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 I'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 Spown. 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 Sur [Spows] with probability 0.8 and the signal SpowN [SUP] with probability 0.2. This game and the corresponding payoffs are depicted below: (15,10) (5,5) (20,15) (10,20) R L P=0.8 1-p-0.2 Sop Chance SpowN UP DOWN SUP SDOWN R-P-0.2 P-0.8 Chance R (15,10) (5.5) (20,15) (10,20) 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.