Joel Watson's Game Theory Answers to ALL exercises

This document contains the answers to the exercises from Joel Watson's Strategy book about Game Theory that the book does not include. These answers come with a procedure and explanation.

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Strategy: An Introduction to Game Theory
Second Edition
Instructors’ Manual
Joel Watson with Jesse Bull
April 2008
Strategy: An Introduction to Game Theory, Second Edition, Instructors’ Manual,
version 4/2008.
Copyright 2008, 2002 by Joel Watson. This document is available, with the per-
mission of W. W. Norton & Company, for use by textbook adopters in conjunction
with the textbook. The authors thank Pierpaolo Battigalli, Takako Fujiwara-Greve,
Michael Herron, David Miller, David Reinstein, Christopher Snyder, and Charles
Wilson for pointing out some typographical errors in earlier versions of this manual.
This Instructors’ Manual has four parts. Part I contains some notes on outlining and
preparing a game theory course that is based on the textbook. Part II contains more
detailed (but not overblown) materials that are organized by textbook chapter. Part
III comprises solutions to all of the exercises in the textbook. Part IV contains some
sample examination questions.
Please report any typographical errors to Joel Watson (jwatson@ucsd.edu). Also feel
free to suggest new material to include in the instructors’ manual or web site.
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.
Contents
General Materials
Chapter-Specific Materials
1 Introduction
2 The Extensive Form
3 Strategies and the Normal Form
4 Beliefs, Mixed Strategies,
and Expected Payoffs
5 General Assumptions and Methodology
6 Dominance and Best Response
7 Rationalizability and Iterated Dominance
8 Location and Partnership
9 Nash Equilibrium
10 Oligopoly, Tariffs, Crime, and Voting
11 Mixed-Strategy Nash Equilibrium
12 Strictly Competitive Games
and Security Strategies
13 Contract, Law, and Enforcement
in Static Settings
14 Details of the Extensive Form
15 Backward Induction
and Subgame Perfection
16 Topics in Industrial Organization
17 Parlor Games
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.
CONTENTS
18 Bargaining Problems
19 Analysis of Simple Bargaining Games
20 Games with Joint Decisions;
Negotiation Equilibrium
21 Unverifiable Investment, Hold Up,
Options, and Ownership
22 Repeated Games and Reputation
23 Collusion, Trade Agreements,
and Goodwill
24 Random Events and
Incomplete Information
25 Risk and Incentives in Contracting
26 Bayesian Nash Equilibrium
and Rationalizability
27 Lemons, Auctions,
and Information Aggregation
28 Perfect Bayesian Equilibrium
29 Job-Market Signaling and Reputation
30 Appendices
III
Solutions to the Exercises
2 The Extensive Form
3 Strategies and the Normal Form
4 Beliefs, Mixed Strategies,
and Expected Payoffs
6 Dominance and Best Response
7 Rationalizability and Iterated Dominance
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.
CONTENTS
8 Location and Partnership
9 Nash Equilibrium
10 Oligopoly, Tariffs, Crime,and Voting
11 Mixed-Strategy Nash Equilibrium
100
12 Strictly Competitive Games
and Security Strategies
105
13 Contract, Law, and Enforcement
in Static Settings
106
14 Details of the Extensive Form
111
15 Backward Induction
and Subgame Perfection
112
16 Topics in Industrial Organization
116
17 Parlor Games
120
18 Bargaining Problems
124
19 Analysis of Simple Bargaining Games
127
20 Games with Joint Decisions;
Negotiation Equilibrium
130
21 Unverifiable Investment, Hold Up,
Options, and Ownership
133
22 Repeated Games and Reputation
136
23 Collusion, Trade Agreements,
and Goodwill
139
24 Random Events and
Incomplete Information
143
25 Risk and Incentives in Contracting
145
26 Bayesian Nash Equilibrium
and Rationalizability
147
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.
CONTENTS
27 Lemons, Auctions,
and Information Aggregation
152
28 Perfect Bayesian Equilibrium
155
29 Job-Market Signaling and Reputation
157
30 Appendix B
162
Sample Examination Questions
163
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.
Part I
General Materials
This part contains some notes on outlining and preparing a game theory course for
those adopting Strategy: An Introduction to Game Theory.
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.
Sample Syllabi
Most of the book can be covered in a semester-length (13-15 week) course. Here
is a sample thirteen-week course outline:
Weeks
Topics
Chapters
A. Representing Games
Introduction, extensive form, strategies,
1-3
and normal form
1-2
Beliefs and mixed strategies
4-5
B. Analysis of Static Settings
2-3
Best response, rationalizability, applications
6-8
3-4
Equilibrium, applications
9-10
Other equilibrium topics
11-12
Contract, law, and enforcement
C. Analysis of Dynamic Settings
Extensive form, backward induction,
14-15
and subgame perfection
Examples and applications
16-17
Bargaining
18-19
Negotiation equilibrium and problems of
20-21
contracting and investment
Repeated games, applications
22-23
D. Information
Random events and incomplete information
Risk and contracting
Bayesian equilibrium, applications
26-27
Perfect Bayesian equilibrium and applications
28-29
In a ten-week (quarter system) course, most, but not all, of the book can be
covered. For this length of course, you can easily leave out (or simply not cover in
class) some of the chapters. For example, any of the chapters devoted to applications
(Chapters 8, 10, 16, 21, 23, 25, 27, and 29) can be covered selectively or skipped
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.
without disrupting the flow of ideas and concepts. Chapters 12 and 17 contain ma-
terial that may be regarded as more esoteric than essential; one can easily have the
students learn the material in these chapters on their own. Instructors who prefer
not to cover contract can skip Chapters 13, 20, 21, and 25.
Below is a sample ten-week course outline that is formed by trimming some of
the applications from the thirteen-week outline. This is the outline that I use for my
quarter-length game theory course. I usually cover only one application from each
of Chapters 8, 10, 16, 23, 27, and 29. I avoid some end-of-chapter advanced topics,
such as the infinite-horizon alternating-offer bargaining game, I skip Chapter 25, and,
depending on the pace of the course, I selectively cover Chapters 18, 20, 27, 28, and 29.
Weeks
Topics
Chapters
A. Representing Games
Introduction, extensive form, strategies,
1-3
and normal form
1-2
Beliefs and mixed strategies
4-5
B. Analysis of Static Settings
2-3
Best response, rationalizability, applications
6-8
3-4
Equilibrium, applications
9-10
Other equilibrium topics
11-12
Contract, law, and enforcement
C. Analysis of Dynamic Settings
Backward induction, subgame perfection,
14-17
and an application
Bargaining
18-19
7-8
Negotiation equilibrium and problems of
20-21
contracting and investment
8-9
Repeated games, applications
22-23
D. Information
Random events and incomplete information
Bayesian equilibrium, application
26-27
Perfect Bayesian equilibrium and an application
28-29
Instructors' Manual for Strategy:
Copyright 2002, 2008 by Joel Watson
An Introduction to Game Theory
For instructors only; do not distribute.