Answer Happy

PROBLEM: 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!