Biblical Games: Game Theory and the Hebrew Bible

Rating:
Summary: Five Stars if Accompanied with Brams' Theory of Moves
Review: Brams' Biblical Games is one of the most fascinating reads that I have encountered in some time. Presented are accounts of significant events recorded in the Old Testament, all of which are logically and mathematically examined by Brams, who uses aspects of game theory to determine the rationality of each person or assembly involved.

Throughout the chapters, Brams looks at every character as a player in a game, which, by itself, is touted as a challenge whose outcome is dependent upon the type of decisions executed. He subsequently utilizes payoff matrices, which are 2x2 geometric patterns that represent the outcomes of at least four different courses of action, where the results are weighed in as follows: 4=Best, 3= Next Best, 2= Next Worst, and 1=Worst. For each game, Brams places these numbers in ordered pairs; for example, (1,1) would be the result of a worst case scenario for both parties, a (4,2) might be interpreted as a situation where Player/Group #1 has the best possible outcome at the expense of Player/Group #2, who must settle for what is interpreted as next to worst.

In Biblical Games, Brams makes transitions from one decision-making conflict to another. Some of the so-called games exclusively involve bitter enemies, others concern those who typically have one another's best interests at heart, and some just implicate those who are essentially indifferent about the next person's fate or welfare. As he proceeds from section to section, Brams surprises the reader with scenarios that can run counter to one's expectations by showing that regardless of the nature of the game or conflict, there can potentially exist a win-win outcome between enemies and an unmitigated disaster that can be brought forth between friends.

Interesting are the interpretations of the numbers assigned in each matrix. Brams often interprets a player's score of 1 (worst case) as being the result of that particular player's ineptness to make adequate decisions and that this insufficiency could be due to either recklessness or lack of fortitude, or both. A 2, on the other hand, though a next to worst, has the capacity to be esteemed as the outcome of a most logical decision made by a player who lacks the resources to put him/herself into a better situation but enough to avoid disaster. Not only does Brams weigh the outcome of what actually happened, but he also presents the logic, or lack thereof, of alternate decisions and how they all would likely have turned out.

Biblical Games is very thought provoking, even sobering. Ideally, it should help one to weigh more carefully and more wisely the consequences of the decisions that he or she makes.

On its own, Biblical Games gets four stars, but tied in with Brams' Theory of Moves, it easily gets five. From the latter book, you will have tied in with appreciating the logic of what actually happened and what might have otherwise happened à la Biblical Games a more refined, more exact analysis of potential moves and countermoves that can be applied to personal challenges in the distant future.

Rating:
Summary: pay no attention to oil and water
Review: He didn't read the book and misinterpreted the whole concept of it. Just because your jewish does't make you an expert on the old testament.

Rating:
Summary: Great primer on game theory
Review: I'm enjoying this book far more than all the other elementary game theory textbooks I've plowed through. I'm a doctoral student in economics, and I'm reading this book for a readings class. I highly recommend it for anyone interested in dipping their feet into game theory. It's very readable and uses no mathematics, thus making it accessible to the non-technician and beginner.

Brams uses 2x2, non-cooperative models of complete information for the most part. He uses both game trees and normal expressions of the situations under analysis. This is, I think, one of the strengths of the book. The stories are familiar, if you are familiar with the Judeo-Christian religion, and thus this captures one's attention in ways that abstract stories about prisoners, and husband and wives and other classic illustrations in game theory may not. God is included as a player in situations Brams analyzes, and his interpretations are, at the very least, illuminating. While reading it, I was reminded of an Edmund Burke quote which more or less says that even heresy is valuable insofar as it stirs the stagnant waters of science such that progress can be made. I am finding that even when I disagree with Brams interpretation, his game theoretic explanation nonetheless sheds some light on the story, as well as on broader spiritual ideas like faith and rationality.

