Von Neumann, Morgenstern, and Theory of Games: Critical Reassessment of Zero-Sum Games

This chapter gives a brief yet critical account of the theory of games as jointly developed by the two superstars in the twentieth century; namely, gifted mathematician John von Neumann and brilliant economist Oskar Morgenstern. There are two memorial years for game theory: 1928 as the Year of Birth for Game Theory and 1944 as the Year of Maturity for Game Theory. Even after the basic mathematical skeleton for game theory was provided by von Neumann in his 1928 paper, giving its real body and substance to the skeleton was a difficult job for Morgenstern. In both his 1928 paper and 1935 paper, Morgenstern paid a special attention on the duel between Sherlock Holmes and Professor Moriarty in Conan Doyle’s famous detective story, finding an unsolved puzzle between an infinite chain of “out-thinking” and a finite concept of general equilibrium. In 1944, the collaboration of von Neumann and Morgenstern finally produced a difficult bulky book Theory of Games and Economic Behavior, whose academic reaction was initially rather quiet, requiring many years for its full recognition by social and natural scientists. It is of utmost importance to draw a definite line between “games under risk,” represented by The Final Problem in Doyle’s detective stories, and “games under uncertainty,” shown by The Adventure of the Empty House. We believe that the second kind of games, in which “animal spirits” a la John M. Keynes play a key role in decision-making, remain to be fairly unexplored, requiring for future research.