Whereas games of cooperation are games in which there is no conflict of interest and the pay-offs are identical for both players; and whereas zero-sum games are games in which the players' interests are totally opposed and what is good for one player is necessarily bad for the other; mixed-motive games come somewhere between the two.

In a mixed-motive game, the sum of the pay-offs differs from strategy to strategy, so they are sometimes called variable-sum games, although the term is not strictly accurate since cooperative games are also variable. They rarely produce pure solutions, but they are interesting for the real-life situations they represent and for providing an insight into the nature of conflict resolution.

Even the simplest mixed-motive games, represented by two-by-two matrices, have many strategically distinct types. There are 12 distinct symmetrical two-by-two mixed-motive games, of which eight have single stable Nash equilibrium points and four do not (Rapoport & Guyer, 1966). The first section of this chapter refines some familiar concepts for use in mixed-motive games and illustrates the features of the eight mixed-motive games that have stable Nash equilibrium points (Figure 6.4). The group of four games that do not have Nash equilibria is more interesting and is considered in detail in the second section.