Table Of ContentSpringer Texts in Business and Economics
Felix Munoz-Garcia
Daniel Toro-Gonzalez
Strategy and
Game Theory
Practice Exercises with Answers
Second Edition
Springer Texts in Business and Economics
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More information about this series at http://www.springer.com/series/10099
(cid:1)
Felix Munoz-Garcia Daniel Toro-Gonzalez
Strategy and Game Theory
Practice Exercises with Answers
Second Edition
123
Felix Munoz-Garcia DanielToro-Gonzalez
Schoolof Economic Sciences Schoolof Economics andBusiness
Washington State University Universidad Tecnológica deBolívar
Pullman,WA, USA Cartagena,Bolivar, Colombia
ISSN 2192-4333 ISSN 2192-4341 (electronic)
SpringerTexts inBusiness andEconomics
ISBN978-3-030-11901-0 ISBN978-3-030-11902-7 (eBook)
https://doi.org/10.1007/978-3-030-11902-7
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Preface
This textbook presents worked-out exercises on Game Theory, with detailed
step-by-stepexplanations,whichbothundergraduateandmaster’sstudentscanuse
to further understand equilibrium behavior in strategic settings. While most text-
booksonGameTheoryfocusontheoreticalresults,see,forinstance,Tirole(1991),
Gibbons(1992)andOsborne(2004),theyofferfewpracticeexercises.Ourgoalis,
hence, to complement the theoretical tools in current textbooks by providing
practice exercises in which students can learn to systematically apply theoretical
solution concepts to different fields of Economics and Business, such as industrial
economics, public policy, and regulation.
The textbook provides many exercises with detailed verbal explanations
(153exercisesintotal),whichcoverthetopicsrequiredbyGameTheorycoursesat
theundergraduatelevel,andbymostcoursesatthemaster’slevel.Importantly,our
textbook emphasizes the economic intuition behind the main results and avoids
unnecessary notation when possible, and thus is useful as a reference book
regardless of the Game Theory textbook adopted by each instructor. Importantly,
these points differentiate our presentation from that found in solutions manuals.
Unlike these manuals, which can be rarely read in isolation, our textbook allows
studentstoessentiallyreadeachexercisewithoutdifficulties,thankstothedetailed
explanations, figures, and intuitions. Furthermore, for presentation purposes, each
chapterranksexercisesaccordingtotheirdifficulty(withaletterAtoCnexttothe
exercisenumber),allowingstudentstofirstsettheirfoundationsusingeasyexercises
(type-A),andthen move on to harder applications (type-Band C exercises).
Organization of the Book
Wefirstexaminegamesthatarerequiredinmostcoursesattheundergraduatelevel,
and then advance to more challenging games (which are often the content of
master’s courses), both in Economics and Business programs. Specifically, Chaps.
1–6 cover complete-information games, separately analyzing simultaneous-move
and sequential-move games, with applications from industrial economics and reg-
ulation, thus helping students apply Game Theory to other fields of research.
Chapters 7–9 pay special attention to incomplete information games, such as
v
vi Preface
auctions and signaling games, while Chaps. 10 and 11 discuss cheap-talk games
andequilibriumrefinements.Thesetopicshaveexperiencedasignificantexpansion
inthelasttwodecades,bothinthetheoreticalandappliedliterature.Yettothisday
most textbooks lack detailed worked-out examples that students can use as a
guideline,leadingthemtoespeciallystrugglewiththistopic,whichoftenbecomes
themostchallengingforbothundergraduateandgraduatestudents.Incontrast,our
presentation emphasizes the common steps to follow when solving these types of
incomplete information games and includes graphical illustrations to focus stu-
dents’ attention to the most relevant payoff comparisons at each point of the
analysis.
Changes in the Second Edition
First, thesecond edition includesall theerratafile identified bytheauthorsand by
several readers who generously pointed them to us. Thanks again for your nice
comments, and don’t hesitate to let us know if you find any errata on the second
edition!
Second,weaddedover40newexercisestoChaps.1–10,foratotalofmorethan
200 new pages. The exercises in the first edition included many exercises at the
graduatelevel(mainlymaster’s,butalsosomeatthePh.D.level),butrelativelyfew
exercises that undergraduate students in introductory or intermediate-level courses
couldusetoimprovetheirpreparationonthesubject.Wetooknotice,soalmostall
new exercises in the second edition are appropriate for the undergraduate courses
on Game Theory and Industrial Organization.
