onsider the following two person static game where Player 1 is the row player and Player 2 is the column player
C | D | E | |
A | 1,1 | 0,2 | 2,0 |
B | 0,0 | 1,-1 | -1,3 |
a. |
There is an equilibrium where Player 1 plays A with probability 3/4. |
|
b. |
There is an equilibrium where Player 1 plays A with probability 2/3. |
|
c. |
There is an equilibrium where Player 1 plays A with probability 1/2. |
|
d. |
There is no mixed strategy Nash equilibrium. |
C |
D |
E |
|
A |
1 1 |
0 2 |
2 0 |
B |
0 0 |
1 -1 |
-1 3 |
We assign probability p and 1-p to strategy A and B respectively of Player 1. Similarly, we assign probability of q1 , q2 and 1-q1-q2 to strategy C , D and E respectively of Player 2.
To derive the mixed strategy nash equilibrium: we need to calculate the expected pay off of the players.
Player 1 chooses probability p such that player 2 is indifferent between C and D
Thus,
p. (1) + 1-p (0) = p(2)+1-p(-1)
p=2p-1+p
p-3p = -1
p=1/2
Similarly, Player 1 chooses probability p such that player 2 is indifferent between D and E
p(2)+1-p(-1) = p(0) + 1-p (3)
2p-1+p= 3-3p
3p-1= 3-3p
6p = 4
p=2/3
This is impossible. Therefore we donot have mixed strategy naash equilibrium for this game
onsider the following two person static game where Player 1 is the row player and Player...
Consider the following two person static game where Player 1 is the row player and Player 2 is the column player C D A 1, 0,2 2,0 B 0,0 1,3 O a. There is an equilibrium where Player 1 plays A with probability 3/4 O b. There is no mixed strategy Nash equilibrium O c. There is an equilibrium where Player 1 plays A with probability 2/3. O d. There is an equilibrium where Player 1 plays A with probability...
1. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, 2. The game is presented in the following matrix: a b c d w 3,3 1,1 0,0 0,0 x 2,1 1,2 1,0 0,5 y 0,2 1,0 3, 2 0,2 z 2,1 1,4 1,1 3,1 (a) Find the set of rationalizable strategies. (b) Find the set of Nash...
3. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, z. The game is presented in the following matrix: W Z X y a 3,3 2,1 0,2 2,1 b 1,1 1,2 1,0 1,4 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1 с Find all the Nash equilibria in the game in pure strategies.
2) True or false: The strategy
profile where player 1 plays B and player 2 plays C is a Nash
equilibrium
3) True or false: The strategy profile where player 1 plays B
and player 2 plays B is a Nash equilibrium?
True or false: The strategy profile where player 1 plays B and player 2 plays C is a Nash equilibrium? Player 2 A 4,4 1,1 Player 1 B 1,1 1,1 C 5,0 0,0
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