Game Theory
⌈ 1 4 6 ⌉
⌊ 3 8 5 ⌋
What is the equilibrium pair of this matrix game?
⌈ 1 4 6 ⌉
⌊ 3 8 5 ⌋
lowest in rows : { 1 3 } ; max = 3
greatest in columns : { 3 8 6 } ; min = 3
max min : { 1st row , 1st column }
⌈ 11 5 9 ⌉
⌊ 15 7 10 ⌋
What is the equilibrium pair of this matrix game?
⌈ 11 5 9 ⌉
⌊ 15 7 10 ⌋
lowest in rows : { 5 7 } ; max = 7
greatest in columns : { 15 7 10 } ; min = 7
max min : { 2nd row , 2nd column }
⌈ 5 2 4 6 ⌉
| -3 -5 -2 -4 |
⌊ 3 -1 0 1 ⌋
What is the equilibrium pair of this matrix game?
⌈ 5 2 4 6 ⌉
| -3 -5 -2 -4 |
⌊ 3 -1 0 1 ⌋
lowest in rows : { 2 -5 -1 } ; max = 2
greatest in columns : { 5 2 4 6 } ; min = 2
max min : { 1st row , 2nd column }
⌈ -4 3 2 7 ⌉
| -5 2 1 6 |
⌊ -6 -2 5 -8 ⌋
What is the equilibrium pair of this matrix game?
⌈ -4 3 2 7 ⌉
| -5 2 1 6 |
⌊ -6 -2 5 -8 ⌋
lowest in rows : { -4 -5 -8 } ; max = -4
greatest in columns : { -4 3 1 4 } ; min = -4
max min : { 1st row , 1st column }
⌈ 3 5 2 -4 -6 ⌉
| 2 -3 0 -1 4 |
⌊ 1 -4 6 -2 2 ⌋
What is the lower value of this matrix game?
3 5 2 -4 -6
2 -3 0 -1 4
1 -4 6 -2 2
lowest in rows : { -6 -3 -4 } ; max = -3
⌈ -3 -5 -2 4 6 ⌉
| -2 3 0 1 -4 |
⌊ -1 4 -6 2 -2 ⌋
What is the lower value of this matrix game?
⌈ -3 -5 -2 4 6 ⌉
| -2 3 0 1 -4 |
⌊ -1 4 -6 2 -2 ⌋
lowest in rows : { -5 -4 -6 } ; max = -4
⌈ -1 -3 -4 1 ⌉
| 2 1 3 -1 |
⌊ 1 -3 -4 2 ⌋
What is the upper value of this matrix game?
⌈ -1 -3 -4 1 ⌉
| 2 1 3 -1 |
⌊ 1 -3 -4 2 ⌋
greatest in columns : { 2 1 3 2 } ; min = 1
⌈ 2 4 5 0 ⌉
| 0 1 -1 3 |
⌊ 2 6 7 1 ⌋
What is the upper value of this matrix game?
⌈ 2 4 5 0 ⌉
| 0 1 -1 3 |
⌊ 2 6 7 1 ⌋
greatest in columns : { 2 6 7 3 } ; min = 2
⌈ -1 -2 ⌉
| -6 -3 |
⌊ -4 1 ⌋
What is the sum of the lower and the upper values of this matrix game?
⌈ -1 -2 ⌉
| -6 -3 |
⌊ -4 1 ⌋
lowest in rows : { -2 -6 -4 } ; max = -2
greatest in columns : { -1 1 } ; min = -1
sum = -2 + -1 = -3
⌈ 2 3 ⌉
| 7 5 |
⌊ 4 1 ⌋
What is the sum of the lower and the upper values of this matrix game?
⌈ 2 3 ⌉
| 7 5 |
⌊ 4 1 ⌋
lowest in rows : { 2 5 1 } ; max = 5
greatest in columns : { 7 5 } ; min = 5
sum = 5 + 5 = 10
⌈ -3 0 -4 -4 -5 ⌉
⌊ -1 1 -2 2 -6 ⌋
What is the minimax strategy of Player II in this matrix game?
