History Of Game Theory

Game theory, as an independent subject, began in 1944, with a short history of 60 years. However, its pre-history can be traced as early as 18th century. With the advancing status of Game theory in economics, researchers are interested in its history. But the formal historic research has just lasted for less then 20 years, and the pace of the research is somewhat slow. Till now there is not an agreed-on history of Game Theory, even not a unified opinion on how the theory was developed in its rudiment. The researches have been done were mainly form sociological or economic point of view, which were somewhat lopsided. This paper, instead, studies how Game theory was formed from mathematical viewpoint, with the help of methodology and fruits of math history, which basically makes clear the road leading to the foundation of Game theory. The following is the outline of the paper.1. The development of all the theories related to Game theory before the creation of it or its concept. Because game problems were found widely existed, people studied them in various ways and left many master works. With the development of mathematics, learners on this field, very naturally, had a probe into game theory in their own way. The earliest study of game problems in math method appeared in the 18th century, the same time when probability theory was founded, which provided a new tool to game problems.2. The effect of the appearance of calculus on game theory. With the development of calculus, mathematicians tried dealing with game problems in economic and military field, with the new tool. The early studies included Cournot's economic model and Lanchester and Richardson's military fighting model. The mathematical thought reflected in these researches were, actually, different from modern Game theory, but, still, it showed the possibility of dealing with Game problems with mathematic tools, and meanwhile, the thought of differential game theory in the early time was included in these researches, which in a way inspired the establishment of Game theory.3. Further developments of set theory, probability theory and their influences on Game theory. Set theory got developed and was used in solving game problems. The first work in this aspectwas done by Zermelo. Meanwhile, probability theory made progress and became matured. During 1921-1928 Borel considered dealing with some strategic game problems with probability theory, form which he established several useful conceptions in Game theory, and it was at that time that Game theory was found in the rudiment. At this period, Steinhaus, Berol's students Ville and colleagues also contributed to the rudimentary theory. In the meantime, these people's work made up the foundation of Game theory: the evolution of Minimax theory and the founding of some basic conceptions in Game theory.4. Achievement of the thought of aximatization, a new thought in dealing with game problems. In fact, it was with the help of acclimatization that it was able to turn common game problems into math problems, which provided game problems with strict math foundation and made it possible to be a strict science. So it can be thought that dealing with game problems aximatized and the advancing and proving of Minimax theory were the two key elements for the foundation of game theory.5. The paper lays particular emphasis on the master work of modern game theory-game theory and economic behavior, analyzing how it was formed, what were its main ideas, its researching methodology, contributions and influences at that time. We think that the main contributions of the book is in two aspects: one is the revolution of some concepts such as utility theory, aximatization of game, extended game; the other is the breaking through in zero-sum two-person games centered on Minimax and corporation game centered on characteristic function. This was, in fact, the development and extension of Von Neumann's classic game paper of 1928. Our research shows that these contributions were a pure new theoretical creation, rathe...