Towards the end of his life, Brian was working on a short book on game theory. Like many of Brian’s books, the initial plan was for something very short but it slowly expanded into something bigger. The Introduction explains the motivations behind the book. Brian writes, ‘I would not have written this book if I did not believe that [game theory] can contribute to the resolution of some problems that cannot even be clearly stated without it. I shall discuss in what follows some uses (and some abuses) of game theory in political theory. My own suspicion is, however, that there is much more room still left for the application of game theory to political theory, and that the main reason for its limited use is that few political theorists have even an elementary grasp of game theory. This book is not a substitute for a systematic study of game theory. It provides an elementary exposition of basic ideas in game theory and develops these ideas only in directions that bear on issues central to political theory.
Other books that expound game theory and its applications to politics tend to combine sophisticated game theory with rather crude political theory. In this book, by way of contrast, it is the game theory that is rudimentary. There is no algebra and no symbolic logic. Moreover, the examples that are worked through take the simplest form possible. The apparatus used consists only of payoff matrixes and decision trees, both of which are explained with a degree of redundancy that may make some readers impatient. My objective is, however, to break down the resistance of even those most subject to mathematics phobia – provided they actually want to find out about game theory, of course. And my experience has been that there is no substitute for going very slowly. The other side of the picture is that I presuppose a certain familiarity with political theory. In particular, I rework some ideas from Hobbes and Hume in terms of game theory without pausing to explain the broader context within which these ideas occur in Leviathan and the Treatise.’
It is important (again) to remind readers that this is not a finished book and Brian would certainly not have published it in its current form. However, it is a book that he wanted to be useful particularly, but not only, to students and it is added to this site in that spirit.
Here you can download: