Cooperative advertising programs are usually provided by manufacturers to stimulate retailers investing more in local advertising to increase the sales of their products or services. While previous literature on cooperative advertising mainly focuses on a “singlemanufacturer singleretailer” framework, the decisionmaking framework with “multiplemanufacturer singleretailer” becomes more realistic because of the increasing power of retailers as well as the increased competition among the manufacturers. In view of this, in this paper we investigate the cooperative advertising program in a “twomanufacturer singleretailer” supply chain in three different scenarios; that is, (i) each channel member makes decisions independently; (ii) the retailer is vertically integrated with one manufacturer; (iii) two manufacturers are horizontally integrated. Utilizing differential game theory, the openloop equilibriumadvertising strategies of each channel member are obtained and compared. Also, we investigate the effects of competitive intensity on the firm’s profit in three different scenarios by using the numerical analysis.
To increase the sales of their products or services, some manufacturers or service providers utilize cooperative advertising programs, through which they share a part of the retailer’s advertising cost, to stimulate retailers advertising more on their products or services. Generally, advertising can be divided into national advertising and local advertising. The former focuses on building brand image about the products or services. The latter is often price oriented to stimulate consumer to purchase the products or services at once. Supported by subsidies from a manufacturer’s cooperative advertising program, retailers would always increase their local advertising expenditures and thus improve their profits [
Surveys showed that, for many manufacturers or service providers such as General Electric, their advertising budgets to retailers via cooperative advertising programs are more three times of that they spent on national advertising [
The tendency toward increased spending on cooperative advertising has received significant attention from researchers. The cooperative advertising models under study can be divided into two categories: static models [
Retailers in today’s market are increasingly more powerful than manufacturers. Useem found that sales through WalMart accounted for 17% of P&G’s total sales in 2002, 39% of Tandy’s, and over 10% for many other large manufacturers [
The significant contribution of this paper is that it generalizes existing cooperative advertising work on “singlemanufacturer singleretailer” framework to the “twomanufacturer singleretailer” framework. This generalization has provided new analytical results about how the competition affects the advertising efforts and profit for channel member. In detail, we study the openloop equilibrium advertising strategies of each channel member in three different scenarios, including that (i) each channel member makes decisions independently; (ii) the retailer is vertically integrated with one manufacturer; (iii) two manufacturers are horizontally integrated. Specifically, the following research questions are addressed in this paper. (i) For each scenario, what are the equilibrium advertising efforts for each channel member and what is the manufacturer’s optimal participation rate for the retailer’s local advertising expenditures? (ii) When the retailer integrates with one manufacturer, does the manufacturer change its decisions about national advertising expenditures and participation rates? (iii) How does the horizontal integration of two manufacturers affect the decisions of each channel member?
To answer the above questions, we focus on the cooperative advertising problem in a “twomanufacturer singleretailer” framework. The dynamic advertising models are proposed based on the NerloveArrow model. Utilizing differential game theory, the openloop equilibrium advertising strategies of each channel member are obtained and compared in three different scenarios.
The remainder of the paper is structured as follows. Previous literature related to our topic is reviewed in Section
Our work is related to several research streams. First is the stream of literature that focuses on cooperative advertising, which can be divided into two main categories: static models and dynamic models. A primary static model was proposed by Berger [
The above literature is mainly focused on a “singlemanufacturer singleretailer” framework. Few studies address a “multiplemanufacturer singleretailer” framework or any other framework. Kurtuluş and Toktay considered a model including two competing manufacturers and one retailer; the result revealed that the retailer can use the form of category management and the category shelf space to control the intensity of competition between manufacturers to his benefit [
To our best knowledge, research relating to cooperative advertising focused on a “multiplemanufacturer singleretailer” framework in the supply chain has not been explored in literature. In this study, we investigate a cooperative advertising model using the “twomanufacturer singleretailer” framework.
As shown in Figure
We introduce the additional notation in this paper (see Table
Notation.

