Play safe strategy
This page is about the play safe strategy in a zero sum game.
In this strategy, the player(s) choose the option which minimises the possible loss.
Take this pay off matrix for example:
| Player 2 plays C | Player 2 plays D | Player 2 plays E | Row minima | |
|---|---|---|---|---|
| Player 1 plays A | 2 | -1 | 1 | -1 |
| Player 1 plays B | 1 | -2 4 | -3 | -3 |
| Column maxima | 2 | -1 | 1 |
The numbers in the table represent the benefit to player 1 - play 2 loses that amount.
- The row minima is the worst that can happen for each of player 1’s options.
- The play safe strategy for player 1 is to choose the option with the highest row minima - in this case, option A.
- The column maxima is the best that can happen for each of player 2’s options.
- The play safe strategy for player 2 is to choose the option with the lowest column maxima - in this case, option D.
Value of the game
The value of the game for player 1 is the amount that player 1 can expect to win (or lose) if both players play their play safe strategies.
flashcards
| Question | Answer |
|---|---|
| What is the play safe strategy in a zero sum game? | A strategy where the player(s) choose the option which minimises the possible loss. |
| How do you determine the play safe strategy for player 1 from a pay off matrix? | Choose the option with the highest row minimum. |
| How do you determine the play safe strategy for player 2 from a pay off matrix? | Choose the option with the lowest column maximum. |
| In the given pay off matrix, what is the row minima for Player 1 playing A? | -1 |
| In the given pay off matrix, what is the row minima for Player 1 playing B? | -3 |
| In the given pay off matrix, what is the column maxima for Player 2 playing C? | 2 |
| In the given pay off matrix, what is the column maxima for Player 2 playing D? | -1 |
| In the given pay off matrix, what is the column maxima for Player 2 playing E? | 1 |
| Based on the pay off matrix, what is the play safe strategy for Player 1? | Option A. |
| Based on the pay off matrix, what is the play safe strategy for Player 2? | Option D. |
| What is the value of the game for player 1? | The amount that player 1 can expect to win (or lose) if both players play their play safe strategies. |
| What do the numbers in the pay off matrix represent regarding the players? | The numbers represent the benefit to player 1; player 2 loses that amount. |