Two firms (1 and 2) compete in a homogeneous goods market, where the firms produce exactly the same good. The firms simultaneously and independently select quantities to produce. The quantity selected by firm i is denoted q, and must be greater than or equal to zero, for i - 1,2. The market price is given by p-2 - q1 -q2. For simplicity, as sume that the cost to firm i of producing any quantity is zero. Further, assume that each firm's payoff is defined as its profit. That is, firm i's payoff is pqi, where j denotes firm i's opponent in the game. Requried:
Describe the normal form of this game by expressing the strategy spaces and writing the payoffs as functions of the strategies.