Solution for Homework 1
1. Each of three people announces a positive integer. If the three integers are dierent, the
person whose integer is closest to twice the average gets $100. If two or more integers are the same,
$100 is split equally between the pe
Homework 3
1. Consider the following game. Player 1 receives a card that is either
L or H with equal probabilities. Player 2 does not see the card. Player 1
may announce that the card is L and pay $1 to player 2. Player 1 may
also announce that the card i
Solution for homework 5
1. Three players simultaneously decide whether to contribute to the public good. Each player
derives a benet of 1 if at least one player contributes and 0 if none contributes. The cost of
contributing for player i is equal to ci .
Solution for homework 3
1. Consider the following game. Player 1 receives a card that is either
L or H with equal probabilities. Player 2 does not see the card. Player 1
may announce that the card is L and pay $1 to player 2. Player 1 may
also announce th
Homework 6
1. There are two players, a plainti and a defendant in a civil suit. The plainti knows whether
or not he will win if the case goes to trial, but the defendant does not have this information. The
defendant knows that the plainti knows who would
Final exam ISE358
1. Consider the extensive form game shown below. We want to describe its SPE in the
behavior strategy form. Player i makes his move at information sets Ii , Ii , Ii . Payos are
listed vertically in the natural order 1,2,3. Find the SPE o
Solution for homework 2
1. Find all Nash equilibria (pure and mixed) of the game Chicken as it was introduced in
class.
Solution: The two pure strategy equilibria are (S, C) and (C, S). In addition to these, there
may be some mixed strategy equilibria. Le
Homework 1
1. Each of three people announces a positive integer. If the three integers are dierent, the
person whose integer is closest to twice the average gets $100. If two or more integers are the
same, $100 is split equally between the people whose in
Homework 2
1. Find all Nash equilibria (pure and mixed) of the game Chicken as it was introduced in
class.
2. Players 1 and 2 each choose a member of the set cfw_1, . . . , K. If the players choose the
same number then player 2 pays $1 to the player 1; ot
Homework 4
1. Find all feasible individually rational payos of the innitely repeated Bach or Stravinsky
game as it was described in class.
2. Consider the two-player game whose period payo are given in the tables below. The players
choices in the rst peri
Static Games
with Incomplete
Information
Example: Contributing to public good
. Two players make a 0-1 decision about contributing
to a public good
. For the £xed costs q of contributing their payoff is
given by Static Games
with Incomplete
Information
.
Homework 5
1. Three players simultaneously decide whether to contribute to the public good. Each player
derives a benet of 1 if at least one player contributes and 0 if none contributes. The cost of
contributing for player i is equal to ci . Each player k
Solution for homework 1
1. Each of three people announces a positive integer. If the three integers are dierent, the
person whose integer is closest to twice the average gets $100. If two or more integers are the same,
$100 is split equally between the pe
Solution for homework 6
1. There are two players, a plainti and a defendant in a civil suit. The plainti knows whether
or not he will win if the case goes to trial, but the defendant does not have this information. The
defendant knows that the plainti kno
ISE 358 Game Theory
Instructor: Eugene Perevalov
Mohler Lab Rm 483
Tel.: (610) 758-4031
email: eup2@lehigh.edu
Meeting times: MTWTr 1:00-2:35
Course description:
Mathematical analysis of how people interact in strategic situations. Applications include st
Homework 1
1. Each of three people announces a positive integer. If the three integers are dierent, the
person whose integer is closest to twice the average gets $100. If two or more integers are the same,
$100 is split equally between the people whose in
Homework 3
1. Find all feasible individually rational payos of the innitely repeated Bach or Stravinsky
game as it was described in class.
2. Consider the two-player game whose period payo are given in the tables below. The players
choices in the rst peri
Homework 4
1. Three players simultaneously decide whether to contribute to the public good. Each player
derives a benet of 1 if at least one player contributes and 0 if none contributes. The cost of
contributing for player i is equal to ci . Each player k
Solution for homework 3
1. Find all feasible individually rational payos of the innitely repeated Bach or Stravinsky
game as it was described in class.
Solution: The feasible payo lie in the region that has the shape of a triangle with vertices
(2,1), (1,