Explain the concept of repeated games in game theory.

Repeated games in game theory refer to situations where the same game is played multiple times.

In a one-shot game, players make their decisions without considering the future consequences. However, in a repeated game, players can use their past experiences to inform their current decisions. This can lead to different outcomes and strategies.

One approach to analysing repeated games is the concept of a Nash equilibrium. A Nash equilibrium is a set of strategies where no player can improve their payoff by unilaterally changing their strategy. In a repeated game, a subgame perfect Nash equilibrium (SPNE) is a set of strategies that is a Nash equilibrium in every subgame of the repeated game.

Another important concept in repeated games is the notion of cooperation and punishment. In a one-shot game, cooperation may not be rational as there is no incentive to trust the other player. However, in a repeated game, players can use the threat of punishment to encourage cooperation. This can lead to the emergence of cooperative strategies such as tit-for-tat, where a player starts by cooperating and then copies the other player's previous move.

Overall, repeated games provide a richer framework for analysing strategic interactions between players. They allow for the emergence of new strategies and the possibility of cooperation and punishment.