Stability and complex dynamics in a discrete tatonnement model

In this paper we study the dynamics of discrete price adjustment processes. We show that gross substitutability leads to a kind of stability of the process: it guarantees that all prices converge to some bounded region that contains the unique equilibrium price. The dynamics inside this region is by no means trivial. We demonstrate that as the speed of adjustment increases the process undergoes several bifurcations, and the dynamics may become quite complex. Our approach differs from other literature on tatonnement processes in that our systems are not necessarily one-dimensional. (C) 1998 Elsevier Science B.V.