Question

Determine the Nash-Bargaining solution of a prisoner dilemma.

**
C D**

**C** (2,2) (0,3)

**D** (3,0) (1,1)

Answer #1

Player one is the horizontal player and player two is the vertical player.

Consider player one,

If player one knows/thinks that player two will choose to play C, the better option for him is to choose D because his payoff is more with D than C in this case( 3>2). So he would choose D.

If player one thinks that player two will choose to play D, then he will again choose D as he gets more payoff with D(1>0).

So, player one will choose to play D whatever the choice be for player two. It is player one's dominant strategy to play D.

Similarly we can consider player two,

If one chooses C, player two will play D as (3>2)

If one chooses D, player two will play D as well as (1>0)

Thus, playing D is dominant strategy for both players.

The Nash equilibrium for this game will be (D, D) =(1, 1).

Had the players cooperated they could have got payoff of 2 each but they only get payoff of 1 each due to non corporation. This game is called prisoners dilemma as two rational individuals reach a decision that is not Pareto optimal.

1. Consider the following game with players Alice and Bob with
strategies C and D. What is the solution of this game by iterated
strict dominance? Please describe your step.
Table 1: A Game
Bob
Alice
C
D
C
2,2
0,3
D
3,0
1,1
2. For the same game, demonstrate that the Bob and Alice both
playing C is or is not a Nash equilibrium.

A prisoners' dilemma game will always have
A.
two Nash equilibria
B.
a unique Nash equilibrium in dominant strategies
C.
a Nash equilibrium that is efficient
D.
a cooperative equilibrium

Game Theory:
John and Dave are playing a game where they only have two
strategies, either to move left or move right. The payoffs from
this game are the points that each player will earn given the
strategies that each play. The higher the points, the higher the
payoffs each player will receive. The normal form representation of
the game is presented below.
DAVE
Left
Right
Left 1,1
0,3
Right 3,0
2,2
John's name label should be on...

In the prisoner’s dilemma, each prisoner would be best off,
if
Group of answer choices
a) both confess based on what is best for the individual.
b) one confesses based on what is best for the individual, but
the other does not confess.
c) one confesses based on what is best for the individual,
regardless if the other confesses or not.
d) neither confesses based on what is best for the whole not the
individual.

Find two nash equilibria of the game
L
C
R
U
1,-1
0,0
-1,1
M
0,0
1,1
0,0
D
-1,1
0,0
1,-1

Consider the following simultaneous-move game:
Column
L
M
N
P
Row
U
(1,1)
(2,2)
(3,4)
(9,3)
D
(2,5)
(3,3)
(1,2)
(7,1)
(a) Find all pure-strategy Nash equilibria.
(b) Suppose Row mixes between strategies U and D in the
proportions p and (1 − p). Graph the payoffs of Column’s four
strategies as functions of p. What is Column’s best response to
Row’s p-mix?
(c) Find the mixed-strategy Nash equilibrium. What are the
players’ expected payoffs?

Determine the equation of a conic that satisfies the
given conditions:
foci: (-1,2), (7,2)
vertices: (-2,2), (8,2)
b) Identify the conic: circle parabola, ellipse,
hyperbola.
c) Sketch the conic.
d) If the conic is a hyperbola, determine the
equations of the asymptotes.

The function g(x)=x^2/3+x is decreasing on the interval:
a) (-1,0)
b) (-1/3,0)
c) (-3/10,0)
d) (-8/27, 0)

determine the pH of a 0.10 M MgCl2 solution
a. 9.62
b. 11.53
c. 7.00
d. 3.65
Thanks!

1.
A Prisoners Dilemma illustrates the fact that
a.
Rational choices can lead to inefficient outcomes
b.
Rational choices always leads to good outcomes
c.
Rational choices always lead to inefficient outcomes
d.
None of the above
2.
Two roommates John and Joe are playing a simultaneous game of
cleaning the apartment. If neither of them clean, the apartment
gets filthy and both get a utility of 2. If John cleans and Joe
doesn’t, John gets a utility of 1...

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