I think you really need to think about the fighters rather than what they were equipped with, especially if you look into ancient warfare. The majority of soldiers in say, Roman Republican times, were not professional soldiers. Think of the bit in '300' when Leonidas asks the soldiers they meet on the way to war "what is your profession?" and they answer blacksmith etc. They might be strong men, but they were not particularly skilled fighters. They probably couldn't pull off elaborate sword faints, they probably just knew and had drilled for a few hours on some basic techniques. They were also unlikely to have spent much time in combat, known the experience of another man attempting to end your life with a big bit of metal. One also needs to question the desire he has to be in that position. Is he ideologically behind his leader, there out of a sense of duty, a sense of shame at not going to war, perhaps for the money?
The reason I would question all these things is because I think it is very hard for anyone of our generation to appreciate what it is like to line up facing an enemy army, thousands of men, across a battlefield, and to be driven into them, literally to be within touching distance. War hasn't been like that for quite a long time now, and very few of us have even experienced modern warfare. Imagine being put in that situation, and you are likely to be little worse off than the majority of the men standing there. You might not have waved a sword around quite so much, or had to live such an outdoors or physical life, but you are probably far better fed than them, and you probably have more knowledge of battle than them even, because of your interest in history.
So, in essence, on your battlefield you have a few hundred, or a few thousand, terrified, reluctant men. It's going to take quite a lot to make them go anywhere near the opposition. Once they get to within 10 metres, the fear is really going to hit, they're going to be even harder to drive forwards. The only reason you might eventually clash, having stood there for ages shouting and not going anywhere, is because you have one or two complete nutters with no sense of self preservation, or who are drunk, or who are really psyched for this, or have experience of this. If you charge at them, unless you're unlucky, the guy opposite you is probably going to wet himself, and at the least he will forget all the sword/lance/spear/shield training he's ever had.
My point? In this type of battle, I think it mattered very little what weapon you held, it was a question of training, experience, morale, cause, and having a few psychos on your side to lead the charge.
Obviously when you get into the eras of professional armies, and the nature of killing without having to be toe to toe with your foe is very different, but this is a recognised problem right through to the Napoleonic wars. Two battalions of musket soldiers would literally stand 10 metres apart, inside a barn somewhere, and fire blindly into the smokey room, rather than rush forward and face steel. They'd much rather take their chances with the lottery of musket shot.
So, Rock, Paper, Scissors? Later, possibly. Accurate guns will mow down a line of men running at you with swords. Aircraft will be shot down attempting to cross a heavily anti-aircraft fortified frontier.
The nature of weapon and tactic development was to trump the successful weapons of your opponent. If one takes out the user, weapons do kinda work in a RPS way. But when you put the human back in, so so so many more variables, in my opinion.
(Sorry I can't be bothered to reference what I've said, writing this as procrastination from my dissertation...
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