Time 

Goodwill of the product 

Manufacturer 

Retailer’s local advertising efforts for product 

Sales of product 

The national advertising’s competition coefficient 

The local advertising’s competition coefficient 

Manufacturer 

Marginal profit of manufacturer 

Marginal profit of the retailer sells the product 

Diminishing rate of goodwill 

Discount rate of the manufacturers and the retailer 

Profit functions for 

Current value of profit functions for 
As our goodwillbased model is based upon the model of NerloveArrow, the changing of the stock of goodwill of product
In (
The advertising cost functions are quadratic with respect to marketing efforts, namely,
This assumption about the advertising cost function is commonly found in literature [
Without considering advertising expenditures, the marginal profit of manufacturer
In this paper, we assume the participation rate is a constant over time for the following reasons. (i) Although much more literature assumes that the participation rate changes along time [
Please note that
In this scenario, each channel member makes decisions independently, and the profit functions of all channel members are given by (
Taking (
Similarly, we get the retailer’s current value Hamiltonian as
Then using the necessary conditions for equilibrium, we obtain the following results.
When each channel member makes decisions independently and the participation rates
Proposition
Further, we obtain the retailer’s equilibrium advertising efforts for two brands as follows.
When each channel member makes decisions independently and the participation rates
Proposition
Furthermore, when condition
If condition
If conditions
If condition
When the two manufacturers’ participation rates are fixed, the equilibrium advertising efforts for all channel members are given by Propositions
When each channel member makes decisions independently and their advertising efforts are kept as constants, that is,
From (
Substituting (
Differentiating
When all the channel members make decisions independently, the optimal participation rates that the two manufacturers provide to the retailer under the equilibrium condition are
For (
Furthermore, substituting the optimal participation rates into (
Equation (
In second scenario, the retailer integrates with one of the manufacturers. We assume this manufacturer is
Further, the objective of manufacturer 2 is
Taking state equation (
Then using (
When the retailer integrates with manufacturer 1 and the participation rate
Compared to Proposition
When the retailer integrates with manufacturer 1 and the participation rate
Proposition
If we subtract (
It is easy to prove that
Furthermore, combining (
When
If conditions
When
We can calculate the stock of goodwill for the two products and the current value of profits for all channel members, which are given by Proposition
When the retailer integrates with manufacturer M1, and their advertising efforts are kept constant, that is,
Substituting (
Differentiating
When the retailer integrates with manufacturer 1, and the advertising levels are kept as constants, that is,
Subtracting (
We can prove that (
Further, substituting the optimal participation rate into (
Subtracting (
Note that the result of (
When the two manufacturers integrated, it can be seen as a single firm with two different brands in the same product category. Examples in practice include Lenovo. IBM’s personal computing division was acquired by Lenovo in 2004, and the PC of IBM became a subbrand of Lenovo Group named “Thinkpad.” This is a historical precedent of two manufacturers behaving as a single player, yet, as far as we know, previous researches on dynamic cooperative advertising programs have never studied such scenario, a single manufacturer with two different brands. Most previous research investigated a “singlemanufacturer singleretailer” supply chain with a single brand/product. When the manufacturer advertises two different brands, the result does change; therefore, the third scenario must be considered. In this scenario, the integration system’s profit function is
The current value Hamiltonian of the integration system (
Using the necessary conditions for equilibrium, we get the following results.
When the two manufacturers are horizontally integrated and the participation rate
Note that the retailer’s equilibrium local advertising efforts given by (
In addition, comparing (
Equation (
When the two manufacturers are horizontally integrated and all channel members’ advertising efforts are kept as constants, that is,
Substituting (
Differentiating
Note that the above expressions of participation rates are identical with the results of Proposition
In this scenario, the equilibrium advertising efforts for the two manufacturers become lower, but the equilibrium local advertising efforts for the two products are not changed. This could lead to the phenomenon that the retailer has so much power from advertising the two products that the retailer has incentive to prevent the horizontal alliance between the two manufacturers. That is why a successful manufacturer’s horizontal integration in a dominant retailer market is very rare in actual practice.
