I don’t think the claim is exceptional, but I’d love to see more studies on this. Check out the Centipede Game (https://en.m.wikipedia.org/wiki/Centipede_game):

“Parco, Rapoport and Stein (2002) illustrated that the level of financial incentives can have a profound effect on the outcome in a three-player game: the larger the incentives are for deviation, the greater propensity for learning behavior in a repeated single-play experimental design to move toward the Nash equilibrium.”

I recall reading somewhere that people also behave more rationally in other games like the Dictator Game (and exhibit fewer cognitive biases) when the stakes are higher, but can’t remember where.