Number Guessing Game Strategies: A Comprehensive Analysis

Possible strategies for Player 2:

1. Guess '1', '2', '3', '4' in order.
2. Guess '4', '3', '2', '1' in order.
3. Guess randomly without repetition.
4. Guess randomly with repetition.
5. Guess '2', '1', '4', '3' in order.
6. Guess '3', '4', '1', '2' in order.
7. Guess '1', '4', '2', '3' in order.
8. Guess '3', '1', '4', '2' in order.
9. Guess '2', '4', '1', '3' in order.
10. Guess '4', '2', '3', '1' in order.
11. Guess based on previous feedback (e.g. if the last guess was too high, guess lower).
12. Guess based on a pattern or rule (e.g. always guess odd numbers first).
13. Guess based on intuition or psychic ability.
14. Give up immediately and lose $0.

Payoff matrix:

| | 1 | 2 | 3 | 4 | |---|---|---|---|---| | 1 | 0 | -1| -2| -3| | 2 |-1 | 0 | -1| -2| | 3 |-2 |-1 | 0 | -1| | 4 |-3 |-2 |-1 | 0 |

Note: The negative values indicate the amount of money P2 loses for each incorrect guess. The diagonal values are 0 because P2 will always guess correctly eventually.