Read many years ago, today tossing it into the donate box.

It does stick me and I am glad to have read it - especially the long account of 'tit-for-tat'.

Basically, you should cooperate until the other person/side/team 'defects' or breaks the trust. Then you should defect. It they again cooperate you should too until they defect again.

Assume cooperation until proven otherwise is a pretty good strategy, generally. ( )

This book is definitely not Pareto-optimal.

If that means nothing to you, ironically, this book may be for you. That's because it is a very non-technical introduction to game theory -- that is, the branch of mathematics devoted to determining the best "strategy" when confronted with a particular set of choices (euphemistically called "games"). A game might consist of deciding whether a wife should go to an event her husband loves and she despises, because she loves him ("Battle of the Sexes"), whether to turn stool pigeon after being arrested ("Prisoner's Dilemma"), or how often to play heads or tails in a heads or tails matching game. Or it might consist of deciding whether to ratchet up the threat to North Korea or try negotiating instead. All of these are "games"; in theory at least, all of them are the province of game theory.

Game theory has been one of the most intensively studied areas of mathematics in the last half a century, and the results have been vitally important in economics and often useful in other areas as well. And it is in fact a relatively straightforward area of mathematics (generally no calculus needed, e.g.). But it isn't entirely mathematics-free (having the ability to do arithmetic is necessary, and I wouldn't want to try it without algebra, either). Author Barash has attempted to present game theory with as little mathematics as possible -- so little that he doesn't even allow himself to produce mathematical formulae.

Obviously this means that you won't learn any actual game theory from this book. But you will learn a little about what the field can do, and some terminology. Such as Pareto optimality. A situation is Pareto optimal if you can't improve one person's life without making someone else's life worse. Take a very simple example: Suppose you have two people. One of them has a billion dollars; the other has a hundred dollars. If the first guy had a hundred dollars taken away from him by a tax, he would be only very slightly worse off, but if the second guy were given a hundred dollars, he would be much, much better off. Thus, by taking $100 from the first to give to the second, we significantly increase the overall well-being of the two. But this is not Pareto-optimal, because transferring the $100, although it makes one player much better off, makes the other ever so slightly worse off. There is, in this case, a more optimal situation (two guys with half a billion dollars are both in a very fine situation), but there is no way to get from one way to the other without depriving one of them. A plan can only be Pareto-optimal if you can get from the start to the end while making everyone's life better every step along the way.

(Note incidentally that this is why things like tax reform are so hard: We know that a tax system with lower rates and fewer deductions is generally more fair than a system with higher rates and more various deductions that brings in equal revenue, but there is no Pareto-optimal way to get from the latter to the former; someone is always hurt, and so someone screams.)

So: A Pareto-optimal non-mathematical game theory book would be one that you can read -- and then, if you want, turn and go into a real game theory book and learn the mathematics, without the first book getting in your way.

Unfortunately, it isn't possible with this book. That's because it gives you a whole bunch of misleading descriptions of games. Having read most of the book, one that particularly got to me is Barash's description, on p. 172ff., of a game known as "Deadlock". Only he doesn't call it "Deadlock." He calls it a variation of "Prisoner's Dilemma." It is not. It applies in different situations. There are far too many instances of this.

Does the terminology matter? If you just want an idea of how game theory works, then no, it doesn't, and this is a good and interesting volume. But when I first encountered game theory, it was in a similar book that mis-defined the most important game of all, "Prisoner's Dilemma." It took me a very long time to realize that I had gotten a classic game wrong. I had a lot of re-learning to do, and it interfered with my ability to understand the field. The sort of mis-definition Barash engages in could be very handicapping if you want to really learn game theory. So don't get yourself into a place which is not Pareto-optimal. If you want to really learn game theory, bite the bullet and buy a book with some actual math in it. If you are sure you don't want to learn the math -- if you just want to have some fun -- then this book should be just fine.

Signed, the Curmudgeonly Mathematician. ( )