Consider that Cournot competition among oligopolist firms in which two firms produce a homogeneous product and provide it to the market. Let firm 1's supply of this product be denoted by q1, and firm 2's supply of this product be denoted by q2. The inverse demand function of this market is given by: p = 900 4Q 186 0.6Q if 0 5 Q 5 210 if 210 5 Q , where Q represents the aggregate demand of this product, and p represents the price of this product. Let the total cost of producing qi amount of the product be 100qi for each firm i = 1, 2. Then: (1) From the information of this economic environment, define a strategicform game by specifying the strategy set, Ai, for each firm i = 1, 2, and then by specifying the payoff function, ui : A1 A2 R, for each firm i = 1, 2. (2) In the strategic-form game you defined in the question (1), compute the best-response functions B1 (q2) and B2 (q1) of these two firms respectively. (3) Compute the Nash equilibrium of this game. Moreover, explain that this Nash equilibrium is unique in this game. (4) Show that this Nash equilibrium allocation is not optimal.