  Self-interested behavior from individuals can collectively lead to poor
societal outcomes. These outcomes can seemingly be improved through the actions
of altruistic agents, which benefit other agents in the system. However, it is
known in specific contexts that altruistic agents can actually induce worse
outcomes compared to a fully selfish population -- a phenomenon we term
altruistic perversity. This paper provides a holistic investigation into the
necessary conditions that give rise to altruistic perversity. In particular, we
study the class of two-strategy population games where one sub-population is
altruistic and the other is selfish. We find that a population game can admit
altruistic perversity only if the associated social welfare function is convex
and the altruistic population is sufficiently large. Our results are a first
step in establishing a connection between properties of nominal agent
interactions and the potential impacts from altruistic behaviors.
