I didn't know how to copy paste this so here

2) In this question, we're going to use a game tree and backward induction to analyze a Stackelberg problem. In this case, each firm has 3 options: to produce a low level of output, a medium level of output, or a high level of output. The payoffs to each firm given each firm's output choice are: (TA, TB B: High B:Medium B: Low A: High (0,0) (75,50) (1 12.50, 56.25) A: Medium (50,75) (100, 100) (125, 93.75) A: Low (56.25, 112.50) (93.75, 125) (112.50, 112.50) a) What are the Nash equilibria when both firms choose their output at the same time? Explain. You must prove that your answer satisfies the definition of Nash equilibrium. b) Now assume that firm A can choose its output first. Fill in the following game tree for this sequential game. Each of the 9 payoff combinations above corresponds to one of the 9 endpoints of the game tree. I've filled in (Med, High) to get you started.A chooses B chooses A=M, B=H (50,75) c) Now that you've lled in the tree, use backward induction to nd the equilibrium for this game. Briey describe why your answer is different than in 2a. Figure out B 's best response to each of A 's possible actions. Then, pick the one of those three options that maximizes A's prot, given how B will respond