# Rock, Paper, Scissors and game theory

Please see attachment.

Consider the game of Rock, Paper, Scissors. Suppose that Player 1 has a higher payoff when he wins with Rock than when he wins with either Paper or Scissors. Thus, the normal form version of the game is now:

Player 1

Rock Paper Scissors

Rock 0,0 -1,1 5,-1

Player 2 Paper 1,-1 0,0 -1,1

Scissors -1,1 1,-1 0,0

Given this change in Player 1's payoffs, should his Nash equilibrium change from playing each of the three strategies one-third of the time to playing them in some other proportion? Explain why or why not. Find the mixed strategy Nash equilibrium to this game.

Note: the normal rock, paper, scissors setup is:

Player 1

Rock Paper Scissors

Rock 0,0 -1,1 1,-1

Player 2 Paper 1,-1 0,0 -1,1

Scissors -1,1 1,-1 0,0

In the normal setup, the Nash equilibrium is to play each strategy in equal amounts.

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#### Solution Summary

The solution discusses the Rock, Paper, Scissors and Game Theory.