Question

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 |

Answer #1

(M,C) is one Nash equilibrium.

It is so because if player 1 chooses M, then the other player should choose C and vice versa.

There is another mixed Nash equilibrium

So, the other NE is (0.5U+0.5D, 0.5L+0.5R)

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
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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

Find two Nash equilibria in the following game
s1
s2
s3
t1
3,4
4,5
6,4
t2
2,2
6,4
4,3
t3
5,3
5,5
5,6

1. For the following payoff matrix, find these:
a) Nash equilibrium or Nash equilibria (if any)
b) Maximin equilibrium
c) Collusive equilibrium (also known as the "cooperative
equilibrium")
d) Maximax equilibrium
e) Dominant strategy of each firm (if any)
Firm A
Strategy X
Strategy Y
Firm B
Strategy X
200
23
250
20
Strategy Y
30
50
1
500
2. For the following payoff matrix, find these:
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Evaluate the integral ∬ ????, where ? is the square with
vertices (0,0),(1,1), (2,0), and (1,−1), by carrying out the
following steps:
a. sketch the original region of integration R in the xy-plane
and the new region S in the uv-plane using this variable change: ?
= ? + ?,? = ? − ?,
b. find the limits of integration for the new integral with
respect to u and v,
c. compute the Jacobian,
d. change variables and evaluate the...

Player 1 chooses T, M, or B. Player 2 chooses L, C, or R.
L
C
R
T
0, 1
-1, 1
1, 0
M
1, 3
0, 1
2, 2
B
0, 1
0, 1
3, 1
(2 points each)
(a) Find all strictly dominated strategies for
Player 1. You should state what strategy strictly
dominates them.
(b) Find all weakly dominated strategies for
Player 2. You should state what
strategy weakly dominates them.
(c) Is there any weakly...

1. For the following payoff matrix, find these: a) Nash
equilibrium or Nash equilibria (if any) b) Maximin equilibrium c)
Collusive equilibrium (also known as the "cooperative equilibrium")
d) Maximax equilibrium e) Dominant strategy of each firm (if any)
Firm A Strategy X Strategy Y Firm B Strategy X 200 23 250 20
Strategy Y 30 50 1 500

Compute the Nash equilibria of the following location game.
There are two
people who simultaneously select numbers between zero and one.
Suppose
player 1 chooses s1 and player 2 chooses s2 . If si = sj , then
player i gets a
payoff of (si + sj )/2 and player j obtains 1 − (si + sj )/2,
for i = 1, 2. If
s1 = s2 , then both players get a payoff of 1/2.

. Present your formal analysis carefully and compute the Nash
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are two people who simultaneously select numbers between zero and
one. Suppose player 1 chooses s1 and player 2 chooses s2. If si
< sj , then player i gets a payoff of (si+sj ) 2 and player j
obtains 1 − (si+sj ) 2 , for i = 1, 2. If s1 = s2, then both
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