Game Theory and the Social Contract, Vol. 1, Playing Fair.

Ortmann, Andreas

Ken Binmore is a mathematician-turned-game theorist/experimental economist extraordinaire. He argues that "much insight into ethical matters can be gained by approaching them systematically from a game-theoretic perspective" [p. vii]. Not any old game-theoretic perspective, mind you. Binmore has contributed important essays on the foundations of game theory - How to model a rational player? What is common knowledge? - and the relationship between what he termed the "eductive" and "evolutive" approach to non-cooperative game theory [1]. The former signifies the conventional game-theoretic perspective whose somewhat heroic rationality and knowledge requirements have made it a convenient target for those eager to dismiss it. The latter is a complementary approach that gets rid of some of those requirements and tracks by way of evolutionary systems - essentially systems of difference or differential equations - the evolution of a population's actions over time. During the past decade advances in game theory, in particular for games with multiple equilibria, have often been generated by attempts of game theorists and experimental economists to understand better the relationship between the two approaches.

Equipped with these conceptual lenses, Binmore has revisited foundational issues concerning the nature of social contracts, and such constructs as the original position, and the categorical imperative. This inevitably abstract and academic investigation nevertheless has a political subtext. Binmore - a self-declared whig whose thinking on social contract issues can be traced back to the early 80's [2] and the reigns of Thatcher and Reagan - sees his investigation "as a piece of rhetoric aimed at open-minded conservatives" [p. 4].

His investigation's major theme is the claim that there is no such thing as a priori principles of morality or moral absolutes. The social fabric of a society, and hence standards of moral conduct, consists of commonly understood conventions. These conventions are the result of evolutionary processes in which society's members interact repeatedly in a self-interested, though enlightened manner. Consequently, the social fabric, and its underlying seemingly flimsy foundation of commonly understood conventions, ought to be conceptualized as a dynamic equilibrium. This "bottom-up approach to ethical issues" [p. 139] contrasts with top-down teleological approaches to ethical issues like the categorical imperative; it also "requires climbing a different ladder to the notion of a common good than those climbed by Harsanyi or Rawls . . . [whose] nonteleological theories [of the original position] take some versions of homo ethicus as their model of man. . . . I take homo economicus as my model of man in hope of thereby establishing a firm footing for my ladder" [p. 139].

The present volume contains four chapters. Chapter One, titled "A Liberal Leviathan" provides a road-map for the remaining chapters. Its centerpiece is a lengthy, nontechnical section cleverly rifled "DeKanting Rawls." The section title's pun refers to the German philosopher associated with the categorical imperative: act only on the maxim which you can at the same time will to become a universal law. Binmore argues that teleological do-as-you-would-be-done-by principles like Kant's are seriously flawed because they rest on a priori notions of standards of moral conduct or common will that are in conflict with notions of self-interested behavior, and in any case can and should be derived from models of serf-interested actors in repeated games. For example, in a one-shot prisoner's dilemma game one might be tempted to induce cooperative behavior by appealing to the categorical imperative. Unfortunately, as documented abundantly in the experimental literature, individual rationality often leads players to ignore this ethical tenet. However, in a repeated prisoner's dilemma game cooperative behavior emerges, under well-defined conditions, as equilibrium behavior of individuals who are self-interested, albeit in an enlightened manner. As Binmore puts it, "ethical principles are 'no more' than common understandings that have evolved to coordinate the behavior of those acting in their own enlightened self-interest" [p. 17]. Instead of voluntary surrender by all, of their rights and liberties into the hands of a Leviathan, Binmore visualizes the social contract as an "implicit self-policing agreement between members of society to coordinate on a particular equilibrium in the game of life" [p. 35], similar to coordinating conventions that emerge among rational agents in repeated stag-hunt games, or prisoner's dilemma type games. The essence of Binmore's argument is very similar to Kreps's conceptualization of the seemingly flimsy construct, corporate culture [4].

While Binmore's main theme is the conditions that generate moral behavior, his focus is conceptual and foundational problems such as the possibility of intra- and interpersonal utility comparisons. In fact, much of the argument is developed within the confines of a world of only two representative agents. Thus, complications like coalitional issues are not addressed. In this set-up the ability to empathize emerges as a central issue, and the original position - the notion that societal arrangements are negotiated behind a veil of ignorance - is a key device. The author chiefly associated with this device is Rawls, and chapter One fast-forwards through Binmore's theory by contrasting it with that of the younger Rawls and other contributors to the social contract debate, from Hume and Smith to Rawls, Harsanyi, and Gauthier. Topics are homo economicus and other rational fools, the meanings of sympathy, and the nature of legal rules (". . . nothing more than particularly well-codified conventions" [p. 32]). All the while, it is assumed that people's payoffs can be compared. The remainder of the section, and chapters Two through Four probe what it takes to make sense of that assumption.

