Problem Set 2 Solutions
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414 0301
Spring 2015
Exercise 1
1) In the first round of IESDS, we can eliminate strategies F and G from player 1 (they are
both strictly dominated by H).
In the second roun
Problem Set 1 Solutions
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414 0301
Spring 2015
Exercise 1 We can express either player 1 as the column player or as the row player, as
long as we keep the pay-off convention where the first pay-off c
Game Theory (econ 414)
Problem Set 1: Modelling Games and Eliminating the Impossible
Relevant reading: Harrington chapters 1-3 and lectures 1-5.
Due date: Feb 12th.
Instructions (read these carefully before starting):
Write your name (last name, rst name)
ECON 414 Problem set #5
1. (a) Bidder values at 5 and bids 4:
(.2 x .5 x (5-4) + (.8 x 0) = .1
If they bid 5 payoff = 0
If they bid <4 payoff = 0
If they bid 6 payoff = -.85
Therefore, bidding 4 at valuation 5 is a symmetric BNE
Bidder values at 7 and
ECON 414 Problem Set #3
1. A. The SPNE for this game is:
i.
(Buy, Greenmail) which pays off (15, 7) to the Raider and to
Management, respectively.
B. There is another Nash Equilibrium in this game which occur would occur at (Buy/Take
over, No greenmail) w
Econ414 Problem Set 4
1. There are five subgames in this case. There is player 1 choosing between E and F,
player 2 choosing between A and B, player 2 choosing between C and J, player 3
choosing between G and H (not knowing if they are at point B or point
Problem Set 1
Due date: September 9, 2015
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414 0101
Fall 2015
Exercise 1 Express the following games in strategic form:
P1
A
B
P2
C
(1, 2)
D
P2
E
(1, 1)
F
(0, 2)
G
(2, 2)
(1, 3)
P1
A
B
P2
C
D
C
D
P1
Problem Set 3
Due date: September 30, 2015
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414
Summer 2015
Exercise 1 Find all the NE (in pure and in mixed strategies) for the following games:
Player 1
E
F
G
H
Player 2
B C
6,2 10,2
3,4 3,2
2,5 2
Problem Set 5
Due date: October 28, 2015
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414
Fall 2015
Exercise 1 (Exercise extracted from MWG) There are n firms in an industry, indexed by
i. Each can try to convince the congress to give a subsi
Problem Set 4
Due date: October 7, 2015
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414
Summer 2015
Exercise 1 Solve the following game by backwards induction:
P1
A
B
P2
C
(1, 2)
P2
D
E
(1, 1)
F
(0, 3)
G
(2, 2)
(1, 4)
Exercise 2 Consider the
Problem Set 2
Due date: September 16, 2015
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414 0101
Fall 2015
Exercise 1 Find the set of rationalizable strategies for the following games:
Player 1
E
F
G
H
Player 2
B C
6,2 10,2
3,4 3,2
2,5 2,5
4,
Problem Set 4 Solutions
Econ414
Fall 2015
Instructor.: Gustavo Q Saraiva
University of Maryland
Exercise 1 At the last nodes, we can see that it is an optimal decision for player 2 to choose
E (in the contingency that player 1 has chosen A) and choose G (
Problem Set 3 Solutions
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414 0301
Summer 2015
Exercise 1
1) In the first round of IESDS, we can eliminate strategies F and G from player 1 (they are
both strictly dominated by H).
In the second roun
Problem Set 5 Solutions
Instructor.: Gustavo Q Saraiva
University of Maryland
Econ414
Summer 2015
Exercise 1 Given the decisions made by other firms, a generic firm i maximizes
max (h1 + h2 + + hi + + hn ) + (h1 h2 hi hn ) wi h2i .
hi
This function is cle
ECON414 - Sample Final Exam - Fall 2015
Name:
Part 1: Choose 3 of the following 5 problems
1. Consider the following strategic game. Ben and Daisy are trying to decide
whether to eat dinner at Bens favorite steakhouse or at Daisys favorite Italian restaur
ECON 456: Law and Economics
HW 1: Bargaining
Due Tuesday, 19 February (in class)
1. Ron owns a Jeep that he values at $2,000. Andy has $15,000 and values the Jeep at $8,000.
Suppose Ron and Andy bargain over the sale of the Jeep.
a. If the Jeep is transfe
Chapter 7
Credibility and
Subgame Perfect
Equilibrium
1
Subgames and their
equilibria
] The concept of subgames
] Equilibrium of a subgame
] Credibility problems: threats you have no
incentives to carry out when the time
comes
] Two important examples
\ T
Chapter 8
Repeated Games
1
Strategies and payoffs
for games played twice
] Finitely repeated games
] Discounted utility and normalized utility
] Complete plans of play for 22 games
played twice
] Trigger strategies
2
A 22 game played twice
L
L
R
L
L
R
R
L
Chapter 11
Games between
a Principal and
an Agent
1
A Principal and an Agent
A principal is any person or firm
that hires another person or firm to
perform services.
An agent is any person or firm
hired to perform services for a
principal.
2
Principal and
Chapter 10
Signaling,
Screening, and
Sequential
Equilibrium
1
2-Player Signaling Games
] Informed and uninformed players
] Let the buyer beware
] Three varieties of market failure, and one
variety of market success
2
Two-Player Signaling Games
A good item
Chapter 2
Games of Chance
1
A short questionnairepart 1
Question 1
Rank the following gambles:
A:
win $500 million with probability 0
win $100 million with probability 1
win $0 with probability 0
B:
win $500 million with probability .1
win $100 million wi
Chapter 1
An Introduction
to Games and
Their Theory
1
What is a Game?
] Varieties of games
\ board, card, video, field
\ economic games: bargaining, auctions
] Features of a game
\
\
\
\
rule-governed
strategy matters
outcomes
strategic interdependence
2
Chapter 12
Auctions
1
Sealed-Bid Auctions with
Complete Information
] 2-bidder auctions as matrix games
] The 3 principles of bidding
] The relationship of auction equilibrium to
Bertrand equilibrium
2
Bidding Principle 1
Never overbid. As a strategy,
ove
Chapter 3
Nash-Equilibrium
for Two-Person
Games
1
Zero-sum Games and
Constant-sum Games
] Definition of zero-sum games
\ Examples: Poker, Battle of the Networks
] The arrow diagram for a 22 game in
normal form
\ The arrows point towards a Nash equilibrium