Rock, Paper, Scissors (2 points) Draw the payoff  matrix for the game rock=paper-scissors

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Rock, Paper, Scissors (2 points)

1. Draw the payoff  matrix for the game rock=paper-scissors. Assume that a win results in a positive payoff  of 1 util, a tie generates no change in utility, and a loss results in the loss of 1 util.
2. Calculate the expected payoff  one would receive from playing a pure 'rock' strategy.
3. Calculate the expected payoff  one would receive from playing a pure 'paper' strategy.
4. Calculate the expected payoff  one would receive from playing a pure 'scissors' strategy.
5. How many Nash equilibria does this game have? What are[is] they[it]?
6. What is the expected payoff  to each player if both are playing an equilibrium strategy?
7. Your instructor suggests that there exists a can't miss 'behavioral' strategy. Does this make sense? Why or why not?
8. How might a deft RPS player potentially take advantage of their opponent's cognitive bias(es)? Be creative in identifying a potential behavioral response that can be capitalized upon.
9. Suppose you just won a round of RPS (scissors cut paper). Your opponent immediately challenges you to a rematch. You know they are twice as likely to throw a different gesture after a loss, but they are equally likely to choose rock or scissors if they do change their gesture. Repeat items a-e for the rematch.