficacy of different advertising structures in a dual-exclusive channel system and find that the endogenous cost-sharing cannot coordinate the entire supply chain. It remains unknown whether the cost-sharing contract can coordinate the competing supply chains when the cost-sharing rate is determined exogenously.Some literature investigates the cost-sharing efficiency for cooperative advertising in competing supply chains. For instance, Karray and Zaccour [17] discuss a duopoly common retailer channel and suggest that the higher competition leads to a Prisoner’s Dilemma for manufacturers. Yan and Pei [18] investigate channel conflict and coordination in a dual channel and find that the improved retail services effectively alleviate the channel conflict. Pei and Yan [19] investigate the effect of manufacturer advertising on alleviating channel conflictions in a dual channel. Liu et al. [20] discuss manufacturer advertising, retailer advertising and cooperative advertising in a dual-exclusive channel. They find the cost-sharing contract can coordinate the dual channel system under manufacturer advertising, while does not work well under retailer advertising. Most of the literature listed above, however, considers the cost-sharing rate as an exogenous variable and suggest that cost-sharing contract is an effective coordination mechanism. Among the exceptions, Karray and Amin [21] investigate the cost-sharing efficiency in a monopoly common manufacturer channel by assuming the cost-sharing rate to be an endogenous variable. However, the above literature assumes the cost-sharing rate to be endogenous, likewise, it remains unknown whether the cost-sharing contract can coordinate the competing supply chains when the cost-sharing rate is determined exogenously.According to Cachon and Lariviere [22]; they point out that the revenue-sharing contract (RS) particularly suites for the video rental industry. Although the popularity of the revenue-sharing contract, limited literature applies this contract into the cooperative advertising scheme in a dual-exclusive channel. In practice, Apple has revenue-sharing arrangements with its retailers who advertise its products [23]. There are some literatures investigating the efficacy of revenue sharing in a single supply chain. He et al. [24] consider a dynamic advertising strategy in a single supply chain and find that it is not always profitable for the manufacturer to offer a cost-sharing contract. Kunter [23] investigates the efficiency of revenue-sharing and cost-sharing contracts in a single channel. Note that the revenue-sharing contract is not popular to deal with the conflict of cooperative advertising in the offline business. Our work follows this trend but from a different perspective under the revenue-sharing rate assumed to be endogenous or exogenous in a dual-exclusive channel system, and tries to explain why the revenue-sharing contract is far less common in the marketing practices.Furthermore, our study is closely related to Karray and Amin [21] who investigate how competition affects the cost-sharing efficiency in a monopoly common manufacturer channel. Our paper is also closely related to He et al. [24] and Kunter [23] who consider cooperative advertising with cost sharing and revenue sharing in a single channel. However, none of the literature to date has considered the cost-sharing and revenue-sharing efficacies in a dual-exclusive channel. To differ from the previous literature, this study develops two models—one in which each manufacturer determines the sharing rate endogenously or exogenously under the Stackelberg game approach and the other in which each manufacturer and its exclusive retailer cooperatively determine the sharing rate under the Nash bargaining approach, in a dual-exclusive channel. We first investigate a non-cooperative advertising program. Our findings indicate that advertising is never a competitive tool for the small firm if its market share is sufficiently small. We then study the efficiency of cost sharing and revenue sharing with the sharing rate either as an endogenous variable or as an exogenous variable. If the sharing rate is endogenous, neither the cost-sharing contract nor the revenue-sharing contract is an effective coordination mechanism; if the sharing rate is exogenous, both cost-sharing and revenue-sharing are effective coordination mechanisms when the competition is sufficiently small. Further, an optimal sharing rate can be used to deal with the confliction for the cooperative advertising framework under the Nash bargaining approach. Most notably, we find that the cost-sharing contract is more beneficial to the cooperative advertising mechanism than the revenue-sharing contract.The most related studies are presented in Table1. For simplicity, we use symbols, WP, RP, MA, RA, and SR to represent wholesale price, retail price, manufacturer advertising level, retailer advertising level, and sharing rate, respectively.Table 1
Comparison of previous studies with the current study.
AuthorsNumber of channel membersContract typeEndogenous and exogenous sharing rateBargaining sharing rateDecision variablesManufacturerRetailerRSCSHe et al. [24]11√√WP, RP, RA, SRKunter [23]11√√WP, RP, MA, RALiu et al. [20]22√WP, RP, MA, RAKarray and Amin [21]12√WP, RP, MA, RA, SRLi et al. [16]22√√WP, RP, MA, RA, SRThis paper22√√√√WP, RP, MA, RA, SR


