Steven J. Brams, Game Theory and the Humanities
Steven J. Brams, Game Theory and the Humanities, Cambridge, MA: MIT Press, 2011, 319 pages, ISBN 976-026201522-6
Crédits : MIT Press
1According to some commentators and critics, all literary plot lines are variations on the single theme of someone wanting something and someone else trying to prevent them from getting it. Similarly, one might see everyday life as a continual sequence of transactions, in which two (or more) parties enter into a negotiation to exchange something for something else, the negotiation itself being a form of conflict resolution. In 1944 John von Neumann and Oskar Morgenstern published their magisterial treatise Theory of Games and Economic Behavior as a giant initial step toward a mathematical underpinning of such questions of conflict resolution.
As always with mathematical idealizations of the real world, game theory à la von Neumann-Morgenstern came with a host of assumptions. Among them:
Zero-sum, meaning the players interests were diametrically opposed;
Perfect information, so that each player had complete knowledge of the other player’s set of possible actions and the payoffs each would receive from their choices;
Perfect rationality, so that each player acted so as to maximize his or her payoff;
Static, in that the player’s choices were taken only once rather than involving a sequence of choices over time.
2Over the past several decades all of these built-in limitations have been relaxed in different ways leading to a mathematical theory of games that is now edging ever closer to being a practical tool for analyzing real-world conflict situations. Steve Brams’ Game Theory and the Humanities amply illustrates this fact with a dazzling array of situations taken from the humanities in which conflicts that arise can be characterized by a mathematical game. Just to show the scope of Brams’ vision in this regard, let me sketch a few of his examples.
Theology: Pascal’s Wager. Here the two players are Nature and an individual. The individual has two possible actions: Believe in God or do not believe, while Nature has two states: God exists or does not exist. Brams provides a plausible payoff structure for the four possible combinations, and analyzes the Wager and employs game-theoretic arguments to question Pascal’s analysis that it is always better to believe in God’s existence.
Literature: C. P. Snow’s The Masters. In this classic novel of academic intrigue, 13 Fellows of a Cambridge college engage in a zero-sum game to elect one of two candidates to become Master of the college. During the course of the story, the two candidates vie for the support of the other eleven Fellows with at least four different coalitions forming and coming undone before the election. As Brams notes, this is a zero-sum game (since only one of the candidates can be elected) but with thirteen players, not just two.
History: The U.S. Civil War. Brams shows in this situation that the battle between the Union and the Confederacy was a two-party, nonzero-sum game. Game-theoretic analysis is employed to suggest an answer to the question as to why the Confederacy started the Civil War in the first place. The provisional reason suggested is that the Confederacy misjudged its level of threat to the Union at the outset, leading it to overvalue its chances of getting a compromise proposal from the Union instead of the fierce battle that actually ensued.
Law: Jury Selection. The problem of how both the prosecution and defense should best allocate their limited number of peremptory challenges to prospective jurors is another situation that Brams describes in game-theoretic terms. While the rules of the Jury Selection game are too detailed to enter into here, the basic idea is that the game should be played so as to calculate the probability of a juror voting for conviction above which the defense attorney should challenge that juror. The analysis presented in the book is carried out in a sequential fashion as jurors come up for examination. Thus, the simultaneity assumption of classical game theory is dropped in favor of the more realistic dynamic unfolding of the actual selection process in a courtroom.
Political Philosophy: The Free-Rider Problem. The free-rider situation arises when there is a resource like a park or school that users finance through voluntary contributions. There is no problem if all the users pay. But there is a strong motivation for each individual user to assume the others will pay for the resource, and thus not pay for use of the resource himself. Such a non-payer is termed a “free rider.” The book models this problem as an n-person, non-zero-sum Prisoner’s dilemma game, and shows how to resolve the conflict between individual and collective rationality. The analysis presented by Brams shows that cooperation (i.e., for all users to pay) is always the rational way to proceed.
