Consider the broadcasted news scheduling model with three broadcasting stations labeled A, B, and C, facing 600 potential viewers whose ideal watching time is 5 p.m.; 100 viewers whose ideal time is 6 p.m.; and 200 viewers whose ideal time is 7 p.m. Assume that each station can air its news broadcast at one and only one time period. Also assume that each station earns exactly $1 per viewers (as determined by rating surveys conducted during the broadcasting hours). Let ti denote the broadcasting time of station i, i = A, B, C.

(a) Find one Nashequilibrium in broadcasting time. Prove your answer!

(b) We now define the utility of a viewer whose ideal time is t ˆ and watches the program at time t by Ut ˆ(t) def = β −δ  t − t ˆ  . Define the social welfare function and determine whether the Nash equilibrium in scheduling time you found in

(a) is socially optimal. Prove your answer!