Consider the following sequential-move game, where the first value specified in the end nodes is the payoff for Player A, the second value is the payoff for Player B and the third value is the payoff for Player C. Determine its subgame perfect equilibrium. Identify the equilibrium outcome and describe carefully the strategy used by each player in equilibrium (remember, a strategy for a player is a complete specification of what action to take in every possible contingency). N AD n1 S B n₂ C تی u d -1, 4, -2 AND n4 S 0,-1, 3 A ng 3, -2, 10 1,0, 3 N S -4, 6, -1 1, 3, 3

Consider the following sequential-move game, where the first value specified in the end nodes is the payoff for Player A, the second value is the payoff for Player B and the third value is the payoff for Player C. Determine its subgame perfect equilibrium. Identify the equilibrium outcome and describe carefully the strategy used by each player in equilibrium (remember, a strategy for a player is a complete specification of what action to take in every possible contingency). N AD n1 S B n₂ C تی u d -1, 4, -2 AND n4 S 0,-1, 3 A ng 3, -2, 10 1,0, 3 N S -4, 6, -1 1, 3, 3

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.
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