#### Location Game and Hotelling’s Model

Location Game:

Brands compete more vigorously with brands that are close substitutes than with those that consumers view as less close substitutes. Consumers view certain brands as closer substitutes than others. Merely certain brands have particular common characteristics that other lack. I.e. every brand is ‘located’ at a particular point in product characteristic space. Or products sold at near stores are close substitutes. That is every firm is located at a particular address or point in geographic space.

Hotelling’s Model (1929):

* Consider a long and narrow city with only one street which is 1 mile long.

* Consumers are consistently distributed between 0 and 1.

* All has to purchase one unit of product.

* Two stores are selling approximately identical product at the same price and try to maximize profits.

* Consumers will purchase at the nearest store because they have to incur transaction cost (travel, time, waiting, …).

* Suppose two stores have to locate at the similar time before they start to sell. Consumers living on the left of store 1and half of consumers living between store 1 and 2 will choose store 1.

* Store 1’s market share = a + 0.5(1− a − b) = 0.5(1+ a − b)
Store 2’s market share = b + 0.5(1− a − b) = 0.5(1− a + b)

* The equilibrium in this location game is where two stores are located in the center of this linear city. a = 0.5 = (1− b)

* Intuitively, if store 1 is at a = 0.5, then the best response of store 2 is to locate at b = 05. To take full advantage of its share however if store 2 is at (1− b) > 0.5 , then it has less 50% of total share. If store is at a = 0.3 , store 2 can maximize its share by locating at (1− b) = 0.3, right next to store 1.

The equilibrium when there are two firms recommended to Hotelling that ‘Buyers are confronted everywhere with an excessive sameness’ (1929). The result that two firms in either product or geographic space will locate in the middle is often referred to as the principle of minimum differentiation (K. Boulding 1966). The principle does not hold strictly when there are more than two firms. Nevertheless even when there are more than two firms, the equilibrium market configuration is characterized by ‘bunching.’

* Economic Implication- Adopting this model to product Differentiation

Two competitive firms in duopoly will have a strategy for medium consumers as main target in design, character or quality. As well as the degree of differentiation is trivial.

Example: Even in political science USA has two party politics system. Democrats as well as Republican. They take public pledge or commitments which are so similar or vague which are not easily distinguishable.

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