Chapters Two and Three present basic notions of game theory. Binmore emphasizes that the purpose of these chapters is less to teach game theoretic fundamentals, than to argue why game theory's critics are wrong. Toward that end, he presents in chapter Two games like prisoner's dilemma, chicken, or stag-hunt to discuss one-shot games and repeated games, equilibrium concepts and configurations, and what it all means for social contract issues. Thrown in for good measure are discussions of teleology whose aim is to deal with "the fallacy usually signaled by the question: Suppose everybody behaved like that?" [p. 170]. Chapter Three takes on those who try to rationalize what game theorists consider irrational - the use of a strongly dominated strategy. This chapter contains insightful discussions of the work of Gauthier and his theory of constrained maximization, Frank and the strategic role of the emotions, the meaning of experimental results, Axelrod's computer tournaments, and the conditions under which the Harsanyi doctrine - people with similar cultural background, social status, and personality will behave similarly when placed in similar situations - makes sense. In passing, the chapter introduces a number of additional game theoretic ideas (cheap talk and correlated equilibrium, among others); it ends with a discussion of Newcomb's Paradox.

Chapter Four, "Cardinal Comparisons," is heavy on instructional material regarding intra- and interpersonal comparisons of utility. It contains expositions of Von Neumann and Morgenstern utilities, empathetic preferences, how Harsanyi and Rawls go about comparing utilities, what it really takes to make available a common and uncontroversial standard for comparing utilities across individuals, and Bayesian decision theory. The chapter furthermore contains an interesting conjecture regarding the prominent role of the maximin criterion in Rawls's theory, and criticisms of the thick veils of ignorance proposed by "Kanteans" Harsanyi and Rawls. Binmore concludes with the suggestion that a thinner veil of ignorance, one not requiring players to forget who they are, might do in social contract situations.

Binmore imagines three potential types of readers - the Economist, the Politician, and the Philosopher. To accommodate their different knowledge bases, plenty of instructional material on game theory is woven into the narrative. (Those who know Binmore's earlier works, especially his excellent undergraduate text [3] will find that he sampled freely from that material.) This technique is not a fortunate one. The instructional passages on game theory are unlikely to lead to an appreciation of it on the part of the uninitiated, a point that Binmore is quite aware of; they make for an uneven text whose story line meanders quite a bit simply on these grounds. The use of marginal symbols, indicating increasing conceptual depth by way of more nested boxes, customizes the text for different audiences, but does not overcome the problem.

More importantly, though, Binmore at every turn anticipates objections and misunderstandings of what he has to say. Thus, one repeatedly finds him explaining what he is not going to say before he gets to an exposition of an argument, often after lengthy detours. While these detours typically are delightful and insightful, this modus scribandi leads to repetitions and quickly becomes frustrating, especially for readers not familiar with social contract issues. I suspect that a concise development of the material with subsequent discussions of anticipated criticisms of his arguments would have resulted in a dominant strategy for readers.

Because of the idiosyncracies in its construction, the book resembles a movie that has plenty of great lines but a messy storyline with many subplots. (If you had trouble following the story line in Pulp Fiction, you are likely to be in trouble here.) Of course, maybe it's just my problem. (Although, I had no trouble following the plot in Pulp Fiction.) That said, for those interested in the social contract issues, this is an intriguing book worth the reader's time.

Andreas Ortmann Bowdoin College

References

1. Binmore, Ken. Essays on the Foundations of Game Theory. Cambridge: Blackwell, 1990.

2. -----. Game Theory and the Social Contract. In R. Selten, editor, Game Equilibrium Models II. Methods, Morals and Markets. Berlin: Springer-Verlag, 1991.

3. -----. Fun and Games: A Text on Game Theory. Lexington, Mass.: D.C. Heath, 1992.

4. Kreps, David M. "Corporate Culture and Economic Theory," in Perspectives on Positive Political Economy, edited by J. Alt and K. Shepsle. Cambridge: Cambridge University Press, 1990.