• Zero-sum two person games of perfect information
• Why these games are strictly determined
• Generalized forms of zero-sum games
• Mixed strategy and payoff equilibrium
• Von Neumann's minimax theorem
• The utility theorem
• Non-zero-sum games

Two person non-zero-sum games are much more complicated than zero-sum games than zero-sum games, and have many complications that we have not seen in the zero-sum games. There are no clear "this is the correct way" strategy to use, and there are always multiple factors in control of the situation. In a non-zero-sum game, a normal form must give both payoffs, since the loss is not incurred by the loser, but by some other party. To illustrate a few of the problems, let us consider the following payoff matrix.

Now, according to the zero sum reasoning, player 1 should play strategy X 1/3 of the time, and player two should play A 1/3 of the time to get the minimum payoff. This all sounds good until we see that by playing strategy X all the time, player 1 can double his payoff, but if they both do it, they will get nothing.

More information will be posted in the "Other Topics" section of various facets of these types of games. However, to learn more about game theory and non-zero-sum games, you can go to Strategy and Conflict: An Introductory Sketch of Game Theory.