a) In the game Rock-Paper-Scissors, there are three strategies: Rock, Paper, and Scissors. Rock defeats Scissors, Scissors defeats Paper, and Paper defeats Rock. Assuming that you are indifferent between the three kinds of victory (e.g. you don't take a particular pleasure in winning with, say, Rock), what is the mixed-strategy Nash equilibrium? (Hint: remember our discussion of Matching Pennies)

b) Consider the following payoff matrix:

i) Identify any pure-strategy Nash equilibria. (2 points)

ii) Are there any mixed-strategy Nash equilibria? (1 point)

Company B Strategy 1 Strategy 2 Company B's Company B's Strategy 1 Profit: $9 million Profit: $8 million Company A's Company A's Company Profit: $8 million Profit: $7 million A Company B's Company B's Strategy 2 Profit: $8 million Profit: $7 million Company A's Company A's Profit: $10 million Profit: $8 million