Playing for Real: A Text on Game Theory
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Playing for Real: A Text on Game Theory
By Ken Binmore

Publisher: Oxford University Press, USA
Number Of Pages: 656
Publication Date: 2007-03-02

Ken Binmore's previous game theory textbook, Fun and Games (D.C. Heath, 1991), carved out a significant niche in the advanced undergraduate market; it was intellectually serious and more up-to-date than its competitors, but also accessibly written. Its central thesis was that game theory allows us to understand many kinds of interactions between people, a point that Binmore amply demonstrated through a rich range of examples and applications. This replacement for the now out-of-date 1991 textbook retains the entertaining examples, but changes the organization to match how game theory courses are actually taught, making Playing for Real a more versatile text that almost all possible course designs will find easier to use, with less jumping about than before. In addition, the problem sections, already used as a reference by many teachers, have become even more clever and varied, without becoming too technical. Playing for Real will sell into advanced undergraduate courses in game theory, primarily those in economics, but also courses in the social sciences, and serve as a reference for economists.
Summary: A Comprehensive Introduction
As the author of an excellent and innovative text on game theory (Game Theory Evolving, Princeton University Press), Herbert Gintis is far better qualified than this reviewer to provide a substantive evaluation of Ken Binmore's new book; I encourage all prospective buyers to read Gintis' comprehensive review very carefully.
I would, however, like to offer some additional information for the specific audience of mathematicians and students of mathematics who are searching for an introductory text on game theory.
Ken Binmore studied mathematics before becoming an economist; thus, one might expect that this book would provide rigorous proofs for all the results used, and mathematically inclined readers will be happy to hear that this is indeed the case. The intended readership is quite broad, however, and so Binmore ensured that it is possible for those who are inclined to skip the proofs to do so without suffering serious loss of continuity.
In determining whether this text is appropriate for one's specific study or instructional needs, one encounters two problems: (1) the table of contents is not available on Amazon, and (2) even when the chapter titles are made available, they are written in somewhat whimsical language that makes it difficult to determine precisely how the book is organized and precisely what it contains. In order to provide a bit of help in this area, I have provided the prospective buyer with both the chapter titles AND the section headings at the end of this review; I sincerely hope this helps in the process of determining whether this book represents a worthwhile investment, based on the specific needs of the buyer.
One cautionary note for university instructors, especially instructors of mathematics; in the Preface, Binmore states that his book contains enough material for at least two courses in game theory. He writes
"I have tried to make things easy for teachers who want to design a course based on selection of topics from the whole book by including marginal notes to facilitate skipping."
Thus, the instructor who is used to "possible course" charts, showing clear interdependence of chapters and identifying sections that might be skipped without penalty, will not find them in this book. The inclusion of this material would definitely have been a great kindness to university instructors; scouting one's way through this 639-page text to find a realistic and effective one-semester course is not easy!
