  As artificial agents proliferate, it is becoming increasingly important to
ensure that their interactions with one another are well-behaved. In this
paper, we formalize a common-sense notion of when algorithms are well-behaved:
an algorithm is safe if it does no harm. Motivated by recent progress in deep
learning, we focus on the specific case where agents update their actions
according to gradient descent. The paper shows that that gradient descent
converges to a Nash equilibrium in safe games. The main contribution is to
define strongly-typed agents and show they are guaranteed to interact safely,
thereby providing sufficient conditions to guarantee safe interactions. A
series of examples show that strong-typing generalizes certain key features of
convexity, is closely related to blind source separation, and introduces a new
perspective on classical multilinear games based on tensor decomposition.
