In a union-management negotiation, the following are the percentages of annual w

Question

In a union-management negotiation, the following are the percentages of annual wage increase for various combination of union 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

Determine the best mixed strategies for the union and management respectively and the expected percentage of annual wage increase (i.e., value of the game) for the union.

Explanation / Answer

The matrix is
1 3 3
4 2 2
3 2 3
3 4 1
2 1 2
The value is 2.6.
An optimal strategy for Player I is:
(0.2,0,0.6,0.2,0)
An optimal strategy for Player II is:
(0.2,0.4,0.4)

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