Strategic complements and substitutes, and potential games

We show that games of strategic complements, or substitutes, with aggregation are “pseudo-potential” games. The upshot is that they possess Nash equilibria in pure strategies (NE), even if the strategy sets are not convex; and that various dynamic processes converge to NE. In particular, NE exist in Cournot oligopoly with indivisibilities in production.Our notion of aggregation is quite general and enables us to take a unified view of several disparate models.