Consider the following variation to the Rock (R), Paper (P), Scissors (S) game:

• Suppose that the Player 1 (row player) has a single type, Normal.

• Player 2 (column player) has two types Normal and Simple.

• A player of Normal type plays this zero-sum game as we studied in class whereas a player of type Simple always play P.

• Player 2 knows whether he is Normal or Simple, but player 1does not.

a) Suppose player 2 is of type Normal with probability 1/3 and of type Simple with probability (2/3). Find all pure strategy Bayesian Nash Equilibria.

b) Suppose player 2 is of type Normal with probability 2/3 and of type Simple with probability (1/3). Find all pure strategy Bayesian Nash Equilibria.