  We prove that, under appropriate conditions, an abstract game with
quasi-Leontief payoff functions $u_i : \prod_{j=1}^nX_j\to\mathbb{R}$ has a
Nash equilibria. When all the payoff functions are globally quasi-Leontief, the
existence and the characterization of efficient Nash equilibria mainly follows
from the analysis carried out in part I. When the payoff functions are
individually quasi-Leontief functions the matter is somewhat more complicated.
We assume that all the strategy spaces are compact topological semilattices,
and under appropriate continuity conditions on the payoff functions, we show
that there exists an efficient Nash equilibria using the Eilenberg-Montgomery
Fixed Point Theorem for acyclic valued upper semicontinuous maps defined on an
absolute retract and some non trivial properties of topological semilattices.
The map in question is defined on the set of Nash equilibria and its fixed
points are exactly the efficient Nash equilibria.
