in dynamic games (games where moves take place at different times), there might be cases of threat equilibrium. these are those outcomes which can be enforced by a “threatner” who can commit to play a irrational move in order to force the other player to play a different strategy.

Example of Threat Equilibrium

in the above image, if player 1 plays B, the best response for player 2 then is to play c. but what player 2 can do is commit prior that he will play d if player 1 plays B. this is like mutually assured destruction in geopolitical scenarios. playing d after player 1 has played B is irrational, but one can think of this as a higher rationality.

maybe rationality involves being irrational at times.

what the commitment by player 2 does is that it forces player 1 to play A, in which case both players get a payoff of 2.

i found this high quality, very knowledge dense webpage regarding something similar - Game Theory in AI Alignment