Consider a road which is represented by the interval [0,1].letabe anumber such that 0< a < 1.vendor 1 can locate at any point on the interval[0, a] (that is, he can locate at any pointxsuch that 0≤x≤a).vendor 2 canlocate at any point on the interval [a,1].a unit mass of onsumers are uniformlydistributed on [0,1] and each consumer buys one unit of the good from thevendor 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 avendor’s payoff is given by the number of consumers who purchase from him. a) write down the strategy sets and payoff functions in this game. b) supposea= 0.5.show that this game has a unique nash equilibrium inpure strategies. that is, you need to show (i) there is a nash equilibrium, and(ii) there is no other nash equilibrium.