This research is to develop a class of decentralized dynamic processes designed to converge to equilibria. These processes may also be regarded as distributed algorithms for computing solutions of systems of equations--the equations that characterize equilibrium. Unlike most dynamic processes that have been used to study stability of mechanisms, these processes are not given by differential or difference equations. Furthermore, these processes need not be temporally homogeneous. Some characteristics of this class of dynamic processes are: i) There is an agent, personifying an institution such as an organized market, or a central computer, who plays the role of coordinator; ii) no agent, including the coordinator, knows anything about the equilibrium equations of other agents; iii) the coordinator selects and announces points of the message space to the other agents, referred to as private agents. iv) no private agent is required to evaluate his equilibrium function, but only to determine its sign at a given point m. For example, in the setting of a market, it is easier for an agent to estimate whether a given allocation gives him more than he wants (positive excess demand) or less (negative) than to quantify the precise amount by which the allocation differs from his demands. No other computations are performed by the private agents. The researchers will explore new processes of this type for both linear equations, and nonlinear equations.