Third, this edition includesa new chapter, Chap. 10, on cheap-talk games. This
chapterservesasadirectapplicationofthesequential-movegameswithincomplete
information presented in Chap. 9. Cheap-talk games, however, assumes that mes-
sagesarecostlessforthesender,sotheycanbeunderstoodasbeingaspecialtype
game from Chap. 9, helping us use the same approach to predict how players
behave when interacting in this type of settings.
How to Use This Textbook
Some instructors may use parts of the textbook in class in order to clarify how to
apply certain solution concepts that are only theoretically covered in standard
textbooks.Alternatively,otherinstructorsmayprefertoassigncertainexercisesasa
required reading, since these exercises closely complement the material covered in
class. This strategy could prepare students for the homework assignment on a
similartopic, since ourpractice exercises emphasize theapproachstudents needto
followineachclassofgames,andthemainintuitionbehindeachstep.Thisstrategy
mightbeespeciallyattractiveforinstructorsatthegraduatelevel,whocouldspend
Preface vii
more time covering the theoretical foundations in class, asking students to go over
our worked-out applications of each solution concept on their own.
Inaddition,sinceexercisesarerankedaccordingtotheirdifficulty,instructorsat
theundergraduatelevelcanassignthereadingofrelativelyeasyexercises(type-A)
and spend more time explaining the intermediate-level exercises in class (type-
B questions), whereas instructors teaching a graduate-level course can assume that
studentsarereadingmosttype-Aexercisesontheirown,andonlyuseclasstimeto
explain type-C (and some type-B) exercises. In this second edition, there are 153
exercisesintotal:43%aretype-A,45%aretype-B,andtheremaining12%aretype-C.
Acknowledgements
We would first like to thank several colleagues who encouraged us in the prepa-
rationofthismanuscript:RonMittlehammer,JillMcCluskey,andAlanLove.Ana
Espinola-Arredondo reviewed several chapters on a short deadline and provided
extremely valuable feedback, both in content and presentation, and we extremely
thankfulfor her insights.Felix is especiallygrateful tohis teachers andadvisorsat
the University of Pittsburgh (Andreas Blume, Esther Gal-Or, John Duffy, Oliver
Board, In-Uck Park, and Alexandre Matros), who taught him Game Theory and
Industrial Organization, instilling a passion for the use of these topics in applied
settings which hopefully transpires in the following pages. We appreciate several
instructorsusingthefirsteditionofthebookforpointingouttyposandexplanations
thatcouldbeimproved,suchasStephanKroll,fromColoradoStateUniversity,and
AnaEspinola-Arredondo,fromWashingtonState University.Wearealso thankful
to the “team” of teaching and research assistants, both at Washington State
University and at Universidad Tecnologica de Bolivar, who helped us with this
project over several years: Diem Nguyen, Gulnara Zaynutdinova, Modhurima
Amin, Mianfeng Liu, Syed Badruddoza, Boris Houenou, Kiriti Kanjilal, Donald
Petersen, Mursaleen Shiraj, Qingqing Wang, Jeremy Knowles, Xiaonan Liu, Ryan
Bain, Eric Dunaway, Tongzhe Li, Azhar Uddin, Wenxing Song, Pitchayaporn
Tantihkarnchana, Roberto Fortich, Jhon Francisco Cossio Cardenas, Luis Carlos
Díaz Canedo, Dayana Pinzon, and Kevin David Gomez Perez. Thanks also to
Ignace Lasters, Pablo Abitbol, and Andrés Cendales for the comments to the first
edition of the book. We also appreciate the support of the editors at Springer-
Verlag, Rebekah McClure, Lorraine Klimowich, Jayanthi Narayanaswamy, and
Dhivya Prabha. Importantly, we would like to thank our wives, Ana
Espinola-ArredondoandErickaDuncan,forsupportingandinspiringusduringthe
(long!)preparationofthemanuscript.Wewouldnothavebeenabletodoitwithout
your encouragement and motivation.
