Mathematical theory of games 11. (15%) Solve each game. 0 1 -2 (a) 3 2 -3 0 1-2 (b) 2 0 1 1 -2 1 4-1 5 4 -1 51 (e) 1 5 14 5 14-1 22 2 2/ 11. (15%) Solve each game. 0 1 -2 (a) 3 2 -3 0 1-2 (b...
game theory strategy and dominant strategies
E F 1. (5 points) Can the game theory approach described in chapter 10 be used to analyze the model of Perfect Competition? Please explain. 2. (5 points) Use the following payoff matrix for a simultaneous move one shot game to answer the following questions Player 2 Strategy с D Player 1 A 6, 14 7, 11 18, 20 10, 19 B 12, 5 15, 1 7, 25 16, 17 (a) Does player 1...
Game Theory:
I only need help with 5 (a & b).
Will rate for correct and descriptive answers!
4 Draw the normal-form matrix for each of the following extensive-form games. C 0,0 E 2,2 F3,4 1 U 4,0 (b) 11 3,2 5) Use your normal-form matrix for (4a) above. Assume that ơi-( Find the following: , , ). a. ui(oi, CE
Find the determinant of each matrix: 3 2 A. 1 4 B. -3 2 51 1 4 0 -1 2. 6] 22 2 2 1 C. -4 2. T 0 -9 0 0 2 0 0 0 2. 8. D. 7 | 09 1 0 -4 -36 0 5
Write 2-4 sentences comparing the equilibrium you solved for with Cournot competition to the Nash equilibria we would solve for with simultaneous games in our game theory unit. Is a partial equilibrium with Cournot competition a Nash equilibrium? (3 points)
Problem E Solve each equation for 0 so<2.1. Answers must be in radians. 51 1) 2V3 - 6tan (+ Зл 2) 2sin (@+ I 4) 2cos @ + 1 - 3cos0 --4cos e 3) -6tan -2V3 5) V2sin e + 3cos e - 2 sin cos 0 + 3cos e 6) 2tan 8 + 2tan? 0 - 1 + 3tan?
Each game you play, you win with probability p, 0<p<1. You plan to play 5 games, but if you win the fifth game, you will keep playing until you lose. Assume the outcome of each game is independent of all others. a) Find the expected number of games you loss. b) Find the expected number of games you win.
Game
Point_Differential Assists
Rebounds Turnovers Personal_Fouls
1 15 15 38
11 9
2 36 20 43
8 13
3 16 21 29
7 13
4 45 22 46
11 11
5 12 11 40
7 22
6 -10 10 31
13 26
7 11 19 45
11 7
8 12 16 32
16 14
9 3 16 27
18 15
10 19 9 34
17 17
11 40 16 41
9 17
12 44 12 29
9 22
13 16 ...
find the eigen space of 4a and 4c
Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6.
Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...
2 3 S1 0 1 0 114 4 13 1 0 15 7 2 4 1 14 3|15 12 8 4 5 6 7 8 9 10 11 12 13 14 15 1 2 15 11 8 3 10 6 12 5 9 0 7 4 14 2 13 1 10 6 12 11 9 5 3 8 8 13 6 2 11 15 12 9 7 3 10 5 0 2 4 9 1 7 5 11 0 6...
Solve the matrix game. 5 0 1 -3 7 4 PE (Type an integer or simplified fraction for each matrix element.)