2. [8 points] In this well-known game, there are two players and two stages in the game. Player 1 rst decides whether to play B (Burn Money) or N (Not Burn Money). Aer observing the action of Player 1, the two players play a simultaneous-move game: L R Player 2 1's Payoff=9 l's Payoff=3 U 2's Payoff=5 2's Payoff=3 1's Payoff=0 1's Payoff=5 D 2's Payoff=0 2's Payoff=9 Player 1 Note that the game in the second stage has two equilibria: (U ,L) and (D,R). Player 1 prefers (U, L) since his payoff is 9 in that equilibrium, whilst (D,R) gives him only 5. However, if Player 1 played B in the rst stage, his payoff is reduced by 3. His payoff is not reduced if he played N in the rst stage. Player 2's payoff is not affected by what Player 1 did in the rst-stage. So, for instance, if Player 1 played B followed by U, and Player 2 played L after she saw B, the payoffs are (9 3, 5) = (6, 5) for the two players. (a) We will investigate this game in strategic form. For Player 1, BU denotes the strategy \"B followed by U", BD denotes \"B followed by D\2. (continued) (b) Find all the pure strategy Nash equilibria of the strategic-form game in (a). (c) One of the Nash equilibria can be obtained by iterated deletion of weakly dominated strategies. Which one? Show the sequence of deletions that lead to this equilibrium. In this equilibrium, what is Player 1's payoff? does he have to burn money? Answer: The sequence of deletions is Player 1 deletes which is strictly/weakly dominated by ; then Player 2 deletes which is strictly/weakly dominated by after previous deletions; then Player 1 deletes which is strictly/weakly dominated by after previous deletions; the Player 2 deletes which is strictly/weakly dominated by after previous deletions (Continue iterated deletion if necessary) The equilibrium that remains after these deletions is: Player 1 uses the strategy and Player 2 uses the strategy In this equilibrium, Player 1 gets the payoff and he does/ does not (circle the right answer) have to burn money