Both in game theory and in general equilibrium theory, there exists a number of universally converging adjustment processes. In game theory, these processes typically serve the role of selecting a nash equilibrium. Examples are, the tracing procedure of harsanyi and selten or the equilibrium selection procedure proposed by mckelvey and palfrey. In general equilibrium, the processes are adjustment rules by which an auctioneer can clear all markets. Examples are the processes studied by smale, kamiya, van der laan and talman, and herings. The underlying reasons for convergence have remained rather mysterious in the literature, and convergence of different processes has seemed unrelated. This paper shows that convergence of all these processes relies on browder’s fixed point theorem.