Find the (iterated) dominant equilibrium and (mixed strategy) Nash equilibria in the following games
Game 1
|
S1 |
S2 |
|
|
T1 |
3, 2 |
1, 1 |
|
T2 |
1, 1 |
2, 3 |
Game 2
|
S1 |
S2 |
S3 |
|
|
T1 |
3,5 |
4,3 |
6,4 |
|
T2 |
2,4 |
6,6 |
4,3 |
|
T3 |
5,3 |
5,5 |
2,1 |
Find the (iterated) dominant equilibrium and (mixed strategy) Nash equilibria in the following games Game 1...
(ECONOMICS OF STRATEGY, GAME THEORY) QUESTIONS PLEASE
ANSWERR
Find the mixed strategy NASH EQUILIBRIUM of the following game.
Also calculate each player's EXPECTED PAY OFF.
P1\P2LR 3,5 1,2 D 2,1 6,4
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down
a) Eliminate strictly dominated strategies.b) If the game does not have a pure strategy Nash equilibrium,find the mixed strategy Nash equilibrium for the smaller game(after eliminating dominated strategies). Player 2Player 1abcA4,33,22,4B1,35,33,3
4. Compute the mixed-strategy equilibria of the following games. 1 А в \ L M R 2,4 0,0 3. 6,3 | 3,5 5,5 B 1,6 | 3,7 4,8 5,2 | 3,7 4,9
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
6. Consider the following game: a. Identify all Nash Equilibria (Pure Strategy and Mixed) of this simultaneous game. b. Draw the two extensive form games that arise from each firm moving first. What are the Subgame Perfect Equilibria of these games? c. Identify a trigger strategy for each player that sustains (B,B) as an equilibrium. For what interest (discount) rates will this outcome be sustainable?
a.) Find all pure-strategy Nash equilibria.
b.) *Find all mixed-strategy Nash equilibria.
c.) Explain why, in any mixed-strategy equilibrium, each player
must be indifferent between the pure strategies that she randomizes
over.
Consider the following game: - 2 LR 2
Find all of the pure and mixed strategy Nash equilibrium of the following game: Top 2 Center Right 2,1 8,8 6,5 2,7 2.2 Left 5,10 3,7 2,5 1 Middle Bottom Figure 1: A Random Game
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5
Find all of the pure and mixed strategy Nash equilibrium of the
following game:
Left 5,10 3.7 2,5 Top 1 Middle Bottom 2 Center Right 4,4 8.8 6.5 2,7 2,2 2,1 Figure 1: A Random Game