9.4 Nonzero-Sum Games

This section parallels the development of Section 9.3, except that the more general case of nonzero-sum games is considered. This enables games with any desired degree of conflict to be modeled. Some decisions may even benefit all players. One of the main applications of the subject is in economics, where it helps to explain the behavior of businesses in competition.

The saddle-point solution will be replaced by the Nash equilibrium, which again is based on eliminating regret. Since the players do not necessarily oppose each other, it is possible to model a game that involves any number of players. For nonzero games, new difficulties arise, such as the nonuniqueness of Nash equilibria and the computation of randomized Nash equilibria does not generally fit into linear programming.