Consider an industry with two firms, each having marginal costs and total costs equal to zero. The industry demand is P = 100 Q where Q = Q1 + Q2 is total output.

7. Now, assume that players interact infinitely. Hence the game is an infinitely repeated game. Is it possible to have cartel as an outcome using tit-for-tat? If yes, give the condition on the discount factor for which cartel is sustainable. Cartel is a sustainable outcome of the repeated game if while firm 2 plays grim-trigger, there exists no profitable one-shot deviation from tit-for-tat for firm 1. Sicne the firms are identical, you don't need to check the profitable deviations of firm 2. They will be the same. Let's start with completing the table below. Keep in mind that firm 2 is following tit-for-tat and firm 1 is deviationg from tit-for-tat only in period 2.

8.Now, using the discount factor calculate the total payoffs from the two cases. You will need to use formulas for infinite series. Now, find values which make the total payoff from no deviation bigger than the total payoff from one-shot deviation. For these values of the discount factor, firm 1 will not deviate from tit-for-tat. Since firms are identical, the same condition applies to firm 2 as well.