TEST BANK FOR Strategy An Introduction to Game Theory 3rd Edition By Joel Watson

Contents
I General Materials 7
II Chapter-Specic Materials 12
1 Introduction 13
2 The Extensive Form 15
3 Strategies and the Normal Form 18
4 Beliefs, Mixed Strategies,
and Expected Payos 21
5 General Assumptions and Methodology 23
6 Dominance and Best Response 24
7 Rationalizability and Iterated Dominance 27
8 Location, Partnership, and Social Unrest 29
9 Nash Equilibrium 32
10 Oligopoly, Taris, Crime, and Voting 34
11 Mixed-Strategy Nash Equilibrium 35
12 Strictly Competitive Games
and Security Strategies 37
13 Contract, Law, and Enforcement
in Static Settings 38
14 Details of the Extensive Form 41
15 Sequential Rationality
and Subgame Perfection 43
16 Topics in Industrial Organization 45
17 Parlor Games 46
3
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
CONTENTS 4
18 Bargaining Problems 48
19 Analysis of Simple Bargaining Games 50
20 Games with Joint Decisions;
Negotiation Equilibrium 52
21 Unveriable Investment, hold up,
Options, and Ownership 54
22 Repeated Games and Reputation 56
23 Collusion, Trade Agreements,
and Goodwill 58
24 Random Events and
Incomplete Information 60
25 Risk and Incentives in Contracting 63
26 Bayesian Nash Equilibrium
and Rationalizability 65
27 Lemons, Auctions,
and Information Aggregation 66
28 Perfect Bayesian Equilibrium 68
29 Job-Market Signaling and Reputation 70
30 Appendices 71
III Solutions to the Exercises 72
2 The Extensive Form 73
3 Strategies and the Normal Form 76
4 Beliefs, Mixed Strategies,
and Expected Payos 79
6 Dominance and best response 80
7 Rationalizability and Iterated Dominance 81
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
CONTENTS 5
8 Location, Partnership, and Social Unrest 83
9 Nash Equilibrium 86
10 Oligopoly, Taris, Crime, and Voting 89
11 Mixed-Strategy Nash Equilibrium 95
12 Strictly Competitive Games
and Security Strategies 102
13 Contract, Law, and Enforcement
in Static Settings 103
14 Details of the Extensive Form 108
15 Sequential Rationality
and Subgame Perfection 110
16 Topics in Industrial Organization 114
17 Parlor Games 117
18 Bargaining Problems 119
19 Analysis of Simple Bargaining Games 121
20 Games with Joint Decisions;
Negotiation Equilibrium 123
21 Unveriable Investment, Hold Up,
Options, and Ownership 127
22 Repeated Games and Reputation 131
23 Collusion, Trade Agreements,
and Goodwill 135
24 Random Events and
Incomplete Information 138
25 Risk and Incentives in Contracting 140
26 Bayesian Nash Equilibrium
and Rationalizability 142
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
CONTENTS 6
27 Lemons, Auctions,
and Information Aggregation 145
28 Perfect Bayesian Equilibrium 148
29 Job-Market Signaling and Reputation 151
30 Appendix B 155
IV Sample Questions 156
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
7
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.
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
8
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
1 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
5 Other equilibrium topics 11{12
5 Contract, law, and enforcement 13
C. Analysis of Dynamic Settings
6 Extensive form, backward induction, 14{15
and subgame perfection
7 Examples and applications 16{17
8 Bargaining 18{19
9 Negotiation equilibrium and problems of 20{21
contracting and investment
10 Repeated games, applications 22{23
D. Information
11 Random events and incomplete information 24
11 Risk and contracting 25
12 Bayesian equilibrium, applications 26{27
13 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
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
9
without disrupting the ow 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 innite-horizon alternating-oer 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
1 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
5 Other equilibrium topics 11-12
5 Contract, law, and enforcement 13
C. Analysis of Dynamic Settings
6 Backward induction, subgame perfection, 14-17
and an application
7 Bargaining 18-19
7-8 Negotiation equilibrium and problems of 20-21
contracting and investment
8-9 Repeated games, applications 22-23
D. Information
9 Random events and incomplete information 24
10 Bayesian equilibrium, application 26-27
10 Perfect Bayesian equilibrium and an application 28-29
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
10
Experiments and a Course Competition
In addition to assigning regular problem sets, it can be fun and instructive to
run a course-long competition between the students. The competition is mainly for
sharpening the students' skills and intuition, and thus the students' performance in
the course competition should not count toward the course grades. The competi-
tion consists of a series of challenges, classroom experiments, and bonus questions.
Students receive points for participating and performing near the top of the class.
Bonus questions can be sent by e-mail; some experiments can be done by e-mail as
well. Prizes can be awarded to the winning students at the end of the term. Some
suggestions for classroom games and bonus questions appear in various places in this
manual.
Level of Mathematics and Use of Calculus
Game theory is a technical subject, so the students should come into the course
with the proper mathematics background. For example, students should be very
comfortable with set notation, algebraic manipulation, and basic probability theory.
Appendix A in the textbook provides a review of mathematics at the level used in
the book.
Some sections of the textbook benet from the use of calculus. In particular, a
few examples and applications can be analyzed most easily by calculating derivatives.
In each case, the expressions requiring dierentiation are simple polynomials (usually
quadratics). Thus, only the most basic knowledge of dierentiation suces to follow
the textbook derivations. You have two choices regarding the use of calculus.
First, you can make sure all of the students can dierentiate simple polynomials;
this can be accomplished by either (a) specifying calculus as a prerequisite or (b)
asking the students to read Appendix A at the beginning of the course and then
perhaps reinforcing this by holding an extra session in the early part of the term to
review how to dierentiate a simple polynomial.
