5. Agent Goodie is planning to break into Evil Doctor Fiendish's secret base.
He uses game theory to determine whether to approach the base from air, sea or land.
Evil Doctor Fiendish decides each day which of three possible plans he should use to protect his base.
Agent Goodie evaluates the situation. He assigns numbers, negative indicating he fails in his mission, positive indicating success, to create a pay-off matrix. The numbers range from - 3 (he fails in his mission and is captured) to 5 (he successfully achieves his mission and escapes uninjured) and the pay-off matrix is shown below.
| Fiendish uses plan 1 | Fiendish uses plan 2 | Fiendish uses plan 3 |
| Air | 0 | 4 | 5 |
| Sea | 2 | -3 | 1 |
| Land | -2 | 3 | -2 |
- Reduce the game so that Agent Goodie has only two choices, explaining your reasoning.
- Use game theory to determine Agent Goodie's best strategy.
- Find the value of the game to Agent Goodie.