Hi, I am trying to finish up my Game Theory Problem Set and I save this one for last, and I am struggling on parts b and d of the question. I have provided everything I've gotten for a and c and the games for a, b, and c below. Any help is appreciated
1. For each of the following games, answer the following questions: a. How many pure strategies (complete plans of action) are available to each player? List all of the pure strategies for each player. b. Write the game in strategic form. Find all of the Nash equilibria. c. Identify the subgame perfect equilibria (rollback equilibria) in each game by giving the complete equilibrium strategy for each player. What is the equilibrium outcome in each case? d. For any equilibria from part (b) that are not subgame-perfect, identify the credibility problems. (a) MINERVA 3,0 2,1 1, 1 MINERVA a ALBUS 15,0 S M 1,3,1 (b) MINERVA 3,3 N 5,2 14 4 ALBUS ALBUS 2,4.0 10,4 MINERVA 1, 6 SEVERUS a 10,2.3 ALBUS MINERVA MINERVA 10,4,4 4, 1,5 MINERVA ALBUS a ) a. Albus has three strategies: N, E, and S. Minerva has eight strategies: aaa, aab, aba, abb, baa, bab, bba, and bbb (where the first letter is for the action following N, the second for the action following E, and the third for the action following S). b. c. The unique subgame-perfect equilibrium in this case is (N, bab). The equilibrium outcome is along the path (N, b), which yields payoffs of (2,1). d. a. Albus has four strategies: NN, NS, SN, and SS (where the first letter is the action at the initial node and the second letter is the action following the history (N, b)). Minerva has six strategies: aa, ab, ba, bb, ca, and cb (where the first letter is the action following the history N and the second letter is the action following the history S). b. c. The unique subgame-perfect equilibrium in this case is (SN, ca). The equilibrium outcome is along the path (S, a), which yields payoffs of (2,2). d. C) a. Albus has four strategies: NN, NS, SN, and SS (where the first letter is the action at the initial node and the second letter is the action following the history (N, a, X)). Minerva has four strategies: aa, ab, ba, and bb (where the first letter is the action following the history N and the second letter is the action following the history (N, a, Y)). Severus has two strategies: X and Y. b. c. The unique subgame-perfect equilibrium in this case is (SS, ba, Y). The equilibrium outcome is along the path (S), which yields payoffs of (2,1,1) d
