3. Consider a road which is represented by the interval [01]. Let a be a number such that 0

3. Consider a road which is represented by the interval 101]. Let a be a number such that 0 < a < 1. Vendor 1 can locate at any point on the interval [0, a] (that is, he can locate at any pointa: such that 0 a; a). Vendor 2 can locate at any point on the interval p, 1]. A unit mass of onsumers are uniformly distributed on 10, 1] and each consumer buys one unit of the good from the vendor who is closest to him. If the two vendors locate at the same pointa, then each gets one*half of the consumers. The game. is as follows. Vendors choose locations simultaneously, and a vendor's payoff is given by the number of consumers who purchase. from him. a) Write. down the stratekv sets and payoff functions in this game. b) Suppose. a = 0.5. Show that this game, has a unique Nash equilibrium in pure strategies. That is, you need to show (i) there is a Nash equilibrium, and (ii) is no other Nash equilibrium. c.) Suppose < 0.5. Show that the game does not have a Nash equilibrium in pure strategies. 4) Suppose that stratekvs, is strictly dominated for playeri. Show that it cannot be played by i in any Nmsh EXIuilibrium. Provide. an example to show that a weakly dominated strategy may be played in a Nash equilibrium.