⌈ -3 0 -4 -4 -5 ⌉
⌊ -1 1 -2 2 -6 ⌋
greatest in columns : { -1 1 -2 2 -5 } ; min = -5
⌈ 4 1 7 5 6 ⌉
⌊ 3 0 6 -1 8 ⌋
What is the minimax strategy of Player II in this matrix game?
⌈ 4 1 7 5 6 ⌉
⌊ 3 0 6 -1 8 ⌋
greatest in columns : { 4 1 7 5 8 } ; min = 1
⌈ (-2, -4) (-1, -1) (-5, -3) ⌉
| (-6, -2) (-2, -3) (-4, -4) |
⌊ (-5, 0) (-3, -4) (-3, -2) ⌋
What is the Nash equilibrium pair of this bimatrix game?
⌈ (-2, -4) (-1, -1) (-5, -3) ⌉
| (-6, -2) (-2, -3) (-4, -4) |
⌊ (-5, 0) (-3, -4) (-3, -2) ⌋
(greatest in column, greatest in row) = (-1 , -1)
⌈ (3, 5) (2, 2) (6, 4) ⌉
| (8, 4) (4, 5) (7, 7) |
⌊ (9, 3) (6, 7) (8, 5) ⌋
What is the Nash equilibrium pair of this bimatrix game?
⌈ (3, 5) (2, 2) (6, 4) ⌉
| (8, 4) (4, 5) (7, 7) |
⌊ (9, 3) (6, 7) (8, 5) ⌋
(greatest in column, greatest in row) = (6 , 7)
⌈ (5, -5) (4, -4) (6, -6) ⌉
| (5, -5) (4, -4) (6, -6) |
⌊ (3, -3) (1, -1) (-2, 2) ⌋
Is this a zero sum matrix game?
⌈ (5, -5) (4, -4) (6, -6) ⌉
| (5, -5) (4, -4) (6, -6) |
⌊ (3, -3) (1, -1) (-2, 2) ⌋
Yes
⌈ (-5, 5) (-4, 4) (-6, 6) ⌉
⌊ (-3, 3) (-1, 1) (2, -2) ⌋
Is this a zero sum matrix game?
⌈ (-5, 5) (-4, 4) (-6, 6) ⌉
⌊ (-3, 3) (-1, 1) (2, -2) ⌋
Yes
⌈ -3 -5 0 -2 -1 ⌉
⌊ -4 1 -8 -3 0 ⌋
What is the guaranteed value for Player I in this matrix game, if Player I chooses 2nd row?
⌈ -3 -5 0 -2 -1 ⌉
⌊ -4 1 -8 -3 0 ⌋
min in 2nd row = -8
⌈ 4 6 1 3 2 ⌉
⌊ 6 1 10 5 7 ⌋
What is the guaranteed value for Player I in this matrix game, if Player I chooses 2nd row?
⌈ 4 6 1 3 2 ⌉
⌊ 6 1 10 5 7 ⌋
min in 2nd row = 1
⌈ 3 -2 -4 ⌉
| -5 -4 4 |
| 2 0 5 |
⌊ -3 -2 -4 ⌋
What is the maximin strategy for Player I in this game ?
⌈ 3 -2 -4 ⌉
| -5 -4 4 |
| 2 0 5 |
⌊ -3 -2 -4 ⌋
lowest in rows : { -4 -5 0 -4 } ; max = 0
⌈ -2 3 -3 ⌉
| 7 6 -2 |
| 1 3 -1 |
⌊ 8 5 4 ⌋
What is the maximin strategy for Player I in this game ?
⌈ -2 3 -3 ⌉
| 7 6 -2 |
| 1 3 -1 |
⌊ 8 5 4 ⌋
lowest in rows : { -3 -2 -1 4 } ; max = 4