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Consider a Hotelling Game with three homogeneous firms. Customers are uniformly distributed on the interval [ 0 , 1 ] and each customer goes to the...

Consider a Hotelling Game with three homogeneous firms. Customers are uniformly distributed on the interval [0, 1] and each customer goes to the firm that is the closest to his own location. If firms are located at the same spot, they share the customers evenly. Firms choose their location to maximize customers.
Which of the following statements is correct?
 There is a unique Nash equilibrium and all three firms choose to locate at x = 1/2. 
 There is a unique Nash equilibrium and at least one firm chooses not to locate at x = 1/2. 
 Nash equilibrium does not exist. 
 There are multiple Nash equilibria. 

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