3. Terry and June play a zero-sum game. The pay-off matrix shows the number of points that Terry scores for each combination of strategies.
| \cline { 2 - 4 }
\multicolumn{2}{c|}{} | June |
| \cline { 3 - 4 }
\multicolumn{2}{c|}{} | Option X | Option Y |
| \multirow{4}{*}{Terry} | Option A | 1 | 4 |
| \cline { 2 - 4 } | Option B | - 2 | 6 |
| \cline { 2 - 4 } | Option C | - 1 | 5 |
| \cline { 2 - 4 } | Option D | 8 | - 4 |
- Explain the meaning of 'zero-sum' game.
- Verify that there is no stable solution to the game.
- Write down the pay-off matrix for June.
- Find the best strategy for June, defining any variables you use.
- State the value of the game to Terry.
Let Terry play option A with probability \(t\).
- By writing down a linear equation in \(t\), find the best strategy for Terry.