Their argument turned into a petty game of tit for tat.
tit for tat
idiomEquivalent retribution; an act of returning exactly what one gets; an eye for an eye.
Origin
disputed originUncertain; conjectured to be ultimately from Dutch dit voor dat (“this for that”) or French tant pour tant (“equal for equal”). Compare earlier tip for tap (“(a) blow for (a) blow”), from tip + tap; compare also dialectal tint for tant and tit (“a light blow or hit”). The vowel sequence follows a typical ablaut reduplication pattern.
The two neighbors were locked in a cycle of tit for tat, constantly reporting each other for minor property violations.
The diplomatic negotiations collapsed as both nations engaged in a destructive cycle of tit for tat, responding to every new sanction with an equally severe retaliatory measure.