We study the subgame perfect equilibria of two player stochastic games with perfect monitoring and geometric discounting. A novel algorithm is developed for calculating the discounted payoﬀs that can be attained in equilibrium. This algorithm generates a sequence of tuples of payoﬀs vectors, one payoﬀ for each state, that move around the equilibrium payoﬀ sets in a clockwise manner. The trajectory of these “pivot” payoﬀs asymptotically traces the boundary of the equilibrium payoﬀ correspondence. We also provide an implementation of our algorithm, and preliminary simulations indicate that it is more eﬃcient than existing methods. The theoretical results that underlie the algorithm also yield a bound on the number of extremal equilibrium payoﬀs.