  We study heterogeneous $k$-facility location games. In this model there are
$k$ facilities where each facility serves a different purpose. Thus, the
preferences of the agents over the facilities can vary arbitrarily. Our goal is
to design strategy proof mechanisms that place the facilities in a way to
maximize the minimum utility among the agents. For $k=1$, if the agents'
locations are known, we prove that the mechanism that places the facility on an
optimal location is strategy proof. For $k \geq 2$, we prove that there is no
optimal strategy proof mechanism, deterministic or randomized, even when $k=2$
there are only two agents with known locations, and the facilities have to be
placed on a line segment. We derive inapproximability bounds for deterministic
and randomized strategy proof mechanisms. Finally, we focus on the line segment
and provide strategy proof mechanisms that achieve constant approximation. All
of our mechanisms are simple and communication efficient. As a byproduct we
show that some of our mechanisms can be used to achieve constant factor
approximations for other objectives as the social welfare and the happiness.
