2. Rock, Rock, Rock, Rock, Paper, Scissors (8 marks total) Suppose that two players play the following modified version of rock, paper, scissors. A fair coin is flipped. The first player (player 1) looks at the coin (it remains hidden from player 2). After the coin flip, both players play a single round of rock, paper, scissors. Here is the catch: if the coin shows heads (which happens with probability), then player 1 must play rock. (a) (2 marks) Draw a game tree for this game, clearly indicating the move by Nature (the coin flip), (b) (2 marks) Convert the game from extensive form to normal form. Construct the expected payoff (c) (2 arks) Find the MSNE for the game. How should player 1 mix when the coin flip is tails? as well as information sets for both players. matrix How should player 2 mix in general? (d) (2 marks) Suppose that after the game, the loser must pay the winner S100 (i.e. payoffs are 100 and 100). Would you rather play as player 1 or player 2? How much would you be willing to pay for the opportunity to play this game in your preferred role? 2. Rock, Rock, Rock, Rock, Paper, Scissors (8 marks total) Suppose that two players play the following modified version of rock, paper, scissors. A fair coin is flipped. The first player (player 1) looks at the coin (it remains hidden from player 2). After the coin flip, both players play a single round of rock, paper, scissors. Here is the catch: if the coin shows heads (which happens with probability), then player 1 must play rock. (a) (2 marks) Draw a game tree for this game, clearly indicating the move by Nature (the coin flip), (b) (2 marks) Convert the game from extensive form to normal form. Construct the expected payoff (c) (2 arks) Find the MSNE for the game. How should player 1 mix when the coin flip is tails? as well as information sets for both players. matrix How should player 2 mix in general? (d) (2 marks) Suppose that after the game, the loser must pay the winner S100 (i.e. payoffs are 100 and 100). Would you rather play as player 1 or player 2? How much would you be willing to pay for the opportunity to play this game in your preferred role