I recall reading a science fiction story in one of the magazines like “Analog” several decades ago that used this concept as a major plot point. Two Planets wer

I recall reading a science fiction story in one of the magazines like “Analog” several decades ago that used this concept as a major plot point. Two Planets were at risk of all out war and were evenly matched such that the results would be devastation for both. They negotiated a solution whereby each would proceed to “invade” the other’s planet and rule but each would observe how well the other ruled and could retaliate. This caused them to be scrupulously fair in their ruling. I don’t recall the name of the story or the author. This was likely in the late 60’s or early 70’s. I’m not sure why, if they could negotiate such a complex solution that they couldn’t just negotiate a secession of hostilities but the point of the story was to illustrate the cake principle.