Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 18H / b

Table of contents
- Solution b

Solution

A pure optimum is a saddle point: an entry minimal in its row and maximal in its column. In

A_{1}

,

c

at

(2, 1)

is a saddle; in

A_{2}

,

c

at

(2, 2)

is a saddle. Matrix

A_{3}

has row maximin

b

and column minimax

c

, so no saddle exists. Thus

A_{1}, A_{2} admit pure optimal strategies; A_{3} does not .

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