In a Union-Management negotiation, the following are the annualpercentages of wage increases for Union for various combinations ofunion and management strategies:

Management

M1 M2 M3

U1 1 3 3

U2 4 2 2

Union U3 3 2 3

U4 3 4 1

U5 2 1 2

9a. (5 points) After eliminating all possible dominatedstrategies, list the Union payoff matrices for the 4 subgames thatare developed by taking 3 of the 4 Union strategies to match the 3Management strategies.

9b. (5 points) Find the best strategy and value of the game forUnion with the following payoff matrix for one of the subgames:

Management

M1 M2 M3

U2 4 2 2

Union U3 3 2 3

U4 3 4 1

9c. (10 points) We have solved in class the best strategy andvalue of the game for Union with the following payoff matrix forone of the subgames:

Management

M1 M2 M3

U1 1 3 3

Union U3 3 2 3

U4 3 4 1

Let q1, q2, and q3 be the respective probabilities forManagement to play strategies M1, M2, and M3. Then use the samePrinciple of Maximin as in deraiving the best mixed strategy forUnion to find the best strategy and value of the game forManagement. Specifically,

9c1 (5 points) show the three independent linear equations forq1, q2, and q3.

9c2 (5 points) Show the correct solution for these 3probabilities from these 3 independent linear equations.