The folk theorem says that as long as the discount factor...

The Folk Theorem says that, as long as the discount factor $\delta$ is high enough, there are a whole range of payoffs that are possible in equilibria of an infinitely repeated game. What are the two conditions that a payoff vector must satisfy in order to be an equilibrium payoff in an infinitely repeated game?

Transcript

00:01 In an infinite repeated prisoner's time, the player can use the tactics that involve co -operative and punishment to sustain co -operative over time.

00:18 The strategy provided involves alternating between co -operation with his team and interaction with his team in a periodic manner.

00:32 The actor will analyze the strategy to find the threshold he saw, which is δb, for which he then has equilibrium.

00:49 So the strategy is the following.

00:52 First is co -operative in all periods and the second is in each period.

01:19 So if the player succeeds from rule 1, if any player deviates from rule 1, he succeeds in all subsequent periods.

01:51 So we'll denote the discount factor as δs.

02:06 And the player cares not only about their immediate payoff, but also about the future payoff, discounted by δ in each period.

02:15 So the payoff in each period is given by the payoff provided.

02:19 So here, the player of the strategy in each period receives for co -operation, co -operation c in all.

02:35 Both players receive the payoff c in each of these periods.

02:40 And for defection in all.

02:45 The player who defects receives the payoff of 4.

02:52 And for co -operating, the player receives the payoff of 0.

03:02 And for co -operation in even.

03:09 Here, both players receive the payoff of 0.

03:16 And for defection in even periods.

03:23 The player who defects receives 1...

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