Rock-Paper-Scissors is a simple game in which two players compete by simultaneously choosing rock, paper, or scissors. According to the classic rules of the game, paper beats rock, scissors beats paper, and rock beats scissors. After watching one particular player compete in this game for many rounds, you have observed that she chooses rock, paper, or scissors based on her previous choice according to the following transition probabilities:

Assume you are competing against this player and that you must decide on all future choices now (before seeing any additional opponent choices).
a. Given the opposing player last chose Rock, what is your best choice in the next round as her opponent?
b. Given the opposing player last chose Rock, show the two-period tree diagram.
c. Calculate Π(2) and use this to find the probability that the opposing player will choose Paper in the second round.

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Previous Choice Rock Paper Scissors Rock 0.27 0.36 0.18 Next Choice Paper 0.42 0.15 0.55 Scissors 0.31 0.49 0.27