In rock-paper-scissors, two people simultaneously choose either Rock, Paper, or Scissors, usually by putting their hands...

 

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In rock-paper-scissors, two people simultaneously choose either Rock, Paper, or Scissors, usually by putting their hands into the shape of one of the three choices. A person choosing Scissors beats a person choosing Paper (scissors cut paper). A person choosing Paper beats a person choosing Rock (paper covers rock). A person choosing Rock beats a person choosing Scissors (because rock breaks scissors). If two players choose the same object, they tie. Their payoffs are as follows: Player 1 Player 2 Rock Scissors Paper 30,-30 -30,30 0,0 30,-30 0,0 Rock 0,0 Scissors -30,30 Paper 30,-30 -30,30 A. Show (prove) that it is the mixed-strategy equilibrium when each player chooses Rock with probability 1/3, Scissors with probability 1/3 and Paper with probability 1/3. B. What is Player 1's best response to the following mixture by Player 2: Rock with proba- bility 0.3, Scissors with probability 0.3 and Paper with probability 0.4? In rock-paper-scissors, two people simultaneously choose either Rock, Paper, or Scissors, usually by putting their hands into the shape of one of the three choices. A person choosing Scissors beats a person choosing Paper (scissors cut paper). A person choosing Paper beats a person choosing Rock (paper covers rock). A person choosing Rock beats a person choosing Scissors (because rock breaks scissors). If two players choose the same object, they tie. Their payoffs are as follows: Player 1 Player 2 Rock Scissors Paper 30,-30 -30,30 0,0 30,-30 0,0 Rock 0,0 Scissors -30,30 Paper 30,-30 -30,30 A. Show (prove) that it is the mixed-strategy equilibrium when each player chooses Rock with probability 1/3, Scissors with probability 1/3 and Paper with probability 1/3. B. What is Player 1's best response to the following mixture by Player 2: Rock with proba- bility 0.3, Scissors with probability 0.3 and Paper with probability 0.4?

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