There are three firms, 1,2, and3, in the market which produce an identical commodity. Firm Each i {1,2,3} has the production cost ;(v;) = 20y;. All three firm observe the market demand, and their total supply directly determines the market price of the commodity : p (y; + y2+3) = 200(y1 +y; +y3) forall y1,y;,y3 2 0. First, the three firms simultaneously announce their own supply quantities, and hence get involved in a Cournot competition. (i) Specify a normal form for this Cournot competition. (ii) Find one Nash equilibria. Second, firms announce their own supply quantities in the following sequence firm1 first announces its supply quantity; firm2 observes firm1's announcement, and then announces its own supply quantity; firm3 observes the announcement of both firm 1,2 and then chooses its own supply quantity. Hance these three firm are involved in a variant of Stackelberg competition (iii) Specify an extensive form for this variant of Stackelberg competition (iv) Find one backward induction solution, and compare firm1's profit to that at the Nash equilibria of