Equilibrium analysis for linear and nonlinear aggregation in network models

Abstract

In this paper, equilibrium analysis for network models is addressed and applied in particular to a network model of multilevel organisational learning. The equilibrium analysis addresses properties of aggregation characteristics and connectivity characteristics of a network. For aggregation characteristics, it is shown how certain classes of nonlinear functions enable equilibrium analysis of the emerging dynamics within the network like linear functions do. For connectivity characteristics, by using a form of stratification for the network's strongly connected components, it is shown how equilibrium analysis results can be obtained relating equilibrium values in any component to equilibrium values in (independent) components without incoming connections. In addition, concerning aggregation characteristics, two specific types of nonlinear functions for aggregation in networks (weighted euclidean functions and weighted geometric functions) are analysed. It is illustrated in detail how by using certain function transformations also methods for equilibrium analysis based on a symbolic linear equation solver, can be applied to make predictions about equilibrium values for them. All these results are applied to a network model for organisational learning. Finally, it is analysed in some depth how the function transformations applied can be described by the more general notion of function conjugate relation, also often used for coordinate transformations.