ExAMPLE 2. Two countries, I and II, are at war. II has two airfields, and can de

Question

ExAMPLE 2. Two countries, I and II, are at war. II has two airfields, and can defend one but not both. Let a, and a denote defending airfield 1 and airfield 2 respectively. Country I can attack only one of the airfields. Denote the two possible strategies 1 and 2. If I attacks a defended airfield, it will immediately withdraw with no loss to either side. If I attacks an undefended airfield, the airfield will be destroyed. Airfield 1 is twice as valuable as airfield 2 to II. Letting 1 denote the value (to II) of airfield 2, it follows that the loss matrix is 0 02 602 | 1 | 0 This is a zero-sum game, providing the values to I of the destruction of the airfields are the same as the values of the airfields to II.

Explanation / Answer

Minimax strategy will be the minimum of rows and maximum among them. Hence, it is 0 in this case.

Similarly, Minimax strategy will be the maximum of columns and minimum among them. Hence, it is 1 in this case.

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