## 2. Model Formulation and Notation

Consider a dual-exclusive channel where each manufacturer sells its goods through an exclusive retailer. The manufacturer and the retailer in each channel engage in price and advertising competitions with rivals. The dual-exclusive channel system is not rare in real life. In China, McDonald and Coca-Cola constitute a supply chain to compete with other supply chains such as Kentucky Fried Chicken and Pepsi-Cola. Advertising is a crucial tool to improve a firm’s competitiveness and market share, and it may come from both manufacturers and retailers. To model the influence of advertising on sales, we employ the framework of Xie and Wei [14] and Liu et al. [20] to characterize the demand for channel i,(1)Di=Yi−θY3−i−pi+θp3−i1−θ2,where Yi=Ai+HmiKmiemi+HriKrieri. The impact of advertising is embedded in Yi. Ai is channel i’s initial base market share; To obtain simplicity, a new parameter called “the demand ratio,” Ω≡A1/A2, is added to measure the degree of asymmetry between the two channels. The demand ratio is symmetric if Ω=1; otherwise, it is asymmetric. Ω>1 means channel 1’s market size is larger than channel 2’s. HmiandHri equal to 0 or 1, which is the indicator of whether manufacturer (retailer) i advertises; Kmi and Kri represent the advertising efficacy of manufacturer i and retailer i. For simplicity, Kmi and Kri are normalized to 1. emi and eri represent manufacturer i’s advertising level and retailer i’s advertising level; pi is the retail price and wi is the wholesale price. θ (0 < θ < 1) captures the competition between channels 1 and 2. It is worth noting that, the above demand function is different from the general demand function adopted by Barman et al. [25]; Sana [26]; Sana [27], and Taleizadeh et al. [28].To obtain more management insights, we use the forms ofemi2 and eri2 provided by He et al. [24] and Liu et al. [20] to characterize advertising expenditures for manufacturer i and retailer i, respectively (Most of our results continue to be held if advertising expenditures are assumed to be in forms of emi and eri). Moreover, to encourage retailer i performs advertising, we assume manufacturer i will announce a cooperative advertising policy, such as cost-sharing contract, revenue-sharing contract, or neither of them, to its retailer. Under such assumption, the profit functions for manufacturer i (πmi) and retailer i (πri) are as follows:(2)Maxπmiwi,emi,Φi,ψi=1−ψiwi−ciDi−Hmiemi2−HriΦieri2,Maxπripi,eri=pi−wiDi+ψiwiDi−Hri1−Φieri2subjectto:0<wi<pi<1,0≤Φi<1,0≤ψi<1where Φi0≤Φi<1 and ψi0≤ψi<1 represent cost-sharing rate and revenue-sharing rate respectively; ci represents channel i’s operation and production cost, without losing generality, ci is l is normalized to zero. For brevity, we use the subscripts NN, AA, RAA, CC, and RR to denote the corresponding incentive scheme, respectively. Scenario NN: neither manufacturers nor retailers advertise (Hmi=0, Hri=0, Φi=0, ψi=0); Scenario AA: both manufacturers and retailers advertise (Φi=0, ψi=0); Scenario RAA: Retailers advertise solely (Hmi=0, Φi=0, ψi=0); Scenario CC: cooperative advertising with cost-sharing contract (ψi=0); RR: cooperative advertising with revenue-sharing contract (Φi=0).


## 3. Advertising without Sharing

In order to examine how the advertising effort affects the profitability of advertisers, we first study the advertising program without any incentive schemes.


### 3.1. Comparison: AA versus NN

In Scenario AA, each manufacturer first announces its wholesale price and advertising level using the response functions of retailers 1 and 2, and then each retailer determines its retail price and advertising level given the wholesale prices and manufacturer advertising levels. Through the comparison of the equilibrium outcomes with and without advertising, we can check whether a channel member has an incentive to advertise.Theorem 1.
Although advertising is a dominant strategy and equilibrium, advertising is never a viable competitive tool for small firms; The advertising Pareto zone for retailers is larger than that for manufacturers. Such that,(i)
AA benefits a channel member with a larger base demand (e.g., region C orD);(ii)
AA benefits manufacturers and retailers in region A, and benefits retailers in region B.Theorem1 tells us an interesting result that both manufacturers and retailers have incentives to advertise, and these incentives critically depend on the relative demand ratio. Advertising benefits the channel member with a larger base demand but hurts the one with a smaller base demand. Note that only the market share gap between two channels is sufficiently large can the small advertiser be worse off. In practice, the market share gap between Pepsi Cola and Coca-Cola is small in the soft drink market. Hence, Pepsi Cola consistently advertises to maintain its market share; otherwise, it will lose the market share to the other large competitors, such as Coca-Cola. Interestingly, Theorem 1 also reveals that retailers have a larger advertising Pareto zone than manufacturers, which implies that retailers at the end of the market and thereby undertake more effective advertising. This observation can be used to explain the prevalence of retailer advertising without manufacturer subsidies in current business practices. Note that if we extend our discussion to the symmetry case (Ω=1), the conclusion in Theorem 1 still holds for manufacturers. For the retailer's perspective, they always get the best performance in Scenario AA. It is evident that the asymmetric market share does change the nature of equilibrium in our model.As shown in Figure1, it is mutually beneficial for manufacturers and retailers to advertise in region A. This is because wiNN<wiAA, piNN<piAA, DiNN<DiAA in region A, and thereby increases the revenue of channel members. In region B, advertising only benefits retailers. Figure 1 also shows that advertising benefits channel member 1 (2) but hurts channel member 2 (1) in region C (region D).To explain why a channel member with a smaller base market does not advertise in equilibrium, we will explore properties for price elasticity.Figure 1
Manufacturers’ (M) and retailers’ (R) preferences with and without advertising given Ω≠1.Corollary 1.
Under Scenario AA, a channel member’s price increases with its own base demand/advertising effort but decreases with its rival’s (e.g.,∂j1AA/∂Ω>0and∂j2AA/∂Ω<0j∈w,p).Corollary1 indicates that the large advertising expenditure/base demand unambiguously tends to increase its own price, but to decrease the rival firm (e.g., ∂p1AA/∂em1>0 and ∂p1AA/∂em2<0). This observation means that the advertiser with a smaller base demand triggers a heightened price competition, and thereby the small firm cut price but the large firm raise price, which can be best explained using Figure 2 (e.g., p1NN>p1AA for ΩL<Ω<Ω^p1−1AA−NN ). Consequently, advertising is never a competitive tool for a small advertiser if its market shares are sufficiently different from rivals.Figure 2
Channel members’ pricing decisions with and without advertising givenΩ≠1.


