2. Consider that Cournot competition among oligopolistic 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:
1⁄2 900 − 4Q
if 0 5 Q 5 225
if 225 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 strategic-
form 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), derive the
best-response functions B1 (q2) and B2 (q1) of these two firms respectively.
Moreover, show the proof of your answers.
(3) Compute the Nash equilibrium of this game.
(4) Moreover, explain that this Nash equilibrium is unique in this game.
(5) Show that this Nash equilibrium allocation is not Pareto efficient.