Consider the following game where there are two players. Player 1 first chooses UP or DOWN....

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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-0.2¹ Sop Chance SpowN UP DOWN SUP SDOWN R¹-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. 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-0.2¹ Sop Chance SpowN UP DOWN SUP SDOWN R¹-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.

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a Strategies for Player 1 and Player 2 Player 1s strategy Player 1 can choose either UP or DOWN Player 2s strategy Player 2s strategy depends on the s... View the full answer