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Table of Contents
1 Getting Locked In
1.1 What is Game Theory?
1.2 Toy Games
1.3 The Prisoners' Dilemma
1.4 Private Provision of Public Goods
1.5 Imperfect Competition
1.6 Nash Equilibrium
1.7 Collective Rationality
1.8 Repeating the Prisoners' Dilemma
1.9 Which Equilibrium?
1.10 Social Dilemmas
1.11 Roundup
2 Backing Up
2.1 Where Next?
2.2 Win-Or-Lose Games
2.3 The Rules of the Game
2.4 Pure Strategies
2.5 Backward Induction
2.6 Solving NIM
2.7 Hex
2.8 Chess
2.9 Rational Play?
2.10 Roundup
3 Taking Chances
3.1 Chance Moves
3.2 Probability
3.3 Conditional Probability
3.4 Lotteries
3.5 Expectation
3.6 Values of Games with Chance Moves
3.7 Waiting Games
3.8 Parcheesi
3.9 Roundup
4 Accounting for Tastes
4.1 Payoffs
4.2 Revealed Preference
4.3 Utility Functions
4.4 Dicing with Death
4.5 Making Risky Choices
4.6 Utility Scales
4.7 Dicing with Death Again
4.8 When are People Consistent?
4.9 Roundup
5 Planning Ahead
5.1 Strategic Forms
5.2 Payoff Functions
5.3 Matrices and Vectors
5.4 Domination
5.5 Credibility and Commitment
5.6 Living in an Imperfect World
5.7 Roundup
6 Mixing Things Up
6.1 Mixed Strategies
6.2 Reaction Curves
6.3 Interpreting Mixed Strategies
6.4 Payoffs and Mixed Strategies
6.5 Convexity
6.6 Payoff Regions
6.7 Roundup
7 Fighting it Out
7.1 Strictly Competitive Games
7.2 Zero-Sum Games
7.3 Minimax and Maximin
7.4 Safety First
7.5 Solving Zero-Sum Games
7.6 Linear Programming
7.7 Separating Hyperplanes
7.8 Starships
7.9 Roundup
8 Keeping Your Balance
8.1 Introduction
8.2 Dueling Again
8.3 When do Nash Equilibria Exist?
8.4 Hexing Brouwer
8.5 The Equilibrium Selection Problem
8.6 Conventions
8.7 Roundup
9 Buying Cheap
9.1 Economic Models
9.2 Partial Derivatives
9.3 Preferences in Commodity Spaces
9.4 Trade
9.5 Monopoly
9.6 Perfect Competition
9.7 Consumer Surplus
9.8 Roundup
10 Selling Dear
10.1 Models of Imperfect Competition
10.2 Cournot Models
10.3 Stackelberg Models
10.4 Bertrand Models
10.5 Edgeworth Models
10.6 Roundup
11 Repeating Yourself
11.1 Reciprocity
11.2 Repeating a Zero-Sum Game
11.3 Repeating the Prisoners' Dilemma
11.4 Infinite Repetitions
11.5 Social Contract
11.6 The Evolution of Cooperation
11.7 Roundup
12 Getting the Message
12.1 Knowledge and Belief
12.2 Dirty Faces
12.3 Knowledge
12.4 Possibility Sets
12.5 Information Sets
12.6 Common Knowledge
12.7 Complete Information
12.8 Agreeing to Disagree?
12.9 Coordinated Action
12.10 Roundup
13 Keeping Up to Date
13.1 Rationality
13.2 Bayesian Updating
13.3 Bayesian Rationality
13.4 Getting the Model Right
13.5 Scientific Induction?
13.6 Constructing Priors
13.7 Bayesian Rationality in Games
13.8 Roundup
14 Seeking Refinement
14.1 Contemplating the Impossible
14.2 Counterfactual Reasoning
14.3 Backward and Imperfect
14.4 Gang of Four
14.5 Signaling Games
14.6 Rationalizability
14.7 Roundup
15 Knowing What to Believe
15.1 Complete Information
15.2 Bluffing
15.3 Incomplete Information
15.4 Russian Roulette
15.5 Duopoly with Incomplete Information
15.6 Purification
15.7 Incomplete Information about Rules
15.8 Roundup
16 Getting Together
16.1 Bargaining
16.2 Cooperative Game Theory
16.3 Cooperative Payoff Regions
16.4 Nash Bargaining Problems
16.5 Supporting Hyperplanes
16.6 Nash Bargaining Solution
16.7 Collusion in a Cournot Duopoly
16.8 Incomplete Information
16.9 Other Bargaining Solutions
16.10 Roundup
17 Cutting a Deal
17.1 Noncooperative Bargaining Models
17.2 The Nash Program
17.3 Commitment in Bargaining
17.4 Nash Threat Games
17.5 Bargaining Without Commitment
17.6 Going Wrong
17.7 Roundup
18 Teaming Up
18.1 Coalitions
18.2 Coalitional Form
18.3 Core
18.4 Stable Sets
18.5 Shapley Value
18.6 Applying the Nash Program
18.7 Roundup
19 Just Playing?
19.1 Ethics and Game Theory
19.2 Do People Play Fair?
19.3 Social Choice Paradoxes
19.4 Welfare Functions
19.5 Impersonal Comparison of Utility
19.6 More Bargaining Solutions
19.7 Political Philosophy
19.8 Which Fairness Norm?
19.9 Roundup
20 Taking Charge
20.1 Mechanism Design
20.2 Principals and Agents
20.3 Commitment and Contracting
20.4 Revelation Principle
20.5 Providing a Public Good
20.6 Implementation Theory
20.7 Roundup
21 Going, Going, Gone!
21.1 Telecom Auctions
21.2 Types of Auctions
21.3 Continuous Random Variables
21.4 Shading Your Bid
21.5 Designing Optimal Auctions
21.6 Common-Value Auctions
21.7 Multiunit Auctions
21.8 The Chopstick Auction
21.9 Roundup