Game theory: n player of paper scissor rock

Suppose there are $\displaystyle n$ players $\displaystyle (3\leq{n})$ showing Paper, Scissor or Rock

simultaneously. If there is no winner then there is no payoff to any player. If

there are winners and losers (e.g. $\displaystyle k$ play Rock and $\displaystyle (n-k)$ play Scissor), the

losers will pay $\displaystyle \${1}$ each for the winners to divide evenly.

Find a strategic equilibrium for this game.

But i know that playing the strategy uniformly is a SE. But how do we show that?