Globally and Universally Convergent Price Adjustment Processes

We discuss three processes of price adjustment, respectively proposed by Smale (1976), van der Laan and Talman (1987), and Kamiya (1990). The latter two processes are guaranteed to converge to a competitive equilibrium for a generic set of exchange economies for any initial price system and the former process for a generic set of exchange economies for any initial price system such that one of the prices is zero. The simplest way to describe these processes is by characterizing the path of prices that they generate. Convergence proofs then rely on results from differential topology and establish that these paths have a manifold structure. The van der Laan and Talman (1987) process was shown by Herings (1997) to exhibit global and universal convergence. The required tools, involving regular constraint sets and manifolds with generalized boundary, are explained in detail and can be fruitfully applied in other domains as well. The paper concludes with an overview of globally and universally convergent processes in other environments like production economies, economies with price rigidities, and normal-form games.