### 3.2. Comparison: AA versus RAA

In the aforementioned analysis, we present the analysis of advertising performed by all channel members. As a matter of fact, it is natural to see that large retailers, such as Walmart and Target, often advertise certain products so that many of their suppliers do not need to (Note that the result in Theorem2 continues to hold if advertising is performed solely by manufacturers. Therefore, we omit it for brevity). In this regard, compare profits between scenarios AA and RAA to explore if it is necessary for manufacturers to advertise.Theorem 2.
There is no need for manufacturerito advertise if and only if ΩL<Ω≤Ω^m1−1AA−RAA.Theorem2 answers the research question under what market conditions should manufacturer i advertises. Intuitively, one might think that manufacturer i has an incentive to advertise, as advertising is a useful tool for demand creation. However, Theorem 1 indicates that the profitability for manufacturers depends on their base market share. For instance, when a channel obtain the larger basic market share (Ω^m1−1AA−RAA<Ω<ΩU), it is always profitable for the manufacturer with the larger base market to advertise. The reason can be referred to Corollary 1. Further, Theorem Theorem 2 continues to hold when the relative demand ratio is symmetric. Combining Theorems 1 and 2, we obtain Insight 1:Insight 1: Advertising is never a competitive tool for the small firm in competing supply chains.


## 3.1. Comparison: AA versus NN

In Scenario AA, each manufacturer first announces its wholesale price and advertising level using the response functions of retailers 1 and 2, and then each retailer determines its retail price and advertising level given the wholesale prices and manufacturer advertising levels. Through the comparison of the equilibrium outcomes with and without advertising, we can check whether a channel member has an incentive to advertise.Theorem 1.
Although advertising is a dominant strategy and equilibrium, advertising is never a viable competitive tool for small firms; The advertising Pareto zone for retailers is larger than that for manufacturers. Such that,(i)
AA benefits a channel member with a larger base demand (e.g., region C orD);(ii)
AA benefits manufacturers and retailers in region A, and benefits retailers in region B.Theorem1 tells us an interesting result that both manufacturers and retailers have incentives to advertise, and these incentives critically depend on the relative demand ratio. Advertising benefits the channel member with a larger base demand but hurts the one with a smaller base demand. Note that only the market share gap between two channels is sufficiently large can the small advertiser be worse off. In practice, the market share gap between Pepsi Cola and Coca-Cola is small in the soft drink market. Hence, Pepsi Cola consistently advertises to maintain its market share; otherwise, it will lose the market share to the other large competitors, such as Coca-Cola. Interestingly, Theorem 1 also reveals that retailers have a larger advertising Pareto zone than manufacturers, which implies that retailers at the end of the market and thereby undertake more effective advertising. This observation can be used to explain the prevalence of retailer advertising without manufacturer subsidies in current business practices. Note that if we extend our discussion to the symmetry case (Ω=1), the conclusion in Theorem 1 still holds for manufacturers. For the retailer's perspective, they always get the best performance in Scenario AA. It is evident that the asymmetric market share does change the nature of equilibrium in our model.As shown in Figure1, it is mutually beneficial for manufacturers and retailers to advertise in region A. This is because wiNN<wiAA, piNN<piAA, DiNN<DiAA in region A, and thereby increases the revenue of channel members. In region B, advertising only benefits retailers. Figure 1 also shows that advertising benefits channel member 1 (2) but hurts channel member 2 (1) in region C (region D).To explain why a channel member with a smaller base market does not advertise in equilibrium, we will explore properties for price elasticity.Figure 1
Manufacturers’ (M) and retailers’ (R) preferences with and without advertising given Ω≠1.Corollary 1.
Under Scenario AA, a channel member’s price increases with its own base demand/advertising effort but decreases with its rival’s (e.g.,∂j1AA/∂Ω>0and∂j2AA/∂Ω<0j∈w,p).Corollary1 indicates that the large advertising expenditure/base demand unambiguously tends to increase its own price, but to decrease the rival firm (e.g., ∂p1AA/∂em1>0 and ∂p1AA/∂em2<0). This observation means that the advertiser with a smaller base demand triggers a heightened price competition, and thereby the small firm cut price but the large firm raise price, which can be best explained using Figure 2 (e.g., p1NN>p1AA for ΩL<Ω<Ω^p1−1AA−NN ). Consequently, advertising is never a competitive tool for a small advertiser if its market shares are sufficiently different from rivals.Figure 2
Channel members’ pricing decisions with and without advertising givenΩ≠1.


## 3.2. Comparison: AA versus RAA

In the aforementioned analysis, we present the analysis of advertising performed by all channel members. As a matter of fact, it is natural to see that large retailers, such as Walmart and Target, often advertise certain products so that many of their suppliers do not need to (Note that the result in Theorem2 continues to hold if advertising is performed solely by manufacturers. Therefore, we omit it for brevity). In this regard, compare profits between scenarios AA and RAA to explore if it is necessary for manufacturers to advertise.Theorem 2.
There is no need for manufacturerito advertise if and only if ΩL<Ω≤Ω^m1−1AA−RAA.Theorem2 answers the research question under what market conditions should manufacturer i advertises. Intuitively, one might think that manufacturer i has an incentive to advertise, as advertising is a useful tool for demand creation. However, Theorem 1 indicates that the profitability for manufacturers depends on their base market share. For instance, when a channel obtain the larger basic market share (Ω^m1−1AA−RAA<Ω<ΩU), it is always profitable for the manufacturer with the larger base market to advertise. The reason can be referred to Corollary 1. Further, Theorem Theorem 2 continues to hold when the relative demand ratio is symmetric. Combining Theorems 1 and 2, we obtain Insight 1:Insight 1: Advertising is never a competitive tool for the small firm in competing supply chains.


