  This work studies Nash equilibria for games where a mixture of coordinating
and anti-coordinating agents, with possibly heterogeneous thresholds, coexist
and interact through an all-to-all network. Whilst games with only coordinating
or only anti-coordinating agents are potential, also in the presence of
heterogeneities, this does not hold when both type of agents are simultaneously
present. This makes their analysis more difficult and existence of Nash
equilibria not guaranteed. Our main result is a checkable condition on the
threshold distributions that characterizes the existence of Nash equilibria in
such mixed games. When this condition is satisfied an explicit algorithm allows
to determine the complete set of such equilibria. Moreover, for the special
case when only one type of agents is present (either coordinating or
anti-coordinating), our results allow an explicit computation of the
cardinality of Nash equilibria.