In this section, we use numerical analysis to further illustrate the impact of local advertising competition on the profits for all channel members and supplement insights from these theoretical results. In our numerical analysis, we use the following values to establish ranges for model parameters:
To obtain qualitative insight regarding how the current value of each channel member’s profit varies as competition coefficients
Relationships between profits and competition coefficients
Figure
Figure
Relationships between the retailer’s profit and the competition coefficients
From Figure
Finally, Figure
Relationships between the profit of
Previous research primarily focused on a “singlemanufacturer singleretailer” framework, whereas few studies address a “multiplemanufacturer singleretailer” framework. To fill this gap, this paper investigates the advertising strategies for a “twomanufacturer singleretailer” supply chain in three different scenarios: (i) each channel member makes decisions independently; (ii) the retailer integrates with one of the manufacturers; (iii) two manufacturers are horizontally integrated.
Based on the results of the three scenarios, we find the following results. (i) The manufacturer’s equilibrium advertising efforts are independent of the participation rates that the two manufacturers offer to the retailer in all three scenarios. (ii) When the retailer integrates with one manufacturer, the other manufacturer’s equilibrium advertising efforts would not be changed. The retailer would enhance the local advertising efforts for the integrated manufacturer and reduce the local advertising efforts for the other manufacturer. In response, the other manufacturer would offer a higher (compared to scenario 1) advertising cost participation rate to the retailer. (iii) When the two manufacturers are horizontally integrated, they would reduce the national advertising efforts to avoid internal conflict. They also offer the same advertising cost participation rate to the retailer as in scenario 1. (iv) If any two firms (i.e.,
It should be noted that our models only consider the effects of advertising, but this situation may not always hold. In addition, it may be more interesting if we introduce the factors of pricing and quality to the cooperative advertising model. Additionally, our work on the “twomanufacturer singleretailer” framework can be extended into a “multiplemanufacturer singleretailer” framework.
When each channel member makes decisions independently, the current value Hamiltonian of manufacturer 1 is
Then we form the Lagrangian:
Equation (
Solving (
Equation (
Differentiating (
Solving (
Because there is no constraint at
Condition (
Similarly considering manufacturer 2’s profit maximizing problem, we obtain the equilibrium advertising level for manufacturer 1 as follows:
For (
Substituting (
When each channel member makes decisions independently, the current value Hamiltonian of the retailer is:
Then we form the Lagrangian
The necessary conditions for equilibrium are given by
Because
Through a similar proof, we find that
Therefore we can obtain the following results:
There are no relationships between participation rate
In conclusion, we get the following results:
Through a similar proof, we get manufacturer 2’s optimal share rate is
When the retailer integrates with a manufacturer, the current value Hamiltonian of manufacturer 2 is
Then we form the Lagrangian:
At optimality, the necessary conditions are
Proceeding as in the proof for Proposition
When the retailer integrates with a manufacturer, the current value Hamiltonian for integration system is given by
Then we form the Lagrangian:
Proceeding as in the proof for Proposition
Thus, the equilibrium advertising levels for manufacturer 2 are as follows:
Also, we obtain the equilibrium local advertising levels for the two products:
Substituting (
When condition
There are no relationships between participation rate
In conclusion, we get the following results:
When the two manufacturers are horizontally integrated, the current value Hamiltonian for the integration system is given by
Then we form the Lagrangian
At optimality, the necessary conditions are
In most case the advertising effort
Solving (
Equation (
Differentiating (
Proceeding as in the proof of Proposition
Thus, the equilibrium advertising levels for two manufacturers are as follows:
Substituting (
The current value Hamiltonian for the retailer is given by
Then we form the Lagrangian:
Proceeding as in the proof of Proposition
Then we get the following results:
This work was supported by the National Natural Science Foundation of China (Grants nos. 70901068 and 71271198), the Fund for International Cooperation and Exchange of the National Natural Science Foundation of China (Grant no. 71110107024), and the Chinese Universities Scientific Fund (WK2040160008 and WK2040150005). Qinglong Gou would also like to acknowledge the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant no. 71121061) for supporting his research.