1) Consider the following simultaneous-move game, game G1: COLUMN C1 C2 C3 R1 4, 4 0, 12 -2, -3 ROW R2 6, 10 5, 5 1, 12 R3 8,6 -1, -4 -3, 5 1.1) Using formal notation, explain why the table above is a strategic-form representation of game G1 by referring to the elements that comprise a strategic-form representation. [You do not have to give a complete enumeration of the players' utility functions; an example will be sufficient.] 1.2) Enumerate the joint strategy set of this game using formal notation. 1.3) Does the game have a strictly dominant strategy equilibrium? Briefly explain. Let S = S; for each player i be the player's strategy set, and for n2 1 let S denote those strategies of player i surviving after the nth round of elimination of strictly dominated strategies (IESDS). That is, s¡ e S' if si e S-1 and s is not strictly dominated in S"-1. With "in S"-1" we mean in the (possibly reduced) game which has the joint strategy space S"-1 = Skow x SCOLUMN- (see JR p.309–310.) 1.4) For the above game, determine S for all i for all n > 1. Justify your answers. 1.5) Write down the game's pure strategy Nash equilibrium(s) (NE). 1.6) Explain in what sense the NE solution concept is more precise than the IESDS solution concept.
1) Consider the following simultaneous-move game, game G1: COLUMN C1 C2 C3 R1 4, 4 0, 12 -2, -3 ROW R2 6, 10 5, 5 1, 12 R3 8,6 -1, -4 -3, 5 1.1) Using formal notation, explain why the table above is a strategic-form representation of game G1 by referring to the elements that comprise a strategic-form representation. [You do not have to give a complete enumeration of the players' utility functions; an example will be sufficient.] 1.2) Enumerate the joint strategy set of this game using formal notation. 1.3) Does the game have a strictly dominant strategy equilibrium? Briefly explain. Let S = S; for each player i be the player's strategy set, and for n2 1 let S denote those strategies of player i surviving after the nth round of elimination of strictly dominated strategies (IESDS). That is, s¡ e S' if si e S-1 and s is not strictly dominated in S"-1. With "in S"-1" we mean in the (possibly reduced) game which has the joint strategy space S"-1 = Skow x SCOLUMN- (see JR p.309–310.) 1.4) For the above game, determine S for all i for all n > 1. Justify your answers. 1.5) Write down the game's pure strategy Nash equilibrium(s) (NE). 1.6) Explain in what sense the NE solution concept is more precise than the IESDS solution concept.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Just any help with 1.4, 1.5 and 1.6 please
![1) Consider the following simultaneous-move game, game G1:
COLUMN
C1
C2
C3
R1
4, 4
0, 12
-2, -3
ROW
R2
6, 10
5, 5
1, 12
R3
8, 6
-1, -4
-3, 5
1.1) Using formal notation, explain why the table above is a strategic-form representation of
game G1 by referring to the elements that comprise a strategic-form representation. [You do
not have to give a complete enumeration of the players' utility functions; an example will be
sufficient.]
1.2) Enumerate the joint strategy set of this game using formal notation.
1.3) Does the game have a strictly dominant strategy equilibrium? Briefly explain.
Let S = S; for each player i be the player's strategy set, and for n 2 1 let S} denote those
strategies of player i surviving after the nth round of elimination of strictly dominated
strategies (IESDS). That is, s¡ e S' if s; e S-1 and s; is not strictly dominated in S"-1. With
"in Sn-1" we mean in the (possibly reduced) game which has the joint strategy space S"-1 =
Skow x ScoLUMN- (see JR p.309– 310.)
1.4) For the above game, determine S for all i for all n > 1. Justify your answers.
1.5) Write down the game's pure strategy Nash equilibrium(s) (NE).
1.6) Explain in what sense the NE solution concept is more precise than the IESDS solution
concept.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87b53351-2067-4a4d-a81c-a5cf0ffaa5a8%2F9723d655-6282-4845-892c-3bfa7cde9f7b%2F13dtnpd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1) Consider the following simultaneous-move game, game G1:
COLUMN
C1
C2
C3
R1
4, 4
0, 12
-2, -3
ROW
R2
6, 10
5, 5
1, 12
R3
8, 6
-1, -4
-3, 5
1.1) Using formal notation, explain why the table above is a strategic-form representation of
game G1 by referring to the elements that comprise a strategic-form representation. [You do
not have to give a complete enumeration of the players' utility functions; an example will be
sufficient.]
1.2) Enumerate the joint strategy set of this game using formal notation.
1.3) Does the game have a strictly dominant strategy equilibrium? Briefly explain.
Let S = S; for each player i be the player's strategy set, and for n 2 1 let S} denote those
strategies of player i surviving after the nth round of elimination of strictly dominated
strategies (IESDS). That is, s¡ e S' if s; e S-1 and s; is not strictly dominated in S"-1. With
"in Sn-1" we mean in the (possibly reduced) game which has the joint strategy space S"-1 =
Skow x ScoLUMN- (see JR p.309– 310.)
1.4) For the above game, determine S for all i for all n > 1. Justify your answers.
1.5) Write down the game's pure strategy Nash equilibrium(s) (NE).
1.6) Explain in what sense the NE solution concept is more precise than the IESDS solution
concept.
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