  We study a class of non-cooperative aggregative games -- denoted as
\emph{social purpose games} -- in which the payoffs depend separately on a
player's own strategy (individual benefits) and on a function of the strategy
profile which is common to all players (social benefits) weighted by an
individual benefit parameter. This structure allows for an asymmetric
assessment of the social benefit across players.
  We show that these games have a potential and we investigate its properties.
We investigate the payoff structure and the uniqueness of Nash equilibria and
social optima. Furthermore, following the literature on partial cooperation, we
investigate the leadership of a single coalition of cooperators while the rest
of players act as non-cooperative followers. In particular, we show that social
purpose games admit the emergence of a stable coalition of cooperators for the
subclass of \emph{strict} social purpose games. Due to the nature of the
partial cooperative leadership equilibrium, stable coalitions of cooperators
reflect a limited form of farsightedness in their formation.
  As a particular application, we study the tragedy of the commons game. We
show that there emerges a single stable coalition of cooperators to curb the
over-exploitation of the resource.
