Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 2 (for due date see web page)
1.
Consider the following strategic-form game, where p is a number strictly between 0 and 1 (0 <
p < 1).
Player
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 2 ANSWERS
1.
Since, for every p strictly between 0 and 1, 1 + p < 4, (A,E) is not a Nash equilibrium (player 1
can get a higher payoff with B).
Since, for every p strictly between 0 and 1, 4
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 1 ANSWERS
1. (a) The game is as follows:
Ben
home
You
home
party
2
0
2
2
party
2
2
2
0
0
3
2
2
Chris: home
Ben
home
You
home
party
2
0
2
2
party
0
3
2
3
0
0
0
0
Chris: party
(b) No. (c) The
ECN 122 : Game Theory
Professor Giacomo Bonanno
FALL 2012 - FIRST MIDTERM EXAM: ANSWERS for VERSION 2
1.
(a) For z > 3 .
(b) For z = 3 .
(c) No, because if player 1 plays B and player 3 plays E, then player 2 gets the same
payoff no matter whether she pla
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 3 (for due date see web page)
1. Consider the following game.
2
L
R
1
1
A
2
D
D
C
0
2
2
0
1
2
2
0
0
z
3
w
M
M
L
0
3
3
0
2
0
2
3
1
1
2
2
G
E
y
ECN 122 : Game Theory
Professor Giacomo Bonanno
FALL 2012 - FIRST MIDTERM EXAM: ANSWERS for VERSION 1
1. (a) The game is as follows:
Player
2
10
value:
60
20
30
Player 1
10
30
0
0
50
0
50
value:
20
30
0
20
0
0
40
40
30
30
0
20
0
10
0
(b) For player 1, 10
ECN 122 : Game Theory
Professor Giacomo Bonanno
FALL 2012 - SECOND MIDTERM EXAM: ANSWERS for VERSION 1
1.
(a) The normal form is as follows (player 2s strategy CE means if 1 chooses A I will
choose C and if player 1 chooses B I will choose E; similarly fo
ECN 122 : Game Theory
Professor Giacomo Bonanno
FALL 2012 - THIRD MIDTERM EXAM: ANSWERS for VERSION 1
1. (a) cfw_a,b,c,d, cfw_e,f,g, cfw_h.
(b.2) K2E = E
(b) (b.1) K1E = cfw_b,c,g,h
(b.3) compute from right to left: K1E = cfw_a,d,e,f, K2K1E = cfw_d,e, K3K
ECN 122 : Game Theory
Professor Giacomo Bonanno
FALL 2012 - THIRD MIDTERM EXAM: ANSWERS for VERSION 2
1. Let D be the event that you have the disease and T the event that you give a positive
P (T | D ) P ( D )
. The
P (T | D ) P ( D ) + P (T | D ) P (D )
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 6 ANSWERS
(a) The game is as follows:
NATURE
1 p
p
B
1
0
B
T
1
1
1
0
T
2
A
D
D
0
1
0
2
2
1
(b) The strategic form is as follows:
A
2
2
Player 2
D
A
BB
1
0
1
0
BT
p
1-p
2-p
2(1-p)
TB
1-p
2p
1
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 5 ANSWERS
1. (a) Since the expected value of the lottery $150
$0
is $50 and she considers the
1
2
3
3
lottery to be equivalent to $40, she is risk averse (if she were risk neutral she would
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 4 ANSWERS
1. (a) S = cfw_a, c, K
Bob
S = cfw_a, K Carla S = cfw_c, K Bob K Carla S = , K Carla K Bob S = .
(b) T = cfw_b, d , K BobT = cfw_b, K CarlaT = cfw_d , K Bob K CarlaT = , K Carla K
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 3 ANSWERS
1.
(a) Player 1 has four strategies: AE, AF, BE and BF.
(b) 23 = 8 : LCG, LCH, LDG, LDH, RCG, RCH, RDG, RDH.
(c) Two: the ones that start at player 1s nodes.
(d) First consider the
ECN 122 : Game Theory
Professor Giacomo Bonanno
FALL 2012 - SECOND MIDTERM EXAM: ANSWERS for VERSION 2
1.
(a) Player 1 has 2 strategies (T and B), Player 2 has 3 strategies (A, B and C) and
player 3 has 3 strategies (D, E and F).
(b) One: the one that sta
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 6 (for due date see web page)
Consider the following situation of incomplete information:
1
T
2
1
A
T
2
1
B
D
1
0
0
2
2
A
2
2
B
D
1
0
0
1
1:
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 5 (for due date see web page)
1. When asked if she would rather get $40 for sure or roll a die and get $150 if it shows the
face 1 or 2 (and
Chapter 13:
Problems 2 and 9
Chapter 15:
Problems 1 and 6
NOTE: The problem is a bit unclear on how rankings work. Rankings are determined strictly by the number of first-place votes; second-place votes are only used as tiebreakers if two skaters have the
2.2
(a) (b)
(1) simultaneous; (2) zero-sum; (3) not repeated (though it is possible to play it repeatedly); (4) imperfect information (dont know others chosen move); (5) fixed rules; (6) noncooperative (1) sequential; (2) non-zero-sum (for voters, who are
8.1
Let p be the probability that Row plays Up, and q the probability that Column plays Left. Rows expected payoffs from each strategy are EUU = 4q (1 q) = 5q 1 EUD = q + 2(1 q) = 2 q If q = 1/2, Row is indifferent between the two strategies, if q > 1/2,
13.2 (a)
ESS: Fight
(Fight strictly dominates Share)
(b)
Let p be the proportion of Fighters (so 1p is the proportion of Sharers). Then the expected payoff (fitness) for each type is: F(F) = -50p + 200(1 p) = 200 250p F(S) = 100(1 p) = 100 100p When p = 2
ECN 122 : GAME THEORY
Version
Version 1
FALL 2012 - FINAL EXAM
Professor Giacomo Bonanno
Answer all questions. Explain your answers.
1. [30 points]
Husband (H) and Wife (W) have to decide, independently and simultaneously, whether
to go to a football game
ECON 122 : GAME THEORY
Professor Giacomo Bonanno
FALL 2012 - FINAL EXAM: ANSWERS for VERSION 1
1.
(a) Let the wife be player 1 and the husband player 2 and let q =
4
5
1:
2:
(1 q )
q
wife is loving
wife is independent
(b) The extensive game is as follows
ECON 122 : GAME THEORY
Professor Giacomo Bonanno
FALL 2012 - FINAL EXAM: ANSWERS for VERSION 2
1. (a) The pure-strategy Nash equilibria are (B,E) and (C,F).
(b) For player 1 A is strictly dominated by C and for player 2 D is strictly dominated by E.
Thus
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 1 (for due date see web page)
1.
This evening you face a difficult decision. You have been invited to a party, together
with your friends Ben
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 4 (for due date see web page)
1. Consider the following situation:
Ann is in
San Francisco
BOB
CARLA
Ann is at
Lake Tahoe
Ann is in
San Franc
Eeo 122: Game Theory
Summer Session II, lllll
Professor David Lang
Exam [
20 August 2W3
NAME: k E I
I. Multiple Choice Qaestiens
For each ofthefot'lowlng. cheese the best tamer. Each question will be worth 3
points. Be sure to write the sewers in the