John von Neumann’s Game Theory

Abstract

The fundamental theorem of John von Neumann’s game theory states that in a broad category of games it is always possible to find an equilibrium from which neither player should deviate unilaterally. Such equilibria exist in every two-person game that satisfies the following criteria:

• 1. The game is finite both in that the number of options at each move is finite and in that the game always ends in a finite number of moves.

• 2. It is a zero-sum game: One player’s gain is exactly the other’s loss.

• 3. The game is one of complete information: Each player knows precisely all the options available to him and to his opponent, the value of each possible outcome of the game, and his own and his opponent’s scales of values. (If the game is zero-sum, these two values are the same. There exist non-zero-sum games with complete information content, but von Neumann’s theorem does not encompass them.)