## 4. Advertising with Endogenous Sharing Rate

Cost-sharing and revenue-sharing contracts have been commonly used to coordinate the conflict in cooperative advertising schemes. In this section, we will explore the efficacy of cost sharing and revenue sharing under the sharing rate assumed to be endogenous. In the first stage, each manufacturer decides its sharing rate, advertising level, and wholesale price using the response functions of retailers 1 and 2. In the second stage, each retailer announces its retail price and advertising level conditional on the competitor’s retail price and advertising level. For tractability, the demand ratio is assumed to be symmetric (Ω=1).


### 4.1. Advertising with Endogenous Cost-Sharing Rate

Under the symmetric setting, for a meaningful discussion, the sharing rate and must be non-negative, such thatθ∈0,0.58. Under this constrains, the optimal cost-sharing rate can be characterized by backward induction:Proposition 1.
Under cooperative advertising with cost sharing, there is an optimal cost-sharing rate, which critically depends on the parameters, such that the wholesale price and the manufacturer advertising effort. The optimal sharing rate is(3)ΦmiCS=13−8θ−8θ2−25+32θ−40θ2+16θ424−8θ−12θ2if1−emiCS3<wiCS<1,otherwiseΦmiCS=0,,and decreases with the product substitutability.Proposition1 tells us that manufacturer i’ sharing policy depends on its wholesale price, as well as advertising effort. In particular, if the wholesale price is relatively high such that 1−emiCC/3<wiCC<1, manufacturers will offer advertising allowance to the retailers, otherwise they will offer nothing, which is sharply contrasted with Huang et al. [8] and SeyedEsfahani et al. [10]; as they assume prices as exogenous variables. This finding implies that the higher product substitutability will induce channel members to lower their share rates. Additionally, the cost-sharing rate decreases with the degree of competition and is in the range of 0 to 33%. Proposition 1 also indicates that Scenario CC is equivalent to Scenario AA if the wholesale price is relatively small (e.g., 0<wiCC≤1−eiCC/3).We now investigate how the cost-sharing contract impacts the channel member’s profitability.Theorem 3.
Under cooperative advertising with cost sharing, manufactureri always prefers cost-sharing contract, whereas retailer i always prefers no cost-sharing contract.Intuitively, an advertiser should be benefited from the sharing scheme offered by its partner. Theorem 3, however, shows a counter-intuitive result that retaileri does not have an incentive to participate in the cooperative advertising program, though manufacturer i bears some portion of the advertising expenditures. This finding is in line with Karray and Amin [21] in which cost sharing is not beneficial to competing retailers under certain conditions, but from a different perspective with manufacturer advertising in a dual-exclusive channel. We also depict the result in Figures 3 and 4, cost-sharing benefits manufacturer i but hurts retailer i. In summary, the cost-sharing contract is not an effective coordination mechanism when the cost-sharing rate is decided by the manufacturer.Figure 3
Comparing manufactureri’s profit with and without cost-sharing (Ω=1).Figure 4
Comparing retaileri’s profit with and without cost-sharing (Ω=1).


### 4.2. Advertising with Endogenous Revenue-Sharing Rate

The cost-sharing contract cannot coordinate the entire supply chain system, which motivates us to investigate whether the revenue-sharing contract can work well. Similarly, the optimal revenue-sharing rate is given as follows:Proposition 2.
Under cooperative advertising with revenue sharing, there is an optimal revenue-sharing rate, which depends critically on the parameters, such that the wholesale price and manufacturer advertising effort. The optimal revenue-sharing rate is(4)ΨiRR=1−9−12θ2+4θ436θ−64θ3+16θ5if0<wiRR<1+emiRR−Λ4or1+emiRR+Λ4<wiRR<1,otherwiseΨiRR=0,,and increases and then decreases with product substitutability. Where Λ=1+2emi−11+8θ−8θ2emi2.Similar to Propositions1, Proposition 2 demonstrates that manufacturer i’ revenue-sharing policy depends on their wholesale price, as well as the advertising efforts. However, contrary to Proposition 1, the optimal revenue-sharing rate increases and then decreases with product substitutability. This is because revenue-sharing drives up the wholesale price (e.g., wiRR>wiAA) and the demand (e.g., DiRR>DiAA), which in turn drives up manufacturer advertising level. Further, the revenue-sharing encourages retailer i to raise its advertising effort and thereby intensifies the competition between two channels. The competition erodes manufacturers’ profits. Consequently, manufacturers cut the revenue-sharing rate when the competition is relatively high.Similar to the scenario with cost sharing, comparing profits between Scenarios RR and AA gives the following result:Theorem 4.
Under cooperative advertising with revenue sharing, manufactureri prefers revenue sharing when product substitutability is relatively small, whereas retailer i always prefers no revenue sharing.Similar to the scenario with cost sharing, Theorem4 shows that retailer i has no incentive to participate in the cooperative advertising program. But for manufacturer i, the incentive depends on the degree of substitution between the two channels. Specifically, the higher product substitutability will lead manufacturer i to violate the cooperative advertising program, as shown in Figures 5 and 6 (e.g., πmiRR≤πmiAA for θ∈0.6,0.75). Combined with Theorem 3, the insight can be derived as follows:Insight 2: when the sharing rate is endogenous, cooperative advertising with cost or revenue-sharing contract cannot coordinate the dual-exclusive channel system.Figure 5
Comparing channel manufactureri’s profit with and without revenue-sharing given Ω=1.Figure 6
Comparing channel retaileri’s profit with and without revenue-sharing given Ω=1.


