Rock-Scissors-Paper game is a two player simultaneous move game where each player chooses R, S or P. It is a fact that Rock crushes Scissors, which cuts Paper which in turn covers
PROBLEM (7) Rock-Scissors-Paper game is a two player simultaneous move game where each player chooses R, S or P. It is a fact that Rock crushes Scissors, which cuts Paper which in turn covers Rock; so R beats S, S beats P and P beats R. Winner gets 1 point, loser gets 0 (if they both choose the same strategy; both gets 0). Fill a 3x3 game box with two players’ payoffs in this game and answer the following;
(a) Is there a dominant strategy for Player 1? Any dominated strategy? Answer the same for Player 2.
(b) Is there a Nash Equilibrium in this game?
(c) If player 1 plays first and then player 2 chooses her action, would you like to be player 1 or 2 in this sequential version of the game? Draw the game tree and describe the backward induction solution (sequential Nash equilibria) in this game.
PLEASE ANSWER ALL THE PARTS!
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