5 In each round of a card game two players each have four cards. Every card has a coloured number.
- Player A's cards are red 1 , blue 2 , red 3 and blue 4.
- Player B's cards are red 1 , red 2 , blue 3 and blue 4 .
Each player chooses one of their cards. The players then show their choices simultaneously and deduce how many points they have won or lost as follows:
- If the numbers are the same both players score 0 .
- If the numbers are different but are the same colour, the player with the lower value card scores the product of the numbers on the cards.
- If the numbers are different and are different colours, the player with the higher value card scores the sum of the numbers on the cards.
- The game is zero-sum.
- Complete the pay-off matrix for this game, with player A on rows.
- Determine the play-safe strategy for each player.
- Use dominance to show that player A should not choose red 3 . You do not need to identify other rows or columns that are dominated.
- Determine, with a reason, whether the game is stable or unstable.