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2. The Model
We established a three-stage game model. In the first stage, firm A decide whether to customize the products and firm B decide whether to advertise the products or adjust the competitive market location at the same time. The second stage is Hotelling competition stage. If firm B choose the capability of market location in the previous stage, it would determine the exact market location point this stage. However, if firm B choose the capability of advertising, it would determine the exact quantities of advertising. Finally, in the third stage, the two firms would enter into a price competition.
Assume there are two firms in the market, which are firm A and firm B. And they produce two different products. Firm A produce product Aand firm B produce product B. Consumers in the market are equally distributed. The product characteristics produced by the two firms locate at the each endpoint on consumer preferences line separately. Firm Alocate at x0and firm Blocate at x1. We use a constant t, which represents the negative utility arose in the differences between the preference of consumers and the characteristics of the product. The larger t means the greater intensity of their preference to the product. Consumers could be satisfied only when their preference index exactly equal to 0 or 1. The farther between the product characteristics and their preferences are, the lower the utility consumers could get.
In the following, we would introduce four situations at first. Two situations are whether firm Acustomizes products. And the other two are whether firm B chooses to advertise the products or adjust the market location. Then, we would introduce the Hotelling game of each situation in the second stage. The equilibrium of four situations under the second stage would be discussed in third stage.
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2.1 Situation 1: Firm A chooses not to customize products, and firm B chooses to adjust market location to compete with.
Before introducing that firm Bcan maximize its own profits by adjusting market location, we introduce the situation firm B without the capability at first. Because firms Aand firms B locate at each endpoint on consumer preferences line, which are 0 and 1, the utility U x y( , ) which consumer x V is the highest price which consumers are willing to pay. Assume V is large enough so that each consumer could buy exactly one unit of product Aor B.1 Under the premise that firm Bcould maximize profit by adjusting the market location to y1(y1(0,1]), if consumer xy1 In addition, to simplify our analysis, we only discuss the situations that both firms exist in the equilibrium. Under the situation 1, a market segmentation point x1 would split market into two parts which are [0, ]x1 and [ ,1]x1 . That is, whenever consumer x1 gets the same utility from purchasing products Aor B, the profit
1 In the following, we also assume that V is large enough so that each consumer could buy exactly one unit of product Aor B.
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2.2 Situation 2: Firm A chooses not to customize products, and firm B chooses to advertise its products to compete with.
Assume the advertisement of firm B has positive effect on increasing consumers’ utility. That is, the more advertisement firm B input, the higher utility consumers get from purchasing product B .3 Given the advertising input
B, the utility of the consumer x gets from purchasing product Aor B is: Similarly, we only discuss the situations that both firms exist in the equilibrium.
Under the situation 2, a market segmentation point x2 would split market into two parts which are [0,x2] and [ ,1]x2 . That is, whenever consumer x2 gets the
we define k as a cost coefficient of advertising and
2
( B2)
k is the total cost of
2 The cost of adjusting market location of firm B will in the form of quadratic in the following. It is the similar as the quadratic way of product transportation costs which is set in ’Aspremont et al. (1979).
3 Related literature are as follows: Cengiz et al. (2007) descript the efficiency of the advertisement will affect consumer loyalty for this product. Chung et al. (2012) descript ads will increase the motivation of consumers to buy products, and it would make closer relationship between consumers and the firm.
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2.3 Situation 3: Firm A chooses to customize products, and firm B chooses to adjust market location to compete with.
We assume firm A can exactly meet the consumers’ preference by customizing products under the situation. And we followed the setting in Loginova (2010) that consumers would not have a negative effect on the differences between the product characteristics and their own preferences. That is, t doesn’t exist. In addition, as situation 1, before introducing that firm Bcan maximize its own profits by adjusting market location, we introduce the situation firm B without the capability at first. Because firms Aand firms Blocate at each endpoint on consumer preferences line, which are 0 and 1, the utility
( , ) Under the premise that firm B can maximize its profits by adjust its market location, if consumer x y 3, (3) can be rewrite as: Similarly, we only discuss the situations that both firms exist in the equilibrium.
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Under the situation 3, a market segmentation point x3would split market into
two parts which are [0, ]x3 and [ ,1]x3 .4 That is, whenever consumer x3 gets
them, we follow the setting in Loginova (2010) that we define CA as the total cost of product customization of firm B.5
2.4 Situation 4: Firm A chooses to customize products, and firm B chooses to advertise its products to compete with.
Similar to situation 3, consumers will not have a negative effect on the differences between the characteristics of products and their own preferences.
And we assume the more advertisement the firm B input, the higher utility consumers get from purchasing product B as situation 2. Given the original market location of firm B and the advertising input amount B4, under the premise that firm A chooses to customize products, the utility which consumer
x gets from purchasing products Aand B is: Under the situations that both firms exist in the equilibrium, in the situation 3, there is a market segmentation point x4 would split market into two parts which
4 In the following, we assume t is not big enough, so we don’t take the situation into account: some of the consumer close to x1 might choose to buy the product of firm A.
5 In the following, we assume the customization cost CA as a fixed cost. In the future, we also can assume the cost would be related to the distance between the firm and the consumer
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立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
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are [0,x4] and [ ,1]x4 . That is, whenever consumer x4 gets the same utility from purchasing products Aor B, the profit of firm Ais A4 P xA4 4CA, and
the profit of firm B is B2 PB4(1x4)k(B4)2.
In the following, we adopt the concept of subgame perfect equilibrium to find the equilibrium. And we analyze the interaction of two firms’ decision by backward introduction.