Two players play a standard Rock-Paper-Scissors game. Namely, they simul- taneously select one of three actions {R, P,S}. If players select the same actions then their payoffs are zero. Otherwise, P beats R, R beats S, and S beats P. The player who is "beaten pays 1 to her opponent. 1. Find a Nash equilibrium. 2. Draw a game tree for this simultaneous-move game. Remember that there is a non-trivial information set there. 3. Find a perfect Bayesian equilibrium. (Hint: Normally we would not use a perfect Bayesian equilibrium to solve this game as Nash equilibrium is adequate. But we can! The only difference is that a perfect Bayesian equilibrium will have not only strategy profile, like in the Nash equi- librium above, but also a belief system which specifies what the player believes in each information set)