Introduction to Repeated Games in Game Theory
Folk theorems in repeated games are a set of theorems that describe the possible outcomes of a repeated game in which players use strategies that are not necessarily rational. In repeated games, players have the opportunity to punish each other for past behavior, and these punishments can lead to outcomes that are not predicted by traditional game theory models. The folk theorems are a set of results that show that, under certain conditions, almost any outcome is possible in a repeated game.
One of the key conditions required for the folk theorems to hold is that players must be able to use strategies that are not necessarily rational. This means that players can use strategies that are not optimal in the short run, but can lead to better outcomes in the long run. For example, a player might choose to cooperate with their opponent even if it means that they will lose in the short run, because they believe that their opponent will reciprocate in the future.
Another important condition is that players must have a way of punishing each other for past behavior. This can take many forms, such as reducing the level of cooperation, imposing fines or other penalties, or simply refusing to interact with the other player in the future.
The folk theorems have many practical applications, including in economics, political science, and international relations. They can be used to model situations in which players have repeated interactions and can learn from each other's behavior over time. They can also be used to analyze situations in which players have incomplete information about each other's preferences and beliefs.
However, the folk theorems also have some limitations. For example, they assume that players have perfect information about each other's strategies and beliefs, which is often not the case in real-world situations. They also assume that players are rational and can always make optimal decisions, which may not be true in practice.
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