  Dynamic games arise when multiple agents with differing objectives choose
control inputs to a dynamic system. Dynamic games model a wide variety of
applications in economics, defense, and energy systems. However, compared to
single-agent control problems, the computational methods for dynamic games are
relatively limited. As in the single-agent case, only very specialized dynamic
games can be solved exactly, and so approximation algorithms are required. This
paper extends the differential dynamic programming algorithm from single-agent
control to the case of non-zero sum full-information dynamic games. The method
works by computing quadratic approximations to the dynamic programming
equations. The approximation results in static quadratic games which are solved
recursively. Convergence is proved by showing that the algorithm iterates
sufficiently close to iterates of Newton's method to inherit its convergence
properties. A numerical example is provided.
