Game theory

Rani and Greg play a zero-sum game. The pay-off matrix shows the number of points that Rani scores for each combination of strategies.

Explain what the term ‘zero-sum game’ means.

State the number of points that Greg scores if he plays his strategy 3 and Rani plays her strategy 3.

Verify that there is no stable solution to this game.

Reduce the game so that Greg has only two possible strategies. Write down the reduced pay-off matrix for Greg.

Find the best strategy for Greg and the value of the game to him.

A two-person zero-sum game is represented by the following pay-off matrix for player A.

Verify that there is no stable solution to this game.

Find the best strategy for player A.

A two-person zero-sum game is represented by the following pay-off matrix for player A.

Reduce the game so that player B has only two possible actions.

Write down the reduced pay-off matrix for player B.

Find the best strategy for player B and the value of the game to him.

Laura and Sam play a zero-sum game. This game is represented by the following pay-off matrix for

Find the best strategy for Laura and the value of the game to her.

In game theory, explain the circumstances under which column (x) dominates column (y) in a two-person zero-sum game.

Liz and Mark play a zero-sum game. This game is represented by the following pay-off matrix for Liz.

Verify that there is no stable solution to this game.

Find the best strategy for Liz and the value of the game to her.

The game now changes so that when Liz plays 1 and Mark plays 3 the pay-off to Liz changes from 2 to 4. All other pay-offs for this zero-sum game remain the same.

Explain why a graphical approach is no longer possible and briefly describe the method Liz should use to determine her best strategy.