6 Xander and Yvonne are playing a zero-sum game.
The game is represented by the pay-off matrix for Xander.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Yvonne}
Xander
| Strategy | \(\mathbf { Y } _ { \mathbf { 1 } }\) | \(\mathbf { Y } _ { \mathbf { 2 } }\) | \(\mathbf { Y } _ { \mathbf { 3 } }\) |
| \(\mathbf { X } _ { \mathbf { 1 } }\) | - 4 | 1 | - 3 |
| \(\mathbf { X } _ { \mathbf { 2 } }\) | 4 | - 3 | - 3 |
| \(\mathbf { X } _ { \mathbf { 3 } }\) | - 1 | 1 | - 2 |
\end{table}
6
- Show that the game has a stable solution.
6 - State the play-safe strategy for each player.
Play-safe strategy for Xander is \(\_\_\_\_\)
Play-safe strategy for Yvonne is \(\_\_\_\_\)
6 - The game that Xander and Yvonne are playing is part of a marbles challenge.
The pay-off matrix values represent the number of marbles gained by Xander in each game.
In the challenge, the game is repeated until one player has 24 marbles more than the other player.
Explain why Xander and Yvonne must play at least 3 games to complete the challenge.