## 4.1. Advertising with Endogenous Cost-Sharing Rate

Under the symmetric setting, for a meaningful discussion, the sharing rate and must be non-negative, such thatθ∈0,0.58. Under this constrains, the optimal cost-sharing rate can be characterized by backward induction:Proposition 1.
Under cooperative advertising with cost sharing, there is an optimal cost-sharing rate, which critically depends on the parameters, such that the wholesale price and the manufacturer advertising effort. The optimal sharing rate is(3)ΦmiCS=13−8θ−8θ2−25+32θ−40θ2+16θ424−8θ−12θ2if1−emiCS3<wiCS<1,otherwiseΦmiCS=0,,and decreases with the product substitutability.Proposition1 tells us that manufacturer i’ sharing policy depends on its wholesale price, as well as advertising effort. In particular, if the wholesale price is relatively high such that 1−emiCC/3<wiCC<1, manufacturers will offer advertising allowance to the retailers, otherwise they will offer nothing, which is sharply contrasted with Huang et al. [8] and SeyedEsfahani et al. [10]; as they assume prices as exogenous variables. This finding implies that the higher product substitutability will induce channel members to lower their share rates. Additionally, the cost-sharing rate decreases with the degree of competition and is in the range of 0 to 33%. Proposition 1 also indicates that Scenario CC is equivalent to Scenario AA if the wholesale price is relatively small (e.g., 0<wiCC≤1−eiCC/3).We now investigate how the cost-sharing contract impacts the channel member’s profitability.Theorem 3.
Under cooperative advertising with cost sharing, manufactureri always prefers cost-sharing contract, whereas retailer i always prefers no cost-sharing contract.Intuitively, an advertiser should be benefited from the sharing scheme offered by its partner. Theorem 3, however, shows a counter-intuitive result that retaileri does not have an incentive to participate in the cooperative advertising program, though manufacturer i bears some portion of the advertising expenditures. This finding is in line with Karray and Amin [21] in which cost sharing is not beneficial to competing retailers under certain conditions, but from a different perspective with manufacturer advertising in a dual-exclusive channel. We also depict the result in Figures 3 and 4, cost-sharing benefits manufacturer i but hurts retailer i. In summary, the cost-sharing contract is not an effective coordination mechanism when the cost-sharing rate is decided by the manufacturer.Figure 3
Comparing manufactureri’s profit with and without cost-sharing (Ω=1).Figure 4
Comparing retaileri’s profit with and without cost-sharing (Ω=1).


## 4.2. Advertising with Endogenous Revenue-Sharing Rate

The cost-sharing contract cannot coordinate the entire supply chain system, which motivates us to investigate whether the revenue-sharing contract can work well. Similarly, the optimal revenue-sharing rate is given as follows:Proposition 2.
Under cooperative advertising with revenue sharing, there is an optimal revenue-sharing rate, which depends critically on the parameters, such that the wholesale price and manufacturer advertising effort. The optimal revenue-sharing rate is(4)ΨiRR=1−9−12θ2+4θ436θ−64θ3+16θ5if0<wiRR<1+emiRR−Λ4or1+emiRR+Λ4<wiRR<1,otherwiseΨiRR=0,,and increases and then decreases with product substitutability. Where Λ=1+2emi−11+8θ−8θ2emi2.Similar to Propositions1, Proposition 2 demonstrates that manufacturer i’ revenue-sharing policy depends on their wholesale price, as well as the advertising efforts. However, contrary to Proposition 1, the optimal revenue-sharing rate increases and then decreases with product substitutability. This is because revenue-sharing drives up the wholesale price (e.g., wiRR>wiAA) and the demand (e.g., DiRR>DiAA), which in turn drives up manufacturer advertising level. Further, the revenue-sharing encourages retailer i to raise its advertising effort and thereby intensifies the competition between two channels. The competition erodes manufacturers’ profits. Consequently, manufacturers cut the revenue-sharing rate when the competition is relatively high.Similar to the scenario with cost sharing, comparing profits between Scenarios RR and AA gives the following result:Theorem 4.
Under cooperative advertising with revenue sharing, manufactureri prefers revenue sharing when product substitutability is relatively small, whereas retailer i always prefers no revenue sharing.Similar to the scenario with cost sharing, Theorem4 shows that retailer i has no incentive to participate in the cooperative advertising program. But for manufacturer i, the incentive depends on the degree of substitution between the two channels. Specifically, the higher product substitutability will lead manufacturer i to violate the cooperative advertising program, as shown in Figures 5 and 6 (e.g., πmiRR≤πmiAA for θ∈0.6,0.75). Combined with Theorem 3, the insight can be derived as follows:Insight 2: when the sharing rate is endogenous, cooperative advertising with cost or revenue-sharing contract cannot coordinate the dual-exclusive channel system.Figure 5
Comparing channel manufactureri’s profit with and without revenue-sharing given Ω=1.Figure 6
Comparing channel retaileri’s profit with and without revenue-sharing given Ω=1.


## 5. Advertising with Exogenous Sharing Rate

From Theorems3 and 4, we find that if the manufacturer is allowed to decide both its sharing rate and wholesale price in the first stage, the game will have unreasonable outcomes. In the following, the major concern is whether the sharing parameter determined exogenously is capable of leading channel members to achieve Pareto improvement in their profits.


