Question

Red 0, 1, 3,3 3, 0, 3,2 Dorothy Top 2, 4,3, A Scarecrow Up reen Tinman Right 0, 2, 3,1 Bottom Lion Down 1, 3, B, 2 1,4, 2, 2 Top Left Tinman 3, C, 1,2 Bottom Red 1, 3,4, 2 Blue Yellow Down Scarecrow D, 3,3,3 Dorothy 1,3,4,2 How many complete strategies does Tinman have? List them. (3 pts) How many complete strategies does Dorothy have? List them. (3 pts) If the game follows the path of Left, Bottom, Up, who receives the payoff of "1"? (1 pt) Find the rollback equilibrium if A-O, B-O, C-O, D-O . State your answers in terms of complete strategies and the resulting payoff. (6 pts) What values will A, B, C, & D take in order for rollback equilibrium, expressed in complete strategies to be, L:Right; S:Bottom, Down; T: Bottom, Up, D: Blue, Blue? Express your values for A, B, C, & D as inequalities. What is the minimum payoff, when all values must be greater than zero and whole numbers? What values will A, B, C, & D take in order for rollback equilibrium, expressed in complete strategies to be, L:Left, S:Bottom, Down; T: Bottom, Down, D: Red, Blue? Express your values for A, B, C, & D as inequalities. What is the minimum payoff, when all values must be greater than zero and whole numbers? 1. 2. 3. 4. 5. 6.

Answer 5-6. Payoff Order (Lion, Scarecrow, Tinman, Dorothy)

Answer 1

Thus A > 3, c < 3, B < 3, D < 2 80 minimum Payoff rightarrow (2, 4, 3, A) so min Payoff, A = 4. A > 3 Solving Backwards, (D) will choose Blue, If A > 3 then scarecrow will choose Down, If C < 3 then (T) will choose up if B < 3 finally lion will select b/w (D, 3, 3, 3) & (2, 4, 3, A) So D < 2, to select Right SPNE: (shown by green) Min Payoff, (2, 4, 3, A), A > 3 A = 4 (If whole number) So (D) will choose Red If A < 3, then (s) will choose down If C < 3. (T) will choose Down If B > 3. then lion will choose b/w. (D, 3, 3,3) & (1, 3, B, 2) So D > 1 Min Payoff (D, 3, 3, 3) with D > 1 (D, 3,3,3) D = 2(If whole Number)