A feasible rational payoff that is not an equilibrium payoff in the repeated game
It is true because of the discounting. If the discount parameter were $\delta = 1$ then players 1 and 2 could alternate playing TL and MR in equilibrium and then reach the average payoff vector $1,1,5$. But if $\delta &lt; 1$ someone will not play along. Suppose the players are supposed to start with TL. Then MR would follow in the next round then, then TL again, and so on. In this case
$$
U_1 = 0 + 2 \cdot \delta + 0 \cdot \delta^2 + 2 \cdot \delta^3 + ...
$$
Yet by always playing B player 1 would achieve the payoff
$$
U_1' = 1 + 1 \cdot \delta + 1 \cdot \delta^2 + 1 \cdot \delta^3 + ...
$$
which is larger then $U_1$. Similarly player 2 would not want to start with MR. So these are not equilibrium playoffs. (Not even Aumann's correlated-equilibrium would do the trick.)