Behaving irrationally in the cause of a higher rationality is called a “doomsday machine”. For example “you touch my daughter I kill you”. It may be irrational to kill him if he touches your daughter, by if you convince him you are crazy enough to do it, he probably won’t touch your daughter.
Kissinger employed a similar tactic in the Vietnam War, suddenly restarting the bombing to make the Vietnamese think he was capable of causing them great harm, even though it made no rational sense.
Similarly the efforts to track down every minor player in the killing of Jews in WW2 down to the last conscript who worked in a labor camp sends a strong message “don’t fuck with us or we I’ll do what it takes to make you pay”.
If your response to provocation is wildly disproportionate, no one will fuck with you. This is why reporters are afraid of Muslims: Journalists know that Muslims will kill them if they criticize Muhammad. Likewise, governments know that blacks will burn cities if provoked. Both groups get their way.