Weird sort of mathematics/logic problem

So I have the following situation: we have two people are playing a game. Something simple where each person has some sort of input and that is compared to see who wins. Like rock-paper-scissors, or rolling dice and comparing the rolls or such.

However, they are in a place where they can't actually see each other. They can only send messages back and forth (and not simultaneously).

Is there some scheme where they could play this game in such a way that eliminates the possibility of cheating?