On a Game Theory based on the Maximin Principle

Abstract

     After critically reviewing two types of the traditional game theories, one originated with von Neumann and the other originated with Nash, a new game theory based on the maximin principle is proposed. A typical example having the rational choice based on the maximin principle, which is different from the rationality assumed in Nash's game theory, is so-called chicken game. In this game, a rational choice for each of the players is "cooperation." The rational choice leads to a better choice than the mixed Nash equilibirum, which is equivalent to the ESS (evolutionarily stable strategy). This logical consequence seems to rationalize the nuclear deterrence, which is one of the significant issues in sociology.