I've been researching this game and found this:

The origins of this game are ancient -- tracing all the way back to ancient Middle Eastern cultures, influenced by an influx of trade from cultures beyond the Caucus Mountains.

The game actually began as War (the fist), Appeasement (the flattened hand), and Peace (the two-fingered peace sign -- you probably didn't know that that sign had such ancient origins, eh?).

When they were developing the game they concluded that appeasement would trump war, peace was better than appeasement, and war ended peace.

The game was short-lived because nobody could actually play it without, you know, WAR breaking out over the philosophical underpinnings of the element's claims. Specifically, war wanted to be able to end appeasement and claim victory, while peace always claimed itself as the ultimate goal of the game, and therefore, saw no need to participate in the contest.

So, in order to actually have a game, Scissors, Papyrus, Rock was invented. The earlier representation were lost to history.