### 5.1. Advertising with Exogenous Cost-Sharing Rate

The equilibrium threshold value is difficult to be solved analytically for the retaileri if the cost-sharing rate is decided exogenously, we will use Plot3D (Mathematica procedure) to analyze the efficiency of cost sharing on channel members’ profitability. Combing Figures 7 and 8, there must be a threshold Φ^riCC−AA∈0,Φ^miCC−AA to coordinate the overall supply chain.Figure 7
Manufactureri (Mi) preference with and without cost-sharing given Ω=1.Figure 8
Comparing retaileri’s profit with and without cost-sharing given Ω=1.Theorem 5.
Under cooperative advertising with cost sharing, a cost-sharing threshold value can be used to coordinate the entire supply chain system when the cost-sharing rate is relatively low.Although we might have expected retaileri could be better off if its partners bear some portion of advertising cost, Theorem 5 is somewhat counterintuitive that retailer i could be worse off when the cost-sharing rate is high. In particular, it is mutually beneficial for both manufacturer i and retailer i to adopt the cost-sharing contract when the cost-sharing rate is sufficient low, since cost-sharing leads all channel members to invest more on advertising expenditures and in turn expand the market demand. However, if the cost-sharing rate becomes high, retailer i will violate the coordination. This is because the advertising subsidy provided by manufacturer i result in a higher retailer advertising level, which intensifies the supply chain competition and in turn erodes retailer i’ profit. Moreover, manufacturer i can recover its advertising subsidy by increasing the wholesale price. Hence, only manufacturer i prefers the cost-sharing mechanism. As the cost-sharing rate becomes sufficiently larger such that ΦmiRR−AA<Φ<ΦmiU, neither manufacturer i nor retailer i have incentives to participate in the coordinate mechanism, as shown in Figures 7 and 8.Given the asymmetric setting, there exists a cost-sharing threshold value to coordinate the confliction in cooperative adverting program. As shown in Figure9, when the competition is low, CC is a dominated strategy for manufacturers and retailers in region A, which implies there is a common feasible area to guarantee all channel members to be better off. As the competition intensifies, CC benefits the manufacturers, while hurting the retailers. It is worth noting that the advertising with cost-sharing Pareto zone is larger for manufacturers.Figure 9
Manufacturers (M) and retailers (R) preferences with and without cost-sharing given Φ=0.125.


### 5.2. Advertising with Exogenous Revenue-Sharing Rate

The game rule is similar to the scenario with cost-sharing when the revenue-sharing rate is exogenous. By comparing channel members’ profits with and without revenue sharing, we obtain the following theorem:Theorem 6.
Under cooperative advertising with revenue sharing, a revenue-sharing threshold value (ψriRR−AA) can be used to coordinate the entire supply chain as long as 0<ψ<ψriRR−AA. Such that both manufacturer i and retailer i prefer revenue sharing to no revenue sharing as long as 0<ψ≤ψriRR−AA,where ψriRR−AA=45−72θ−264θ2+144θ3+452θ4−64θ5−304θ6+64θ8/3−2θ299+36θ−294θ2−72θ3+264θ4+32θ5−64θ6.Theorem6, is similar to Theorem 5, it also reveals that the revenue-sharing contract can coordinate the entire supply chain when the demand ratio is symmetric. The reason is identical to the scenario with cost sharing. We also depict Theorem 5 in Figure 10, both manufacturer i and retailer i benefit from the revenue-sharing contract in Region A, while only manufacturer i prefer the contract in Region B. Note that in region C, if the revenue-sharing rate is high and the competition is moderate, both manufacturer i and retailer i will violate the cooperation. This result implies that the higher revenue-sharing rate intensifies the horizontal competition.Given the asymmetric setting, there is also a Pareto improvement zone for both manufacturers and retailers. As shown in Figure11, RR is a dominated strategy for the manufacturers and the retailers in region A. RR is a dominated strategy for the manufacturers in region A. It is worth noting that the revenue-sharing contract fails to solve the confliction for the cooperative advertising framework when the competition becomes fierce. Additionally, the advertising with revenue sharing or cost-sharing Pareto zone is larger for manufacturers, which is sharply contracted with Theorem 1. Combing Theorems 5 and 6 gives us insight 3:Insight 3: Given the sharing rate exogenous, cooperative advertising with cost or revenue-sharing contract is capable of coordinating the dual-exclusive channel system when the competition is low. Nerveless, neither the cost-sharing nor the revenue-sharing works well when the completion is fierce.Figure 10
Manufactureri (Mi) and retailer i (Ri) preferences with and without revenue-sharing given Ω=1.Figure 11
Manufacturers (M) and retailers (R) preferences with and without revenue-sharing given ψ=0.125.


### 5.3. Comparison: Revenue Sharing versus Cost-Sharing

So far, we have discussed the cost-sharing and the revenue-sharing efficiencies for channel members in the aforementioned sections. In the foregoing section, we will check which contract is better for the whole channel. Given the exogenous sharing rate assumption, we fail to analytically solve the equilibrium results. For simplicity, givenθ=0.2, θ=0.6, and Ω=1, which can deliver us more management insights.For a channel perspective, as vividly shown in Figures12 and 13, the cost-sharing contract is more beneficial to channel i, which means that cost-sharing contract more suites for coordinating the conflict in the cooperative advertising program. This observation can be used to explain the reason why the cost-sharing is widely used in market practices. Note that Li et al. [29] demonstrate that the revenue-sharing contract is suite for the green supply chain.Insight 4: Given the sharing rate exogenous, the cost-sharing efficiency outperforms the revenue-sharing efficiency under the cooperative advertising framework.Figure 12
Comparing channeli’s profit: revenue sharing versus cost-sharing given θ=0.2 and Ω=1.Figure 13
Comparing channeli’s profit: revenue sharing versus cost-sharing given θ=0.6 and Ω=1.


