Pure strategy equilibria in large demographic summary games

Many economic environments involve interaction between small numbers of large players as well as large numbers of small players whose individual actions are macroscopically negligible even while summary behavior within various demographic groups may impact the entire economy. We examine Nash equilibria of such mixed size, multi-demographic summary games. In particular, we establish existence theorems for equilibria in which small players universally pursue pure strategies, even when large player behavior must be simultaneously considered.