Pullman, USA Felix Munoz-Garcia
Cartagena, Colombia Daniel Toro-Gonzalez
Contents
1 Dominance Solvable Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Exercise 1—From Extensive Form to Normal Form
Representation-IA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Exercise 2—From Extensive Form to Normal Form
Representation-IIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Exercise 3—From Extensive Form to Normal Form
Representation-IIIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Exercise 4—Representing Games in Its Extensive FormA . . . . . . . . . . 8
Exercise 5—Prisoners’ Dilemma GameA . . . . . . . . . . . . . . . . . . . . . . 8
Exercise 6—Dominance Solvable GamesA. . . . . . . . . . . . . . . . . . . . . 11
Exercise 7—Applying IDSDS (Iterated Deletion of Strictly
Dominated Strategies)A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Exercise 8—Applying IDSDS When Players Have Five
Available StrategiesA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Exercise 9—Applying IDSDS in the Battle of the Sexes GameA. . . . . 17
Exercise 10—Applying IDSDS in Two Common GamesA . . . . . . . . . 19
Exercise 11—Applying IDSDS in Three-Player GamesB. . . . . . . . . . . 20
Exercise 12—IDSDS and RationalityA. . . . . . . . . . . . . . . . . . . . . . . . 23
Exercise 13—Iterated Deletion of Strictly Dominated
Strategies (IDSDS)A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Exercise 14—Unemployment BenefitsA . . . . . . . . . . . . . . . . . . . . . . . 28
Exercise 15—Finding Dominant Strategies in Games with I (cid:3) 2
Players and with Continuous Strategy SpacesB. . . . . . . . . . . . . . . . . . 29
Exercise 16—Equilibrium Predictions from IDSDS
Versus IDWDSB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Exercise 17—Different Equilibrium Predictions from
IDSDS and IDWDSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 PureStrategy NashEquilibriumandSimultaneous-MoveGames
with Complete Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Exercise 1—Prisoner’s DilemmaA . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
ix
x Contents
Exercise 2—Battle of the SexesA. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Exercise 3—Pareto Coordination GameA . . . . . . . . . . . . . . . . . . . . . . 42
Exercise 4—Finding Nash Equilibria in the Unemployment
Benefits GameA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Exercise 5—Hawk-Dove GameA. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Exercise 6—Generalized Hawk-Dove GameA. . . . . . . . . . . . . . . . . . . 47
Exercise 7—Cournot Game of Quantity CompetitionA . . . . . . . . . . . . 48
Exercise 8—Games with Positive ExternalitiesB. . . . . . . . . . . . . . . . . 51
Exercise 9—Traveler’s DilemmaB . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Exercise 10—Nash Equilibria with Three PlayersB. . . . . . . . . . . . . . . 56
Exercise 11—Simultaneous-Move Games with n (cid:3) 2 PlayersB . . . . . 61
Exercise 12—Political Competition (Hoteling Model)B. . . . . . . . . . . . 64
Exercise 13—TournamentsB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Exercise 14—Lobbying GameA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Exercise 15—Incentives and PunishmentB . . . . . . . . . . . . . . . . . . . . . 72
Exercise 16—Cournot Competition with Efficiency ChangesA. . . . . . . 76
Exercise 17—Cournot Mergers with Efficiency GainsB. . . . . . . . . . . . 80
3 Mixed Strategies, Strictly Competitive Games, and Correlated
Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Exercise 1—Game of ChickenA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Exercise 2—Lobbying GameA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Exercise 3—A Variation of the Lobbying GameB. . . . . . . . . . . . . . . . 95
Exercise 4—Finding a Mixed Strategy Nash Equilibrium in the
Unemployment Benefits GameA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Exercise 5—Newlyweds Buying an Apartment GameA. . . . . . . . . . . . 100
Exercise 6—Finding Mixed Strategies in the Hawk-Dove GameB . . . . 104
Exercise 7—Finding Mixed Strategies in the Generalized
Hawk-Dove GameB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Exercise 8—Mixed Strategy Equilibrium with N > 2 PlayersB . . . . . . 109
Exercise 9—Randomizing Over Three Available ActionsB . . . . . . . . . 111
Exercise 10—Rock-Paper-Scissors GameB. . . . . . . . . . . . . . . . . . . . . 114
Exercise 11—Penalty Kicks GameB. . . . . . . . . . . . . . . . . . . . . . . . . . 118
Exercise 12—Pareto Coordination GameB . . . . . . . . . . . . . . . . . . . . . 120
Exercise 13—Mixing Strategies in a Bargaining GameC . . . . . . . . . . . 123
Exercise 14—Depicting the Convex Hull of Nash
Equilibrium PayoffsC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Exercise 15— Correlated EquilibriumC . . . . . . . . . . . . . . . . . . . . . . . 130
Exercise 16—Relationship Between Nash and Correlated
Equilibrium PayoffsC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Exercise 17—Identifying Strictly Competitive GamesA. . . . . . . . . . . . 141
Exercise 18—Maxmin StrategiesC . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
