Repeated Games

Question 1

Finitely repeated games

Answer 1

Players know when the game will end, and the end round is the most important. Players act like it’s a one shot-game however, and both play their dominant strategy. This just means everyone plays their dominant strategy throughout the game.

NE is no different to one-shot.

Question 2

Infinitely repeated games

Answer 2

Players do not know when the game will end. Therefore, the is an incentive to cooperate to prevent retaliation from other players in the next round if you break the agreement.

There is a trade-off between short term benefit and long term costs of non-cooperation.

Question 3

Tit for Tat

Answer 3

Players copy each other’s behaviour in the next round. If player one cooperates in round one, then player two will also cooperate in round two.
Punishes non-cooperation and rewards co-operation.

Question 4

Grim Trigger Strategy

Answer 4

Players will only co-operate if the other has co-operated in all previous rounds. Otherwise, they will never co-operate again, regardless of the other player changing their strategy.

Question 5

Is non-co-operation worth it?

Answer 5

Non-co-operation is only worth it if the probability of meeting the other player again is low, and if you discount the future heavily.