Question

Consider the following two-person zero-sum game. Assume the two
players have the same three strategy options. The payoff table
below shows the gains for Player A.

Player B |
|||

Player A |
Strategy |
Strategy |
Strategy |

Strategy |
3 |
2 |
?4 |

Strategy |
?1 |
0 |
2 |

Strategy |
4 |
5 |
?3 |

Is there an optimal pure strategy for this game? If so, what is it?
If not, can the mixed-strategy probabilities be found
algebraically? What is the value of the game?

Answer #1

B | ||||||

b1 | b2 | b3 | Row minimum | |||

A | a1 | 3 | 2 | -4 | -4 | |

a2 | -1 | 0 | 2 | -1 | Maximin | |

a3 | 4 | 5 | -3 | -3 | ||

Column Maximum | 4 | 5 | 2 | |||

Minimax |

The value of the game lies between -1 and 2

As you can see there is no pure strategy for the game we have to find the optimal solution algebraical method or linear programming method

Player A linear program

Maximize Z = v

Subject to

v-3x1+x2-4x3<=0

v-2x1+0x2-5x3<=0

v+4x1-2x2+3x3<=0

x1,x2,x3>=0 , v is unrestricted

For B linear program

Minimize Z= v

Subject to

v-3y1-2y2+4y3>=0

v+y1+0y2-2y3>= 0

c-4y1-5y2+3y3>=0, v is unrestricted

Optimal value of game lies between -1 to 2

Consider the following two-person zero-sum game. Assume the two
players have the same two strategy options. The payoff table shows
the gains for Player A.
Player B
Player A
strategy b1
strategy b2
strategy a1
3
9
Strategy a2
6
2
Determine the optimal strategy for each player. What is the
value of the game?

Find the optimal strategies and the value of the game. Indicate
whether it is a fair or a strictly determinable game:
b1
b2
b3
b4
a1
2
10
7
0
a2
3
4
9
-1
a3
-6
-3
11
-3
a4
8
5
-4
-5

24. Two players are engaged in a game of Chicken. There are
two possible strategies: swerve and drive straight. A player who
swerves is called Chicken and gets a payoff of zero, regardless of
what the other player does. A player who drives straight gets a
payoff of 432 if the other player swerves and a payoff of −48 if
the other player also drives straight. This game has two pure
strategy equilibria and
a. a mixed strategy equilibrium in...

[Game Theory] Define a zero-sum game in which one player’s
unique optimal strategy is pure and all of the other player’s
optimal strategies are mixed.

4 A) Considering the following two-person zero-sum game,
what percentage of the time should the row player play strategy
X2?
Y1
Y2
X1
6
3
X2
2
8
A. 1/3
B. 2/3
C. 4/9
D. 5/9
4 B)
Considering the following two-person zero-sum game, what
percentage of the time should the column player play strategy
Y1?
Y1
Y2
X1
6
3
X2
2
8
A. 1/3
B. 2/3
C. 4/9
D. 5/9
4...

Two players can name a positive integer number from 1 to 6. If
the sum of the two numbers does not exceed 6 each player obtains
payoff equal to the number that the player named. If the sum
exceeds 6, the player who named the lower number obtains the payoff
equal to that number and the other player obtains a payoff equal to
the difference between 6 and the lower number. If the sum exceeds 6
and both numbers are...

Recall the Lions and Antelopes game. This time there are two
lions and three antelopes. The sizes (values) of the antelopes are
A1 > A2 > A3. As before, if two lions chase the same antelope
they each get half. If they chase different antelopes they each get
the one they chase.
(a) Write down the game payoff matrix.
(b) Show that if A2 < A1/2 then chasing antelope 1 is an
ESS.
(c) Now suppose A2 > A1/2 and...

solve the two person zero sum game with the payoff matrix:
-1 -1/2 1/2 1
4/3 1 -2/3 -1

(4) In this game, each of two players can volunteer some of
their spare time planting and cleaning up the community garden.
They both like a nicer garden and the garden is nicer if they
volunteer more time to work on it. However, each would rather that
the other person do the volunteering. Suppose that each player can
volunteer 0, 1, 2, 3, or4 hours. If player 1 volunteers x hours and
2 volunteers y hours, then the resultant garden...

Mixed Strategies
Consider the following game between two players Bad-Boy and
Good-Girl. Bad-Boy can either behave or misbehave whereas Good-Girl
can either punish or reward. Below payoff matrix shows the game as
pure strategies.
Good Girl
Reward
Punish
Bad Boy
Behave
5, 5
-5,-5
Misbehave
10,-10
-10,-5
Question 41 (1 point)
What is the Nash equilibrium of the game in pure strategies?
Question 41 options:
Behave-Reward
Behave-Punish
Misbehave-Punish
There is no Nash equilibrium in pure strategies.
Question 42 (1 point)...

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