3 Summer and Haf play a zero-sum game.
The pay-off matrix for the game is shown below.
Haf
| Strategy | \(\mathbf { H } _ { \mathbf { 1 } }\) | \(\mathbf { H } _ { \mathbf { 2 } }\) | \(\mathbf { H } _ { \mathbf { 3 } }\) |
| Summer | \(\mathbf { S } _ { \mathbf { 1 } }\) | 4 | - 4 | 0 |
| \cline { 2 - 5 } | \(\mathbf { S } _ { \mathbf { 2 } }\) | - 12 | 0 | 10 |
| \cline { 2 - 5 } | \(\mathbf { S } _ { \mathbf { 3 } }\) | 10 | 4 | 6 |
3
- Show that the game has a stable solution.
3 - State the value of the game for Summer.
3
- (ii) State the play-safe strategy for each player.