4. (Backward induction/normal form) Consider the following sequential move game played by three players; Mars, Mercury and Venus. Mercury Mars P Mars 3 Mercury 4 Venus 1 b T 2 1 3 P 1 2 3 A R Mars a Mars T 530 0 B M 123 Venus N 310 (i) List the strategies of each player. (ii) Find the subgame perfect Nash equilibrium. (iii) Present the strategic form of the game and find all the pure strategy Nash equilibria in the strategic form. (Mars is the row player, Mercury is the column player and Venus is the matrix player.) For each Nash equilibrium in the strategic form that is not subgame perfect in the extensive form, provide a reason why it is not so.

4. (Backward induction/normal form) Consider the following sequential move game played by three players; Mars, Mercury and Venus. Mercury Mars P Mars 3 Mercury 4 Venus 1 b T 2 1 3 P 1 2 3 A R Mars a Mars T 530 0 B M 123 Venus N 310 (i) List the strategies of each player. (ii) Find the subgame perfect Nash equilibrium. (iii) Present the strategic form of the game and find all the pure strategy Nash equilibria in the strategic form. (Mars is the row player, Mercury is the column player and Venus is the matrix player.) For each Nash equilibrium in the strategic form that is not subgame perfect in the extensive form, provide a reason why it is not so.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

This is an easy question from economics NASH EQUILIBRIUM

4.
(Backward induction/normal form) Consider the following sequential
move game played by three players; Mars, Mercury and Venus.
Mars
A
В
a
Mercury
Venus
R
M
Mars
Mars
1
3
P
T
P
2
1
3
2 1
1 2
Mars
3
Mercury
4
3
Venus
1
3 3
(i) List the strategies of each player.
(ii) Find the subgame perfect Nash equilibrium.
(iii) Present the strategic form of the game and find all the pure strategy Nash
equilibria in the strategic form. (Mars is the row player, Mercury is the column player
and Venus is the matrix player.) For each Nash equilibrium in the strategic form that
is not subgame perfect in the extensive form, provide a reason why it is not so.

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Step 1: Define the term Nash Equilibrium

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Step 2: Determine three-player Sequential Move Game

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Step 3: Determine Subgame Perfect Nash Equilibrium

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Step 4: Determine Strategic Form and Nash Equilibria

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