Consider the following sequential move game played by three players, A, B and C. Player A moves first and chooses one of the following two payoff matrices, either Box 1 or Box 2. Following Player A's choice, Players B and C move simultaneously. Player B chooses one of two strategies, Top or Bottom, while Player C chooses one of two strategies, Left or Right. Player A; Box 1: Player B Player A; Box 2: Player B Top Bottom Top Bottom Player C Left 3,3,3 6,5,0 Player C Left 3,6,6 4, 10,0 Right 6,0,5 8, 1, 1 Right 4,0, 10 6,2,2 Each cell in the two boxes contains three numbers. The first number is the payoff to Player A, the second number is the payoff to Player B and the third number is the payoff to Player C. This implies that when choosing their respective strategies, Players B and C will consider the second and third payoff numbers respectively in each cell. Player A, of course, will focus on the first number in each cell in deciding which box to choose. What is the subgame perfect equilibrium (via backward induction) of this game? You must clearly explain your reasoning as to how you arrive at your answer.

Consider the following sequential move game played by three players, A, B and C. Player A moves first and chooses one of the following two payoff matrices, either Box 1 or Box 2. Following Player A's choice, Players B and C move simultaneously. Player B chooses one of two strategies, Top or Bottom, while Player C chooses one of two strategies, Left or Right. Player A; Box 1: Player B Player A; Box 2: Player B Top Bottom Top Bottom Player C Left 3,3,3 6,5,0 Player C Left 3,6,6 4, 10,0 Right 6,0,5 8, 1, 1 Right 4,0, 10 6,2,2 Each cell in the two boxes contains three numbers. The first number is the payoff to Player A, the second number is the payoff to Player B and the third number is the payoff to Player C. This implies that when choosing their respective strategies, Players B and C will consider the second and third payoff numbers respectively in each cell. Player A, of course, will focus on the first number in each cell in deciding which box to choose. What is the subgame perfect equilibrium (via backward induction) of this game? You must clearly explain your reasoning as to how you arrive at your answer.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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