When solving for equilibria in zero sum games you don’t worry about the opponent’s payoffs, just their strategies. The reason is that the opponent’s payoffs are implicitly known—they are always diametrically opposed to yours. But in nonzero sum games, when computing the equilibrium strategies, you have to consider what the opponent’s payoffs are. As you might expect, the solution technique will be a little different.
In 1950, John Nash, as a 21-year-old grad student at Princeton, solved the problem of finding equilibria in nonzero sum games. His idea reinterprets the idea of equilibrium strategies as being best replies to the other’s strategy.
John Nash wrote a number of brilliant papers on game theory and other ...