Question

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.

Answer #1

Ans

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. Present your formal analysis carefully and compute the Nash
equilibria of the following location game in pure strategies. 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...

Consider the following game played between 100 people. Each
person i chooses a number si between 20 and 60 (inclusive). Let a-i
be defined as the average selection of the players other than
player i ; that is, a-i = summation (j not equal to i) of sj all
divided by 99. Player I’s payoff is ui(s) = 100 – (si – (3/2)a-i)2
For instance, if the average of the –i players’ choices is 40 and
player i chose 56,...

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

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...

2) Consider the scenario below: Two firms are merging into a
larger company and must select a computer system for daily use. In
the past, the players have used different systems I and A; each
firm prefers the system it has used in the past. They will both be
better off by using the same computer system than if they use
different systems. The payoff matrix for the two players is given
below:
Player 2
I
A
Player 1
I...

4. Consider the following non-cooperative, 2-player game. Each
player is a middle manager who wishes to get a promotion. To get
the promotion, each player has two possible strategies: earn it
through hard work (Work) or make the other person look bad through
unscrupulous means (Nasty). The payoff matrix describing this game
is shown below. The payoffs for each player are levels of
utility—larger numbers are preferred to smaller numbers. Player 1’s
payoffs are listed first in each box. Find...

A game has two players. Each player
has two possible strategies. One strategy is Cooperate, the other
is Defect. Each player writes on a piece of paper either a C
for cooperate or a D for defect. If both players write
C, they each get a payoff of $100. If both players
write D, they each get a payoff of 0. If one player
writes C and the other player writes D, the
cooperating player gets a payoff of S...

(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...

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...

Two players simultaneously name fractions of the pie
that they would like to take for themselves (between 0 and 1). If
the two fractions add up to 1 or less, both players get the
fractions that they called out. (If they both call out 1⁄2, they
each get 1⁄2). If the two fractions add up to more than 1, they
both get nothing (If they both call out 2/3, they both get
nothing). What are the Nash equilibria of the...

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