  This paper is concerned with complexity theoretic aspects of a general
formulation of quantum game theory that models strategic interactions among
rational agents that process and exchange quantum information. In particular,
we prove that the computational problem of finding an approximate Nash
equilibrium in a broad class of quantum games is, like the analogous problem
for classical games, included in (and therefore complete for) the complexity
class PPAD. Our main technical contribution, which facilitates this inclusion,
is an extension of prior methods in computational game theory to strategy
spaces that are characterized by semidefinite programs.