One criticism I have of the book is, though, that it is limited only to games of complete information. As I said, I do believe that the fact that this book only uses noncooperative games of complete information is its strength, precisely because I believe this book is helpful as a primer to game theory. But, because he omits problems of imperfect information, I am left wondering whether he has truly modeled many of these situations as accurately as he could have. For instance, when dealing with the "sacrifice game" involving God and Abraham, wherein God has ordered Abraham to sacrifice his son, Isaac, Brams seems to treat Abraham as having complete foreknowledge of God's preference rankings of the four various outcomes. It is difficult for me to believe that Abraham, even being an intimate to God, would possess this kind of knowledge. I would have preferred to see Brams introduce models which would allow Abraham to deal with the asymetric information inherent in this kind of situation. Is anything lost by assuming complete information in these games? Not necessarily. Having not worked the alternative problems out for myself, I cannot say, but since Brams is so effective at making game theory accessible in this book, I believe he had ample opportunities in the book to introduce slightly more complicated notions like mixed strategies and signaling. He certainly is talented and creative enough to do so.

All in all, I recommend the book to all students of economics, religion, sociology and political science. I do not necessarily believe that the analysis is hugely valuable for the more generally "spiritual" person, but I definitely would not discourage that person from reading the book. Brams is unusually gracious and respectful of religion, generally, and the characters (including God) in this book. That is definitely a plus. It is rare for anyone to assume rationality when thinking about religion, and when scholars finally do, I tend to be impressed. And I was impressed with Brams, both for the tone of the book, but also for the content. Highly recommended.

Rating:
Summary: pay no attention to oil and water
Review: Just for grins, I decided to actually review this book AFTER I read it. The previous reviewer should consider doing same.

The book was interesting and thought provoking. I would recommend it to anyone with a secular interest in game theory applied to a non-obvious choice of subject. The author isn't presuming to think like God. He is applying game theory to a group of situations many are already familiar with.

Rating:
Summary: Game Theory Used Correctly
Review: To show that game theory is not appropriate in this context involves much more than simply giving a much different example in which a much different theory is inappropriate and expecting us to follow you over the tightrope to the conclusion that this particular case is much the same. Simply gesturing toward a conclusion in this halphazard way shouldn't suffice in a PhD thesis and I'll be damned (forgive me) if I'm going to let it slide here.

Game theory is appropriate for the analysis of strategic decisions made in social situations - it should not matter if these social situations appear in the Bible or in the world oil market. If the "game" analyzed exhibits a solution consistent with certain assumptions (rationality, self-interestedness, and the like) about the players, then we say the player behaves as if they met these assumptions themselves. This is of course the same as the "as if" defense for economics generally, and there is even a (famous) similar defense for quantum mechanics: the only important thing is that particles behave as if they satisfied assumptions made about them. Clearly this is something that falls more in the realm of scientific method generally than in that of the methods of any particular science.

Brams is highly justified from a general modelling standpoint as well (am I the only one who thinks it odd that one should speak of *proving* results like this?). The earth may not be flat, but in so many instances it is modelled as such (or as locally such). Adding the sort of brownian variations from this structure that are clearly present at the very_local_level (or even in the large if you don't live in minnesota!) would for such purposes amount to using a model of unnecessarily high resolution, and while we all know that this implies unnecessary costs in modelling and analysis it is also true that it can disguise the phenomena of interest (remember what you learned about sampling rates in college physics lab!). Brams commits no such sins (forgive me), and while static models are more coarse than many more recent methods, they are particularly suited to the sort of highly-circumscribed interaction one finds in the Old Testament.
His use of dynamic techniques (his own theory of moves) in the analysis of counterfactuals is also instructive - dynamics is all_about_counterfactuals! Of course we see by the limitations of the necessarily_static_text that there are limitations too of such finer methods - another feather in the cap of Brams' (mostly) static analysis.

Some may then complain that the results are trivial - that *of course* the text will exhibit such large agreement with the classical (rational) assumptions used in the models. Not so. Any economics PhD worthy of the badge should be able to name countless examples of experiments in which human participants repeatedly fail to meet these criteria (Daniel Kahneman just won a Nobel for this). It is therefore *really saying something* that the various participants in Biblical "games" can be said to behave in this way.

Of course it's also very noteworthy that the Old Testament should be amenable to such an analysis - that the interactions *are* so circumscribed - that the goal forming/seeking behavior of its prominent figures *is* brought out in such high relief - and that such a clear consideration of the end results *is* so emphatically presented in nearly every instance. The true believer may well see the elucidation of these phenomena as the goal God sought in the writing of the Old Testament, and Brams has simply provided another testament (forgive me) to His success.

Joshua James Wiley