FInd all the Nash Equilibria in these games.
Homework Answers
If Matrix 1 is chose by Player 3 then NE available in this payoff matrix is (1,2,3) & (3,2,1)[ Because Player 1 will choose row 1 if player 2 plays 1st column (1>1)& whill choose row 1 again if player 2 chooses 2nd column (3>-3).
Similarly Player 2 is indifferent between both columns as he will have same payoff in each cases.
On the same line in 2nd matrix we have NE (1,2,3) & (3,2,1) as completely same logic follows
Total NE are 4 and those will be (row1,column1) & (row1,column2) in Matrix 1 ; (row2,column1) & (row2,column2)
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FInd all the Nash Equilibria in these games.
10) Player 1 chooses row Player 2 chooses...
Determine ALL of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following 3 games: Player...
Determine ALL of the Nash equilibria
(pure-strategy and mixed-strategy equilibria) of
the following 3 games:
Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
Find all pure strategy Nash Equilibria in the following games a.) Player 2 b1 b2...
Find all pure strategy Nash Equilibria in the following games a.) Player 2 b1 b2 b3 a1 1,3 2,2 1,2 a2 2,3 2,3 2,1 a3 1,1 1,2 3,2 a4 1,2 3,1 2,3 Player 1 b.) Player 2 A B C D A 1,3 3,1 0,2 1,1 B 1,2 1,2 2,3 1,1 C 3,2 2,1 1,3 0,3 D 2,0 3,0 1,1 2,2 Player 1 c.) Player 2 S B S 3,2 1,1 B 0,0 2,3
Q3 Three-Player Game Consider a 3-player matrix game. The correct interpretation is as follows: the row...
Q3 Three-Player Game Consider a 3-player matrix game. The correct interpretation is as follows: the row indicates which strategy was chosen by player I; the column indicates which strategy was chosen by player II. If player III chooses strategy X, then the three players' payoffs are given by the first matrix; if player III chooses strategy Y , then the three players' payoffs are given by the second matrix. II II LR 4, 7, 5 8, 1, 3 1, 1,8...
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultan...
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
Problem 10 Find all pure-strategy Nash Equilibria of the three-player game below. Notice that player 3...
Problem 10 Find all pure-strategy Nash Equilibria of the three-player game below. Notice that player 3 has four strategies from which to select, represented by the four matrices. Matrix W Matrix X Matrix Y Matrix Z = 5.5" LR LR LR 1,0,3 A B 1,0,3 2,2,2 1,0,3 0,0,1 A B 1,0,3 1,0,3 2,2,2 0,3,3 A B 1,0,2 1,0,2 2,2,2 0,0,1 A B 1,0,2 1,0,2 2,2,2 0,3,3
Find all the Nash equilibria in the following game and indicate which are strict. Player 2...
Find all the Nash equilibria in the following game and indicate which are strict. Player 2 d b a -1,4 1,-3 2,7 W 2,7 Player 1 2.1 0,4 1, 3 1, 2 Y -1,6 6,2 3.2 1,1 Z 7,1 5.2 0.2 3,1 O (Wa) and (W,c). Neither are strict. O (W,c) and (Z,b). Both are strict O (Wc) and (Z,b). Neither are strict. O There are no Nash equilibria in this game.
3. Consider the following game in normal form. Player 1 is the "row" player with strate-...
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.
1. Consider the following game in normal form. Player 1 is the "row" player with strate-...
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...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive"- i.e. higher numbers represent better payoffs. Player 2 Strategy Strategy #2 ii Player 2 Strategy Strategy #1 #1 # 2 R 50 20 Strategy 15 20 100 Strategy 70 20 #1 #1 10 10 20 5 Strategy Strategy 70 Player 2 Strategy Strategy #1 60 100 #2 15 Player 2...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive" -- i.e. higher numbers represent better payoffs. Player 1 Player 2 Strategy Strategy #1 #2 Strategy A 20 B 100 #1 20 No a Strategy No 5 100 Player 2 Strategy Strategy Player 1 Strategy #1 Strategy Player 2 Strategy Strategy #1 #2 15 R 50 70 20 x 20...
Determine ALL of the Nash equilibria
(pure-strategy and mixed-strategy equilibria) of
the following 3 games:
Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
Q3 Three-Player Game Consider a 3-player matrix game. The correct interpretation is as follows: the row indicates which strategy was chosen by player I; the column indicates which strategy was chosen by player II. If player III chooses strategy X, then the three players' payoffs are given by the first matrix; if player III chooses strategy Y , then the three players' payoffs are given by the second matrix. II II LR 4, 7, 5 8, 1, 3 1, 1,8...
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
Problem 10 Find all pure-strategy Nash Equilibria of the three-player game below. Notice that player 3 has four strategies from which to select, represented by the four matrices. Matrix W Matrix X Matrix Y Matrix Z = 5.5" LR LR LR 1,0,3 A B 1,0,3 2,2,2 1,0,3 0,0,1 A B 1,0,3 1,0,3 2,2,2 0,3,3 A B 1,0,2 1,0,2 2,2,2 0,0,1 A B 1,0,2 1,0,2 2,2,2 0,3,3
Find all the Nash equilibria in the following game and indicate which are strict. Player 2 d b a -1,4 1,-3 2,7 W 2,7 Player 1 2.1 0,4 1, 3 1, 2 Y -1,6 6,2 3.2 1,1 Z 7,1 5.2 0.2 3,1 O (Wa) and (W,c). Neither are strict. O (W,c) and (Z,b). Both are strict O (Wc) and (Z,b). Neither are strict. O There are no Nash equilibria in this game.
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.
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...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive"- i.e. higher numbers represent better payoffs. Player 2 Strategy Strategy #2 ii Player 2 Strategy Strategy #1 #1 # 2 R 50 20 Strategy 15 20 100 Strategy 70 20 #1 #1 10 10 20 5 Strategy Strategy 70 Player 2 Strategy Strategy #1 60 100 #2 15 Player 2...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive" -- i.e. higher numbers represent better payoffs. Player 1 Player 2 Strategy Strategy #1 #2 Strategy A 20 B 100 #1 20 No a Strategy No 5 100 Player 2 Strategy Strategy Player 1 Strategy #1 Strategy Player 2 Strategy Strategy #1 #2 15 R 50 70 20 x 20...
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