## 5.1. Advertising with Exogenous Cost-Sharing Rate

The equilibrium threshold value is difficult to be solved analytically for the retaileri if the cost-sharing rate is decided exogenously, we will use Plot3D (Mathematica procedure) to analyze the efficiency of cost sharing on channel members’ profitability. Combing Figures 7 and 8, there must be a threshold Φ^riCC−AA∈0,Φ^miCC−AA to coordinate the overall supply chain.Figure 7
Manufactureri (Mi) preference with and without cost-sharing given Ω=1.Figure 8
Comparing retaileri’s profit with and without cost-sharing given Ω=1.Theorem 5.
Under cooperative advertising with cost sharing, a cost-sharing threshold value can be used to coordinate the entire supply chain system when the cost-sharing rate is relatively low.Although we might have expected retaileri could be better off if its partners bear some portion of advertising cost, Theorem 5 is somewhat counterintuitive that retailer i could be worse off when the cost-sharing rate is high. In particular, it is mutually beneficial for both manufacturer i and retailer i to adopt the cost-sharing contract when the cost-sharing rate is sufficient low, since cost-sharing leads all channel members to invest more on advertising expenditures and in turn expand the market demand. However, if the cost-sharing rate becomes high, retailer i will violate the coordination. This is because the advertising subsidy provided by manufacturer i result in a higher retailer advertising level, which intensifies the supply chain competition and in turn erodes retailer i’ profit. Moreover, manufacturer i can recover its advertising subsidy by increasing the wholesale price. Hence, only manufacturer i prefers the cost-sharing mechanism. As the cost-sharing rate becomes sufficiently larger such that ΦmiRR−AA<Φ<ΦmiU, neither manufacturer i nor retailer i have incentives to participate in the coordinate mechanism, as shown in Figures 7 and 8.Given the asymmetric setting, there exists a cost-sharing threshold value to coordinate the confliction in cooperative adverting program. As shown in Figure9, when the competition is low, CC is a dominated strategy for manufacturers and retailers in region A, which implies there is a common feasible area to guarantee all channel members to be better off. As the competition intensifies, CC benefits the manufacturers, while hurting the retailers. It is worth noting that the advertising with cost-sharing Pareto zone is larger for manufacturers.Figure 9
Manufacturers (M) and retailers (R) preferences with and without cost-sharing given Φ=0.125.


## 5.2. Advertising with Exogenous Revenue-Sharing Rate

The game rule is similar to the scenario with cost-sharing when the revenue-sharing rate is exogenous. By comparing channel members’ profits with and without revenue sharing, we obtain the following theorem:Theorem 6.
Under cooperative advertising with revenue sharing, a revenue-sharing threshold value (ψriRR−AA) can be used to coordinate the entire supply chain as long as 0<ψ<ψriRR−AA. Such that both manufacturer i and retailer i prefer revenue sharing to no revenue sharing as long as 0<ψ≤ψriRR−AA,where ψriRR−AA=45−72θ−264θ2+144θ3+452θ4−64θ5−304θ6+64θ8/3−2θ299+36θ−294θ2−72θ3+264θ4+32θ5−64θ6.Theorem6, is similar to Theorem 5, it also reveals that the revenue-sharing contract can coordinate the entire supply chain when the demand ratio is symmetric. The reason is identical to the scenario with cost sharing. We also depict Theorem 5 in Figure 10, both manufacturer i and retailer i benefit from the revenue-sharing contract in Region A, while only manufacturer i prefer the contract in Region B. Note that in region C, if the revenue-sharing rate is high and the competition is moderate, both manufacturer i and retailer i will violate the cooperation. This result implies that the higher revenue-sharing rate intensifies the horizontal competition.Given the asymmetric setting, there is also a Pareto improvement zone for both manufacturers and retailers. As shown in Figure11, RR is a dominated strategy for the manufacturers and the retailers in region A. RR is a dominated strategy for the manufacturers in region A. It is worth noting that the revenue-sharing contract fails to solve the confliction for the cooperative advertising framework when the competition becomes fierce. Additionally, the advertising with revenue sharing or cost-sharing Pareto zone is larger for manufacturers, which is sharply contracted with Theorem 1. Combing Theorems 5 and 6 gives us insight 3:Insight 3: Given the sharing rate exogenous, cooperative advertising with cost or revenue-sharing contract is capable of coordinating the dual-exclusive channel system when the competition is low. Nerveless, neither the cost-sharing nor the revenue-sharing works well when the completion is fierce.Figure 10
Manufactureri (Mi) and retailer i (Ri) preferences with and without revenue-sharing given Ω=1.Figure 11
Manufacturers (M) and retailers (R) preferences with and without revenue-sharing given ψ=0.125.


## 5.3. Comparison: Revenue Sharing versus Cost-Sharing

So far, we have discussed the cost-sharing and the revenue-sharing efficiencies for channel members in the aforementioned sections. In the foregoing section, we will check which contract is better for the whole channel. Given the exogenous sharing rate assumption, we fail to analytically solve the equilibrium results. For simplicity, givenθ=0.2, θ=0.6, and Ω=1, which can deliver us more management insights.For a channel perspective, as vividly shown in Figures12 and 13, the cost-sharing contract is more beneficial to channel i, which means that cost-sharing contract more suites for coordinating the conflict in the cooperative advertising program. This observation can be used to explain the reason why the cost-sharing is widely used in market practices. Note that Li et al. [29] demonstrate that the revenue-sharing contract is suite for the green supply chain.Insight 4: Given the sharing rate exogenous, the cost-sharing efficiency outperforms the revenue-sharing efficiency under the cooperative advertising framework.Figure 12
Comparing channeli’s profit: revenue sharing versus cost-sharing given θ=0.2 and Ω=1.Figure 13
Comparing channeli’s profit: revenue sharing versus cost-sharing given θ=0.6 and Ω=1.


