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Books : reviews

Steven J. Brams.
Biblical Games: a strategic analysis of stories in the Old Testament.
MIT Press. 1980

rating : 3 : worth reading

Steven J. Brams.
Superior Beings: if they exist, how would we know?.
Springer. 1983

rating : 2.5 : great stuff

The central question posed in this book is: If there existed a superior being who possessed the supernatural qualities of omniscience, omnipotence, immortality, and incomprehensibility, how would he/she act differently from us? The mathematical theory of games is used to define each of these qualities, and different assumptions about the rules of play in several theological games that might be played between ordinary human beings and superior beings like God are posited. Implications of these definitions and assumptions are developed and used to explore such questions as: Are God’s superior powers compatible with human free will? Can they be reconciled with the problem of evil in the world? In what situation is God’s existence “decidable” in gamelike relationships He might have with us?

By endowing omniscience/onmipotence/immortality/imcomprehensibility with unambiguous meanings, the author shows how game theory can help breathe life into questions that have been dismissed too quickly simply because they are metaphysical—outside the world of experience. Thereby he clarifies the structure of our thought about an ultimate reality, whether or not it is viewed as religious.

Steven J. Brams.
Theory of Moves.
CUP. 1994

Steven J. Brams’ Theory of moves, though based on the classical theory of games, proposes major changes in its rules to render it a truly dynamic theory. By postulating that players think ahead not just to the immediate consequences of making moves, but also to the consequences of countermoves to these moves, countercountermoves, and so on, it extends the strategic analysis of conflicts into the more distant future. It elucidates the role that different kinds of power – moving, order, and threat – may have on conflict outcomes, and it also shows how misinformation, perhaps caused by misperceptions or deception, affects player choices. Applied to a series of cases drawn from politics, economics, sociology, fiction, and the Bible, the theory provides not only a parsimonious explanation of their outcomes but also shows why they unfolded as they did. This book, which assumes no prior knowledge of game theory or special mathematical background, will be of interest to scholars and students throughout the social sciences as well as individuals in the humanities and the natural sciences.

Steven J. Brams, Alan D. Taylor.
Fair Division: from cake-cutting to dispute resolution.
CUP. 1996

Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute – such problems of fair division are ubiquitous. Fair division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or “bads,” like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, “I cut, you choose,” the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular, they focus on procedures which provide "envy-free" allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.

Steven J. Brams, Alan D. Taylor.
The Win-Win Solution: guaranteeing fair shares for everyone.
Norton. 1999

Here is a compelling procedure for dispute resolution that will enable you to:
• Divide a contested set of goods equitably and efficiently
• Settle your dispute without time-consuming haggling or expensive litigation
• Remove the risk of losing to a more skillful bargainer
• Feel you got more than half of the total value (sorry, your rival will feel the same way)

This procedure, called “adjusted winner,” applies broadly, from divorce to business to international disputes. Based on a simple point-allocation system, it produces in hours, even minutes, resolutions that can and do take expert negotiators weeks and months to work out. What you really want to know is on which issues you will win, on which you will lose, and on which you will have to compromise. To this question, the authors bring a patented procedure that enables both parties to walk away with their maximum win-win potential.