Consider the following simultaneous-move game:
Column
L
M
N
P
Row
U
(1,1)
(2,2)
(3,4)
(9,3)...
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?
Game Theory:
John and Dave are playing a game where they only have two
strategies, either...
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...
Pure strategy Nash equilibrium
3. In the following games, use the underline method to find all...
Pure strategy Nash equilibrium
3. In the following games, use the underline method to find all
pure strategy Nash equilibrium.
(B ) [0, 4, 4 0, 5, 3]
[4, 0 0 4, 5, 3]
[3, 5, 3, 5 6, 6]
(C) [2, -1 0,0]
[0,0 1,2]
(D) [4,8 2,0]
[6,2 0,8]
(E) [3,3 2,4]
[4,2 1,1]
4. In the following 3-player game, use the underline method to
find all pure strategy Nash equilibria. Player 1 picks the row,
Player 2...
a. i. If a game has a dominant strategy equilibrium, does it
have a Nash equilibrium?...
a. i. If a game has a dominant strategy equilibrium, does it
have a Nash equilibrium?
ii. If a game has a Nash equilibrium, does it have a dominant
strategy equilibrium?
iii. If one firm has a dominant strategy, can another firm take
advantage of that fact in deciding on its optimal strategy?
iv. Can a game have more than one dominant strategy
equilibrium?
v. Can a game have more than one Nash equilibrium?
b) There are only two firms...