An Introduction to the Theory of Games

Abstract

Game theory covers a substantial part of the process of decision-making under uncertainty. In the early years, the development of game theory was indebted to Emilie Borel and John von Neuman for major contributions, although it is not clear who should be regarded as the founder of game theory. In 1953, the famous mathematician Maurice Frechet claimed in the pages of Econometrica that his senior colleague Emilie Borel was actually responsible for initiating the development of game theory. This produced a strong rebuff from John von Neuman claiming that until his proof of the minimax theorem in 1928 there was simply nothing worth publishing in game theory. It appears that it is not quite as simple as that. Although von Neuman was first to provide a rigorous proof of the minimax theorem, Borel established the ground for it in 1921. In fact, it is now known that Earl Waldegrave (1684–1741) worked out the first minimax mixed strategy solution for a two-person card game called le Her. Game theory covers a very wide area and has produced many interesting results. In this and the subsequent chapters of Part II, we shall discuss only some important results of game theory.