Many of you will be familiar with the children's game Rock-Scissors-Paper. In Rock-Scissors-Paper, two people simultaneously choose either "Rock," "Scis sors," or "Paper," usually by puttjng their hands into the shape of one of the three choices. The game is scored as follows. A person choosing Scissors beats a person choosing Paper (because scissors cut paper). A person choosing Paper beats a person choosing Rock (because paper covers rock) . A person choosing Rock beats a person choosing Scissors (because rock breaks scis sors). If two players choose the same object, they tie. Suppose that each indi vidual play of the game is worth 10 points. The following matrix shows the possible outcomes in the game:
|
PLAYER 2
|
|
Rock
|
Scissors
|
Paper
|
|
PLAYER 1
|
Rock
|
0
|
10
|
-10
|
|
Scissors
|
-10
|
0
|
10
|
|
Paper
|
10
|
-10
|
0
|
(a) Suppose that Player 2 announced that she would use a mixture in which her probability of choosing Rock would be 40%, her probability of choos ing Scissors would be 30%, and her probability of Paper, 30%. What is Player l's best response to this strategy choice of Player 2? Explain why your answer makes sense, given your knowledge of mixed strategies.
(b) Find the mixed-strategy equilibrium of this Rock-Scissors-Paper game.