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GAME THEORY. 2
nd
Edition
Copyright
c
2015, 2018 Giacomo Bonanno, all rights reserved
You are free to redistribute this book in pdf format. If you make use of any part of this
book you must give appropriate credit to the author. You may not remix, transform, or
build upon the material without permission from the author. You may not use the material
for commercial purposes.
This book is also available in print in two volumes:
Volume 1: Basic Concepts ISBN-13: 978-1983604638 ISBN-10: 1983604631
Volume 2: Advanced Topics ISBN-13: 978-1985862517 ISBN-10: 1985862514
CreateSpace Independent Publishing Platform
For details see:
http://faculty.econ.ucdavis.edu/faculty/bonanno/GT_Book.html
Giacomo Bonanno is Professor of Economics at the
University of California, Davis
http://faculty.econ.ucdavis.edu/faculty/bonanno/

Preface to the first edition, 2015
After teaching game theory (at both the undergraduate and graduate level) at the
University of California, Davis for 25 years, I decided to organize all my teaching material
in a textbook. There are many excellent textbooks in game theory and there is hardly any
need for a new one. However, there are two distinguishing features of this textbook: (1) it
is open access and thus free,
1
and (2) it contains an unusually large number of exercises
with complete and detailed answers.
I tried to write the book in such a way that it would be accessible to anybody with
minimum knowledge of mathematics (high-school level algebra and some elementary
notions of probability) and no prior knowledge of game theory. However, the book is
intended to be rigorous and it includes several proofs. I believe it is appropriate for an
advanced undergraduate class in game theory and also for a first-year graduate-level class.
I expect that there will be some typos and (hopefully minor) mistakes. If you come
across any typos or mistakes, I would be grateful if you could inform me: I can be reached
at gfbonanno@ucdavis.edu. I will maintain an updated version of the book on my web
page at
http://www.econ.ucdavis.edu/faculty/bonanno/
I also intend to add, some time in the future, a further collection of exercises and exam
questions with detailed answers. Details will appear on my web page.
I am very grateful to Elise Tidrick for meticulously going through each chapter of
the book and for suggesting numerous improvements. Her insightful and constructive
comments have considerably enhanced this book.
I would also like to thank Nicholas Bowden, Lester Lusher, Burkhard Schipper,
Matthieu Stigler, Sukjoon Lee, Minfei Xu and Pedro Paulo Funari for pointing out typos.
1
There may be several other free textbooks on game theory available. The only one I am aware of is the
excellent book by Ariel Rubinstein and Martin Osborne, MIT Press, 1994, which can be downloaded for free
from Ariel Rubinstein’s web page:
http://arielrubinstein.tau.ac.il
. In my experience this book
is too advanced for an undergraduate class in game theory.

Preface to the second edition, 2018
This second edition introduces
substantial reformatting (having translated into L
A
T
E
X the previous file written in
Microsoft Word),
the addition of 15 new exercises (bringing the total to 180),
improved exposition, with additional text and examples, and enhanced topics,
the availability of a printed version of the book, split into two volumes (the first
covering the basic concepts and the second dealing with advanced topics).
I am indebted to Elise Tidrick for the enormous amount of work she put into helping
me with this new edition. Not only did she design the covers of the two volumes with
original artwork, but she spent hours helping me translate the original file into L
A
T
E
X code,
taking care of reformatting the figures and nudging and instructing me on how to modify
the L
A
T
E
X output so as to ensure a smooth flow in the reading of the book.
I would like to thank Dr. Chula Kooanantkul for pointing out several typos and
Mathias Legrand for making the latex template used for this book available for free
(the template was downloaded from
http://www.latextemplates.com/template/
the-legrand-orange-book
).
v.4 8-19

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
I
Games with Ordinal Payoffs
2 Ordinal Games in Strategic Form . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Game frames and games 17
2.2 Strict and weak dominance 24
2.3 Second-price auction 29
2.4 The pivotal mechanism 32
2.5 Iterated deletion procedures 35
2.5.1 IDSDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5.2 IDWDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 Nash equilibrium 39
2.7 Games with infinite strategy sets 44
2.8 Proofs of theorems 46
2.9 Exercises 50
2.9.1 Exercises for Section 2.1: Game frames and games . . . . . . . . . . . . . . . . . 50
2.9.2 Exercises for Section 2.2: Strict/weak dominance . . . . . . . . . . . . . . . . . . . 51
2.9.3 Exercises for Section 2.3: Second price auction . . . . . . . . . . . . . . . . . . . . . 52
2.9.4 Exercises for Section 2.4: The pivotal mechanism . . . . . . . . . . . . . . . . . . . 54
2.9.5 Exercises for Section 2.5: Iterated deletion procedures . . . . . . . . . . . . . . 55
2.9.6 Exercises for Section 2.6: Nash equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 57
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