Game theory: n player of paper scissor rock

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• Apr 2nd 2013, 07:51 PM
alphabeta89
Game theory: n player of paper scissor rock
Suppose there are $n$ players $(3\leq{n})$ 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. $k$ play Rock and $(n-k)$ play Scissor), the
losers will pay $\{1}$ 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?