2 Annie and Brett play a two-person, simultaneous play game. The table shows the pay-offs for Annie and Brett in the form ( \(a , b\) ). So, for example, if Annie plays strategy K and Brett plays strategy S, Annie wins 2 points and Brett wins 6 points.
| | Brett |
| | R | S | T |
| \cline { 3 - 5 }
\multirow{3}{*}{Annie} | K | \(( 7,3 )\) | \(( 2,6 )\) | \(( 5,3 )\) |
| \cline { 3 - 5 } | L | \(( 1,5 )\) | \(( 8,2 )\) | \(( 2,5 )\) |
| \cline { 3 - 5 } | M | \(( 3,2 )\) | \(( 1,5 )\) | \(( 4,6 )\) |
| \cline { 3 - 5 } | | | | |
| \cline { 3 - 5 } |
- Determine the play-safe strategy for Annie.
- Show that the play-safe strategy for Brett is T.
- If Annie knows that Brett is planning on playing strategy T, which strategy should Annie play to maximise her points?
- If Brett knows that Annie is planning on playing the strategy identified in part (b)(i), which strategy should Brett play to maximise his points?
- Show that, for Brett, strategy R is weakly dominated.
- Using a graphical method, determine the optimal mixed strategy for Brett.
- Show that the game has no Nash equilibrium points.