## 6. Advertising with Bargaining

In marketing practices, it is common to find a manufacturer and a retailer bargain on the sharing rate, in which the sharing rate is cooperatively determined by the manufacturer and the retailer instead of a single-channel member. To investigate the impact of bargaining mechanism on cooperative advertising efficiency, we employ the egalitarian bargaining structure first proposed by Nash [30]:(5)argmaxλiBL=argmaxLπmiJ−πmiAAπriJ−πriAA,s. t.πmiJ>πmiAAandπriJ>πriAA,where L = {Φ, ψ}, J = {CC, RR}. The symbols BRR and BCC represent manufacturer i and retailer i bargaining on the revenue-sharing rate and the cost-sharing rate, respectively. To obtain tractability, we will investigate the bargaining case under the symmetric demand ratio. Since we fail to analytically solve the equilibrium results for retailers when the cost sharing is assumed to be exogenous, it is difficult for us to obtain the explicit constrains for the bargaining case. For simplicity, we only investigate the revenue sharing under bargaining case in the following analysis. It is worth noting that the advantage of the bargaining efficiency lies on that it is a Pareto improvement for all participants. Specifically, if J=RR, then the constrains: 0<ψ≤ψriRR−AA.Substituting the equilibrium solutions derived in Scenarios RR and AA into equation (5) gives us the following results:Proposition 3.
Under the bargaining framework, an optimal revenue-sharing rate can be used to coordinate the entire supply chain. Such that:(6)ψiBRR=B1+B2/43+2θ−2θ2B3,where(7)B1=14175−1998θ−86850θ2+5652θ3+202788θ4−5208θ5−229720θ6+2032θ7+131776θ8−704θ9−35840θ10+256θ11+3584θ12,B2=119574225+96446700θ−1364518872θ2−1061272368θ3+6766919820θ4+4957338672θ5−19307303856θ6−12967269696θ7+35356079088θ8+21111660864θ9−43818663168θ10−22467335424θ11+37695627584θ12+15954508032θ13−22679449344θ14−7568178176θ15+9473607680θ16+2354139136θ17−2680696832θ18−458113024θ19+487948288θ20+50266112θ21−51314688θ22−2359296θ23+2359296θ24,B3=2511−1377θ−11754θ2+5160θ3+19932θ4−6692θ5−15192θ6+3408θ7+5216θ8−576θ9−640θ10.Proposition3 demonstrates that the proposed coordination policy can fully coordinate the conflict in cooperative advertising program. Note that if the competition is sufficiently intense, retailer i will reject the coordination policy, because product substitutability should be satisfied that θ∈0,0.34 (shown in Figure 8). It is worth noting that the revenue-sharing rate decreases with product substitutability. Substituting the optimal sharing rate derived in Proposition 3 into the consumer utility function, it easily demonstrates that consumers obtain more utility from Scenario RR. This result is not surprising since revenue-sharing results in lower retail prices when product substitutability is low, which leads consumers to pay less and buy more.Insight 5: when channel members cooperatively determine the revenue-sharing rate, the revenue-sharing contract can coordinate the advertising conflict.


## 7. Conclusions

This work investigates the efficiency of the cost-sharing and revenue-sharing contracts for the cooperative advertising program in a dual-exclusive channel, in which the sharing rate is assumed to be an endogenous variable or an exogenous variable. We first explore the advertising efficiency without cost-sharing and revenue-sharing contracts. Our findings indicate that advertising is never a competitive tool for small firms and the advertising efficiency is more beneficial to retailers. We next explore the advertising efficiency with cost-sharing and revenue-sharing contracts. Our findings indicate that when the sharing rate is assumed to be endogenous, the sharing rate cannot be determined by a single-channel member, this is because neither the cost-sharing contract nor the revenue-sharing contract can coordinate the advertising conflict. When the sharing rate is assumed to be exogenous, it will give us some interesting results. For instance, supply chain coordination critically depends on parameters, such as the basic demand ratio and product substitution. We finally explore the advertising efficiency with bargaining. Our findings indicate that when the channel members cooperatively determine the cost-sharing rate or the revenue-sharing rate, both the cost-sharing contract and the revenue-sharing contract can coordinate the advertising confliction. Most notably, compared to the revenue-sharing contract, we find that the cost-sharing contract is particular suite for the cooperative advertising mechanism. It is should be note that it is difficult for manufacturers to monitor the retailers’ advertising spending. Our analysis also offers some management insights for enterprises, cooperative advertising does work well, but there are some drawbacks of which to be aware. For instance, the higher sharing rate may not be beneficial to retailers.Our analysis might have some limitations. On the one hand, to obtain more management insights, we assume the two channels have symmetric demand share in the bargaining case. On the other hand, our work demonstrates that the cost-sharing contract outperforms the revenue-sharing contract for the cooperative advertising program. Nevertheless, the latter contract is popular in Internet marketing, which accounts for about 80% of the online advertising scheme. It is natural to see that large online retailers, such as Amazon and eBay, adopt the revenue-sharing contract to distribute advertising revenues with their suppliers, and further studies could conduct the revenue-sharing efficiency for the online advertising program. Moreover, Yu et al. [31] point out that the horizontal channel members may cooperate to advertise, and further studies could investigate the horizontal cooperative advertising issue in a dual-exclusive channel system.



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*Source: 1238278-2022-09-29.xml*