Game Theory and Economic Behavior

Author: von Neumann Morgenstern (USA)
Translator: Wang Wenyu, Wang Yu
Publisher:
Publishing Date: 2004-12-01
Features: According to Amartya Sen, the winner of the 1998 Nobel Prize in Economics, game theory and social choice theory are the main achievements of 20th-century social sciences. The landmark events marking the establishment of these two disciplines were the publication of two books; the latter is undoubtedly Arrow's pamphlet Social Choice and Individual Values in 1951, while the former is undoubtedly von Neumann and Morgenstern's monumental work Theory of Games and Economic Behavior in 1944. Game theory has become the core of the entire social sciences, especially economics. Samuelson once quoted a short saying in his classic textbook: "You can make a parrot a trained economist as long as it learns just two words—supply and demand." Now, perhaps they can be replaced with "game" and "equilibrium." The genius mathematician von Neumann (1904-1957) is the "legend of legends." At the age of six, he could perform mental calculations for eight-digit division but unfortunately passed away at the prime age of 53 due to bone cancer. As perhaps the only universal mathematician after Poincaré and Hilbert, his contributions spanned pure and applied mathematics, and he was the pioneer in the formalization of quantum mechanics. He is also considered the true father of modern computers. In Princeton, regarded as the "mathematical center of the universe," there is a saying: "There are two kinds of people—von Neumann and the rest." Such an extraordinary mathematical genius was not an aloof ivory-tower figure; in fact, it is hard to find a more "down-to-earth" mathematician than him. Von Neumann and Wiener records: "He liked restaurants, women, parties, getting richer, and getting richer still, and having political influence"; of course, "he especially loved doing mathematics." Additionally, he was an expert in Byzantine history and one of the main authorities on "European royal genealogies." So, I have some "malicious" speculation that von Neumann was willing to collaborate with Morgenstern to write the classic before the readers, mainly because Morgenstern once "claimed to be the grandson of Emperor Frederick III of Germany." With such genius and a fondness for worldly life, applying his exquisite mathematical talent to the vulgar study of worldly life—"game theory"—seems only natural. Von Neumann's "Maximin Theorem" for two-person zero-sum games in 1928 was a milestone in game theory. During the subsequent years of seclusion, he was already a professor at the Department of Mathematics at Princeton University and the Institute for Advanced Study. When Hitler marched into Vienna, the Austrian Morgenstern, who was visiting Princeton University, stayed behind in the Economics Department. Silvaniana Salamone, in her biography The Princeton Ghosts of Nash, wrote that Morgenstern "strongly desired to do something that was 'truly scientific.'" He persuaded von Neumann to co-author a paper to argue that "game theory is the correct foundation for all economic theories." Moreover, "von Neumann almost independently completed this 1,200-page paper, but finally it was Morgenstern who wrote the provocative introduction and skillfully organized the arguments, which immediately attracted attention from the mathematical and economic communities." Following the footsteps of the translation of Theory of Games and Economic Behavior by Wang Jianhua and Gu Weilin in 1963 from the Science Press, the Sanlian Bookstore translated and published this work, which Bingmei called "whose practical significance is mainly historical." Personally, I think it takes some courage to do so. Regardless, with several popular game theory textbooks translated abroad in recent years, this book is no longer the best introductory reading for learning game theory, although it may not have been in its time either. For later generations "standing on the shoulders of giants," the treasures in this Theory of Games and Economic Behavior have almost been exhausted by experts. Its obsolescence can be attributed to both its strengths and weaknesses. Von Neumann failed to break through the limitations of his "Maximin Theorem" from a decade earlier. A significant portion of the book is devoted to zero-sum games, while broader non-zero-sum games are "transformed" into zero-sum games by introducing a virtual player—Nature. The key is that this transformation's social scientific implications are not entirely clear. The true resolution of this issue came from Nash's contributions. Years later, in his office, von Neumann dismissively referred to the theorem discovered by the young Nash—the second milestone in game theory—as "just another fixed-point theorem." Fortunately, in the preface to the third edition of Theory of Games and Economic Behavior, the old genius fairly acknowledged the arrival of the new genius. Of course, his theorem, combined with his prestige, remains the primary contributor to the promotion and dissemination of game theory. The influence of the "Maximin Theorem" has not faded. The famous statistician Wald of von Neumann's generation regarded statistical decision-making as a two-person zero-sum game between statisticians and Nature, leading statisticians to choose the "Maximin" strategy. Even in Rawls' theory of justice, the difference principle advocating that the worse-off should be relatively better off could be seen as the lingering legacy of this "Maximin Theorem." The young Norwegian mathematician Abel once warned us that progress depends on "learning from the masters, not their students." In my humble opinion, the discussions in this classic work on the strategic and extensive forms of game representations, the solution concepts of cooperative games, particularly the stable set, and the appendix on expected utility functions, still deserve special attention. If you are interested in the "philosophy" of game theory, thinking about why cold, hard mathematics can be used to describe the complex real world, perhaps the introduction by the supporting character can penetrate the thick layers of history. Non-cooperative games seem to occupy a more central position in contemporary game theory research, but it was the perfect synergy between von Neumann and Morgenstern that unveiled the curtain of the revolution in game theory's impact on economics and the entire social sciences, recognized by the Nobel Committee in the 1990s.