Could you please help me with this question?

5. [6 pts] Consider the following game. Two players simultaneously choose a number between 0 and 100. Player i's number is m. If 931 + 2.32 S 100, each player gets 2:,- dollars. If :31 + 22:2 > 100, both players get zero dollars. Players only care about how much money they get, and more money is better. Find all PSNE. 6. [10 pts] Two rms simultaneously choose their output. They can choose either low output L or high output H. The payoffs (prots) are shown below. Firml/Fz'rmZ L (i) [4 pts] Find all pure or mixed strategy Nash equilibria. (ii) [4 pts] The government would like both rms to choose H (perhaps for antitrust reasons maybe, by raising output, prices fall, prots fall, and consumers are better off). It therefore decides to introduce a certain taxation/ redistribution scheme. If a rm chooses L and the other chooses H, the rm choosing L has to pay the other rm an amount t. How should the government set the tax in order for (H, H) to be a Nash equilibrium? (iii) [2 pts] With the tax in place, is the Nash equilibrium (H, H) unique? How much money ends up getting redistributed in equilibrium