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You play rock–paper–scissors for money, except that a win with rock over scissors pays $\$2$ ; the other two wins pay $\$1$ and ties pay nothing. In the symmetric equilibrium, how often is paper played?

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Game theory: dominance, mixing and the indifference condition

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Jane Street, SIG (Susquehanna), Five Rings

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You play rock–paper–scissors for money, except that a win with rock over scissors pays $2\$2$2; the other two wins pay $1\$1$1 and ties pay nothing. In the symmetric equilibrium, how often is paper played?

More games, decision theory and puzzles questions

You play rock–paper–scissors for money, except that a win with rock over scissors pays $\$2$ ; the other two wins pay $\$1$ and ties pay nothing. In the symmetric equilibrium, how often is paper played?