Consider that market 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:

p=12 9004Q if05Q5210 , 186 0.6Q 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) Assume that the two firms play the Cournot Duopoly game. Then, compute the Nash equilibrium of this game. Also, compute the Nash equilibrium payoff allocation.

(2) Assume that the two firms play the Stackelberg Duopoly game, in which the firm 1 is the first mover. Then, compute the Stackelberg equilibrium of this game. Also, compute the Stackelberg equilibrium payoff allocation.

(3) Show that in this Stackelberg Duopoly game, the firm 1 can enjoy the first mover advantage.