www.lesswrong.com/posts/d2HvpKWQ2XGNsHr8s/hell-is-game-theory-folk-theorems

In repeated-game theory, individual rationality is the weak condition that each player gets at least their minmax payoff. It does not include an extra requirement that some player be strictly above minmax.

A standard set of lecture notes from MIT defines it this way: a payoff vector is individually rational if (v_i \ge \underline{u}_i) for all players. A 2023 Journal of Economic Theory article discussing folk theorems under limit-of-means payoff likewise says individual rationality "demands at least the obvious minimal payoff (the minmax payoff) for every player."

So the post is mixing up two different ideas:

• Individually rational: every player gets at least minmax.
• Strictly individually rational (used in some folk-theorem variants, especially discounted ones): every player gets strictly more than minmax.

Adding the clause that "at least one player must get strictly more utility" is therefore not the standard definition of individual rationality, and it is false as stated. A payoff profile can be individually rational even when no player is strictly above minmax (for example, when every player gets exactly their minmax payoff).