Many of you will be familiar with the children’s game rock-paper-scissors. In rock-paper-scissors, two people simultaneously choose either “rock,” “paper,” or “scissors,” usually by putting their...

Many of you will be familiar with the children’s game rock-paper-scissors. 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. The game is scored as follows. A player choosing Scissors beats a player choosing Paper (because scissors cut paper). A player choosing Paper beats a player choosing Rock (because paper covers rock). A player choosing Rock beats a player choosing Scissors (because rock breaks scissors). If two players choose the same object, they tie. Suppose that each individual play of the game is worth 10 points. The following matrix shows the possible outcomes in the game:

(a) Derive the mixed-strategy equilibrium of the rock-paper-scissors game.

(b) Suppose that Lisa announced that she would use a mixture in which her probability of choosing Rock would be 40%, her probability of choosing Scissors would be 30%, and her probability of choosing Paper would be 30%. What is Bart’s best response to this strategy choice by Player 2? Explain why your answer makes sense, given your knowledge of mixed strategies.