Consider the following game where there are two players. Player 1 first chooses UP or DOWN. The move of player 1 is not observable by player 2. Player 1's move is followed by a chance move that selects a signal. Player 2 receives a signal about what player 1 has played: either SUP or SDOWN. The signal player 2 receives is correct with probability 0.8 and wrong with probability 0.2. Namely, if player 1 plays UP [DOWN], player 2 receives the signal SUP[SDOWN] with probability 0.8 and the signal SDOWN[SUP] with probability 0.2. This game and the corresponding payoffs are depicted below: a) Write down the strategies for both player 1 and player 2. b) Find the pure Nash Equilibria (or equilibrium) of this game. c) Find the Perfect Bayesian Nash equilibria (or equilibrium) of this game