1 Arif and Bindiya play a game as follows.
- They each secretly choose a positive integer from \(\{ 2,3,4,5 \}\).
- They then reveal their choices. Let Arif's choice be \(A\) and Bindiya's choice be \(B\).
- If \(A ^ { B } \geqslant B ^ { A }\), Arif wins \(B\) points and Bindiya wins \(- 4 - B\) points.
- If \(A ^ { B } < B ^ { A }\), Arif wins \(- 4 - A\) points and Bindiya wins \(A\) points.
- Assuming that each of the 16 possible outcomes is equally likely to be chosen, show that the average amount won by Arif is 0 .
- Describe how to convert this game to a zero-sum game.
- Construct the pay-off matrix for this zero-sum game, with Arif on rows.