4.4c Folk Theorem

Folk Theorem

The folk theorem states that for an infinitely repeated stage game $G$ with a uniform discount factor $\delta \in (0,1)$, such that $\delta \to 1$. Then, if all players’ payoffs $u_i$ are:

1. Feasible, meaning that they can be achieved arithmetically using some strategy
2. Individually rational, meaning that $u_i>u_i^{\ast }$, where $u_i^{\ast }$ is player $i$‘s worst Nash equilibrium payoff

Then, there exists an SPNE of the repeated game such that each player $i$ receives $u_i$ on average.