Discussion
A company management and the labour unions are negotiating a new three year settlement. Each of these has 4 strategies mentioned below :
(I) : Hard and aggressive bargaining.
(II) : Reasoning and logical approach.
(III) : Legalistic strategy.
(IV) : Conciliatory approach.
The cost to the company are given for every pair of strategy choice.
| Labour Union Strategies / Company Strategies | I | II | III | IV |
|---|---|---|---|---|
| I | 20 | 15 | 12 | 35 |
| II | 25 | 14 | 8 | 10 |
| III | 40 | 2 | 10 | 5 |
| IV | -5 | 4 | 11 | 0 |
Then the value of the game is :
Answer: A
The value of the game is 12.
The entries are costs to the company, so the union (rows) maximises and the company (columns) minimises. Look for a saddle point:
- Row minima: 12, 8, 2, -5; the largest is 12 (row I).
- Column maxima: 40, 15, 12, 35; the smallest is 12 (column III).
Maximin = minimax = 12, so (I, III) is a saddle point and the game has value 12 in pure strategies: the union bargains hard and the company takes the legalistic line.
-5 is the smallest entry, 0 and 2 are other entries of the table; none is both the minimum of its row and the maximum of its column.
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