In the game of rock, scissors, paper, each of two players simultaneously puts out either a fist (for rock), two fingers (for scissors), or an open hand (for paper). If player 1 puts out rock and...

In the game of rock, scissors, paper, each of two players simultaneously puts out either a fist (for rock), two fingers (for scissors), or an open hand (for paper). If player 1 puts out rock and player 2 puts out scissors, then player 1 wins (rock breaks scissors). Alternatively, if player 1 puts out rock and player 2 puts out paper, then player 2 wins (paper covers rock). If player 1 puts out scissors and player 2 puts out paper, then player 1 wins (scissors cuts paper). If both players put out the same

symbol, the game is a draw. The following is the payoff table from player 1 ’s point of view:

Determine the optimal strategies for players I and 2 for this game.