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 Part 5-6

Answer 1

PAYOFF ARE EXPRESSED IN THE ORDER - LION (D), SCARECROW (C), TINMAN (B), DOROTHY (A)

for questions 5 and 6, paths can be traced from the choice of action of the 4 players who want to maximize their payoff, the solution inequalities can be derived by considering their choice to be greater than the next best payoff

5) A > 3 ; B > 3 ; C < 3 ; D < 1

minimum payoffs are - {L,S,T,D} = {1,1,3,3}

the following diagram shows the path according to given choices

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6) A < 3 ; B > 3 ; C > 3 ; D > 1

minimum payoffs are - {L,S,T,D} = {1,3,3,1}

the following diagram shows the path according to given choices