ABSTRACT
All the optimization problems discussed so far have involved a single individual trying to maximize or minimize some function. In 1928 the mathematician John von Neumann introduced the theory of games in an attempt to deal with the more general problem of two or more individuals in competition and to make economics more scientific. The theory of games was developed somewhat later by von Neumann and Morgenstern [167] and has become an important tool, not only in economics, but throughout the social sciences. Two-person zero-sum games provide a nice example of opti-
the programming tools previously discussed. In this chapter we introduce the idea of two-person matrix games and use results from linear programming to prove von Neumann’s “Minimax Theorem,” also called the Fundamental Theorem of Game Theory. Our focus here is on the mathematics; the DVD course by Stevens [193] provides a less mathematical introduction to game theory, with numerous examples drawn from business and economics. The classic book by Schelling [184] describes the roles played by game theory in international politics and warfare.