Second, you can avoid calculus altogether by either providing the students with
non-calculus methods to calculate maxima or by skipping the textbook examples that
use calculus. Here is a list of the examples that are analyzed with calculus in the
textbook:
the partnership example in Chapters 8 and 9,
the Cournot application in Chapter 10 (and the tari and crime applications in
this chapter, but the analysis of these applications is not done in the text),
the Stackelberg example in Chapter 15,
the advertising and limit capacity applications in Chapter 16 (they are based
on the Cournot model),
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
11
the dynamic oligopoly model in Chapter 23 (Cournot-based),
the discussion of risk-aversion in Chapter 25 (in terms of the shape of a utility
function),
the Cournot example in Chapter 26, and
the analysis of auctions in Chapter 27.
Each of these examples can be easily avoided, if you so choose. There are also some
related exercises that you might avoid if you prefer that your students not deal with
examples having continuous strategy spaces.
My feeling is that using a little bit of calculus is a good idea, even if calculus is
not a prerequisite for the game theory course. It takes only an hour or so to explain
slope and the derivative and to give students the simple rule of thumb for calculating
partial derivatives of simple polynomials. Then one can easily cover some of the most
interesting and historically important game theory applications, such as the Cournot
model and auctions.
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
12
Part II
Chapter-Specic Materials
This part contains instructional materials that are organized according to the chapters
in the textbook. For each textbook chapter, the following is provided:
a brief overview of the material covered in the chapter;
lecture notes (including an outline); and
suggestions for classroom examples and/or experiments.
The lecture notes are merely suggestions for how to organize lectures of the textbook
material. The notes do not represent any claim about the \right" way to lecture.
Some instructors may nd the guidelines herein to be in tune with their own teach-
ing methods; these instructors may decide to use the lecture outlines without much
modication. Others may have a very dierent style or intent for their courses; these
instructors will probably nd the lecture outlines of limited use, if at all. We hope
this material will be of some use to you.
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
1 Introduction
This chapter introduces the concept of a game and encourages the reader to begin
thinking about the formal analysis of strategic situations. The chapter contains a
short history of game theory, followed by a description of \noncooperative theory"
(which the book emphasizes), a discussion of the notion of contract and the related use
of \cooperative theory," and comments on the science and art of applied theoretical
work. The chapter explains that the word \game" should be associated with any
well-dened strategic situation, not just adversarial contests. Finally, the format and
style of the book are described.
Lecture Notes
The non-administrative segment of a rst lecture in game theory may run as
follows.
Denition of a strategic situation.
Examples (have students suggest some): chess, poker, and other parlor games;
tennis, football, and other sports; rm competition, international trade, inter-
national relations, rm{employee relations, and other standard economic exam-
ples; biological competition; elections; and so on.
Competition and cooperation are both strategic topics. Game theory is a general
methodology for studying strategic settings (which may have elements of both
competition and cooperation).
The elements of a formal game representation.
A few simple examples of the extensive-form representation (point out the basic
components).
Examples and Experiments
1. Clap game. Ask the students to stand, and then, if they comply, ask them to
clap. (This is a silly game.) Show them how to diagram the strategic situation
as an extensive-form tree. The game starts with your decision about whether to
ask them to stand. If you ask them to stand, then they (modeled as one player)
have to choose between standing and staying in their seats. If they stand, then
you decide between saying nothing and asking them to clap. If you ask them to
clap, then they have to decide whether to clap. Write the outcomes at terminal
nodes in descriptive terms such as \professor happy, students confused." Then
show how these outcomes can be converted into payo numbers.
13
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
1 INTRODUCTION 14
2. Auction the textbook. Many students will probably not have purchased the
textbook by the rst class meeting. These students may be interested in pur-
chasing the book from you, especially if they can get a good deal. However,
quite a few students will not know the price of the book. Without announcing
the bookstore's price, hold a sealed-bid, rst-price auction (using real money).
This is a common-value auction with incomplete information. The winning bid
may exceed the bookstore's price, giving you an opportunity to talk about the
\winner's curse" and to establish a fund to pay students in future classroom
experiments.
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.
2 The Extensive Form
This chapter introduces the basic components of the extensive form in a nontechnical
way. Students who learn about the extensive form at the beginning of a course
are much better able to grasp the concept of a strategy than are students who are
taught the normal form rst. Since strategy is perhaps the most important concept
in game theory, a good understanding of this concept makes a dramatic dierence
in each student's ability to progress. The chapter avoids the technical details of the
extensive-form representation in favor of emphasizing the basic components of games.
The technical details are covered in Chapter 14.
Lecture Notes
The following may serve as an outline for a lecture.
Basic components of the extensive form: nodes, branches. Nodes are where
things happen. Branches are individual actions taken by the players.
Example of a game tree.
Types of nodes: initial, terminal, decision.
Build trees by expanding, never converging back on themselves. At any place
in a tree, you should always know exactly how you got there. Thus, the tree
summarizes the strategic possibilities.
Player and action labels. Try not to use the same label for dierent places where
decisions are made.
Information sets. Start by describing the tree as a diagram that an external
observer creates to map out the possible sequences of decisions. Assume the
external observer sees all of the players' actions. Then describe what it means
for a player to not know what another player did. This is captured by dashed
lines indicating that a player cannot distinguish between two or more nodes.
We assume that the players know the game tree, but that a given player may
not know where he is in the game when he must make any particular decision.
An information set is a place where a decision is made.
How to describe simultaneous moves.
Outcomes and how payo numbers represent preferences.
15
Instructor's Manual for Strategy:
An Introduction to Game Theory
Copyright 2002, 2008, 2010, 2013 by Joel Watson.
For instructors only; do not distribute.