Adv. Math. Econ. 9, 73-97 (2006)

The dawn of modern theory of games

Mikio Nakayama

Department of Economics, Keio University, 2-15-45 Mita, Tokyo 108-8345

Received: January 16, 2006 Revised: January 24, 2006

JEL classification: B41

Mathematical Subject Classification (2000): 91A99

Abstract. The modern theory of games initiated by John von Neumann with the minimax theorem in 1928 has now grown to be an indispensable analytical framework for social sciences, and economics in particular. In this paper, we shall review the early history of game theory from von Neumann to John F. Nash, the founder of the noncooperative game theory, including Émile Borel, Hugo Steinhaus and Oskar Morgenstern, thereby pointing out a hint of why game theory has come to be widely applied in economics.

Key words: Borel, Steinhaus, Kakutani’s fixed-point theorem, Morgenstern, cooperative games, stable sets, Nash, noncooperative games, Nash equilibrium