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Microsoft Word - Exam2EC403S X C A learn-us-east-1-prod-fleet01-xythos.s3.amazonaws.com/5deff46c33361/11002595?response-cache-control=private%20%20max-age%3D21600&response-content-disposition=inline%38%20.. J Microsoft Word - Exam2EC403Sum20.doc 1 / 11 pure 3/3 X 1. [12 points] Consider the following game with two players. As usual, the first component is Row's payoff. A B C Column Player H (3, 0) M (1, 2) (2, 5) L (5, 1) (2, 2) (0, 2) (2, 2) (3, 4) (1, 1) Row Player (a) Find all the pure strategy Nash equilibria, if there is any. (b) Find a mixed strategy Nash equilibrium different from any of your answers in (a). Justify your answer. Row's mixed strategy is [H] + [M] + [L] Column's mixed strategy is [A] + [B] + [C] Hint: First determine which pure strategies will not be used (i.e. assigned probability zero) in the equilibrium. (c) What are the expected payoffs of the equilibrium you found in (b)? Row's Exp. Payoff = Column's Exp. Payoff = (Next page is left blank for Question 1.) Page 1 of 1 1 + e Bo ST 2E 12:36 2020-07-03Microsoft Word - Exam2EC403S X C A learn-us-east-1-prod-fleet01-xythos.$3.amazonaws.com/5deff46c33361/11002595?response-cache-control=private%20%20max-age%3D21600&response-content-disposition=inline%38%20.. J Microsoft Word - Exam2EC403Sum20.doc 3/ 11 pure 3/3 X 2. [12 points] In this well-known game, there are two players and two stages in the game. Player 1 first decides whether to play B (Burn Money) or N (Not Burn Money). After observing the action of Player 1, the two players play a simultaneous-move game: L R Player 2 1's Payoff= 0 1's Payoff=9 U 2's Payoff= 0 2's Payoff=6 1's Payoff=6 2's Payoff=9 I's Payoff= 4 2's Payoff= 4 Player 1 Note that the game in the second stage has two equilibria: (U,R) and (D,L). Player 1 prefers (U, R) since his payoff is 9 in that equilibrium, whilst (D,R) gives him only 6. However, if Player 1 played B in the first stage, his payoff is reduced by 3. His payoff is not reduced if he played N in the first stage. Player 2's payoff is not affected by what Player I did in the first-stage. So, for instance, if Player 1 played B followed by U, and Player 2 played R after she saw B, the payoffs are (9 -3, 6) = (6, 6) 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", etc. For Player 2, LL denotes the strategy "play L regardless of what happened in the first stage", LR denotes "play L if B was seen in the first stage, but play R if N was seen", etc. Fill in the missing payoff values in the strategic form below. LL LR RL RR Player 2 I's Payoff= -3 1's Payoff= 1's Payoff=6 1's Payoff= BU 2's Payoff= 0 2's Payoff= 2's Payoff=6 2's Payoff= 1's Payoff= 3 1's Payoff= 1's Payoff= 1 1's Payoff= BD 2's Payoff= 9 2's Payoff= 2's Payoff= 4 2's Payoff= + 1's Payoff= 1's Payoff= 9 NU 2's Payoff= 1's Payoff= 0 1's Payoff= 2's Payoff= 6 2's Payoff=0 2's Payoff= 1's Payoff 1's Payoff= 4 I's Payoff=6 1's Payoff= e o S 24 12:36 2020-07-03