Game Theory

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Read: The Calculus of Selfishness

Karl Sigmund’s The Calculus of Selfishness applies basic evolutionary game theory to the analysis of cooperation in strategic interactions. Though it is published in the Princeton Series in Theoretical and Computational Biology it is rather addressed to social scientist, economist and psychologist, and in particular undergraduates.

The Calculus starts simple enough and Sigmund introduces whatever mathematics he needs without being too formal in his approach. For a text in applied math the book reads surprisingly well. However, it is still a book in applied math and I fear it is as such not really appealing to an undergraduate in the social sciences. Indeed, I do not believe there are many undergraduate economics students who would enjoy this book and not put it aside after the first few pages, the first chapter at the latest. While this may be a good example of a text in applied math it is not ”good enough” for the nascent social scientist.

On the other hand, it is an excellent introductory text on the evolutionary game theory of cooperation, direct and indirect reciprocity, fairness, reputation, and trust. I only wished Sigmund would have expanded on structured interaction and the co-evolution of subpopulations. He only hints at what results would be obtained when one would look at these things more carefully.

I also particularly appreciate that each chapter ends with a briefly annotated list of references for further, in more depth, reading on the topic and the game theoretic approach that was introduced in the respective chapter. While the terse exposition of the chapter can only serve to raise one’s interest these references are the real treasure trove of The Calculus of Selfishness.

Hence, while I would not recommend the book to any of my undergraduates in economics or social sciences I would happily point any graduate student in its direction.

Read: Game Theory - A Very Short Introduction

Very recently I came across Oxford University Press’ Very Short Introduction series. The series comprises now of almost 300 titles ranging from Archaeology and Art to Medicine and Social Sciences. Of course, there are also some titles dealing with economics and other more quantitative topics; Game Theory is one of them. There could not be a more obvious and substantial difference to popular science books covering Game Theory (in a good sense).

Binmore covers a broad range of topics, from conflict and cooperation to conventions, bargaining and auctions. Most important he links the theory to observed behavior and evolutionary dynamics that may explain deviations from some of the normative predictions of standard Game Theory (under assumptions of perfect rationality and opportunistic preferences). It is these discussions of evolutionary dynamics that made the small book (less than 200 pages) worthwhile for me.

For the most part Binmore’s writing style is crystal clear. However, I had, of course, substantial training in Game Theory and need to apply it quite often. Even though Binmore explanations and definitions are easy to follow I fear that there is still too much jargon, too few definitions and a lack explanations of some of the essential concepts of Game Theory that would be needed for a real introduction.

Read: Rock, Paper, Scissors -- Game Theory in Everyday Life

Len Fisher provides an entertaining glimpse at Game Theory, or at least a part of it. Rock, Paper, Scissors focuses on coordination problems, social dilemmas and possible solutions. The book is very non-technical. Indeed, the reader may not learn any new game theoretic concepts – given that those who will pick up a book with Game Theory in its title are likely to know already the most basic ingredients of Game Theory.

Nevertheless, the book adds some value. The everyday examples of applied Games are as instructive as they the writing is witty. The focus on social dilemmas facilitates attracting some attention. And research results – not his own; he gives, for instance, a recount of Axelrod’s The Evolution of Cooperation – are presented in an easy to understand way. You may hold against Fisher that the favored solution to these dilemmas is presented as something seemingly simple even though it is actually hard to implement: Change the game.