3Throughout the book, the author employs his innovative idea of the theory of moves (TOM) to relax one of the main obstacles to effective employment of game theory in real-world situations. The classical theory of games assumes that players choose strategies simultaneously. But in most, if not all, real-world situations the games start at a state that represents the status quo. The principal question is then whether any player can do better by departing from that state, not just in an immediate myopic sense, but in a longer-term perspective that may involve a sequence of strategic choices.
4 In an early section of the book, Brams summarizes the rules governing how the players can depart from the status quo state, and shows when it is rational for any player to move away from that state. The theory he presents is then employed regularly throughout the book to present a very different picture of the applicability of game theory for conflict resolution than what is usually found in other presentations of “applied” game theory.
5 To illustrate TOM in a simple, two-person game, the author presents the story of Sampson and Delilah as a conflict resolution problem in which Sampson can choose to retain or divulge the secret of his great strength, while Delilah has the option of nagging him for the secret or not nagging. The author assumes that the game begins in the state in which Delilah does not press Sampson for his secret and Sampson remains silent. Using the formalism of the TOM, a sequence of departures from that state leads to a “non-myopic equilibrium”, in which Sampson finally gives up his secret under the pressure of Delilah’s persuasive charms (i.e., nagging!).
6 While there’s no room here to go into details of how the TOM can be used in vastly more complicated situations to add a dynamical element to the choices made by players in real-world games, it can be safely stated that this concept is the primary theoretical contribution offered in the book. And an extremely valuable contribution it is, since the usual static, single simultaneous choice-type of situation from classical game theory can almost never be found in any realistic conflict situation. It’s a pity that the TOM is not more well known outside the circle of game theory professionals, as it opens up a totally new way of thinking about games of strategy and their applicability to problems of everyday life.
7 Mathematical models of every type are an abstraction from the reality they purport to represent. The model necessarily throws away aspects of the real world situation that the modeler believes are irrelevant, or at least of minor influence, on the answers to the questions the model is designed to address. So it’s no criticism to note as we did at the outset that game-theoretic models of conflicts ignore, or dramatically simplify, aspects of the actual conflict that the model is simply incapable of accommodating. All this having been said, the book under review does a spectacular job of both beefing-up the theoretical structures and identifying how to employ and interpret what the mathematics is saying to account for the actual observed behavior under consideration. I was continually amazed at the virtuosity the author displayed in seeing how the resolution of the conflict between Sampson and Delilah or that dividing the Union and the Confederacy in the US Civil War could be easily explained through the application of game-theoretic analysis. The book leaves no doubt that human conflict and its resolution, wherever you find it, can be encompassed within the formal framework of game theory.
8 But what about the other way around? Einstein once famously remarked, “The theory tells you what you can observe,” where one could interpret “theory” to mean the model. So is there any evidence to suggest that practitioners of the humanities and social sciences have been motivated by game-theoretic concepts, and especially models, to give rise to new lines of thought in their works? It’s certainly no criticism of the book under review that there do not appear to be any indications of this “role reversal” to be found within its pages. And despite the fact that certain concepts like a ”zero-sum game” or “a mixed strategy” from game theory have found their way into everyday speech, I’ve found very few clear-cut examples of artists, jurists, writers or sociologists who have been motivated by game theory to develop their art in new directions suggested by the theory. Perhaps the book under review will serve to energize such activity. This book is certainly an excellent place to start for anyone seeking new ideas to explain conflict resolution. One can but hope that it will smoke out new applications across the humanistic spectrum.
Pour citer cet article
John L. Casti, « Steven J. Brams, Game Theory and the Humanities », Œconomia, 2-4 | 2012, 513-516.
John L. Casti, « Steven J. Brams, Game Theory and the Humanities », Œconomia [En ligne], 2-4 | 2012, mis en ligne le 01 décembre 2012, consulté le 24 avril 2017. URL : http://oeconomia.revues.org/1258Haut de page
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