Equilibrium Analysis for Linear and Nonlinear Aggregation in Network Models: Applied to Mental Model Aggregation in Multilevel Organisational Learning

In this paper, equilibrium analysis for network models is addressed and applied in particular to a network model of multilevel organisational learning. Equilibrium analysis can take into account both properties of aggregation characteristics and properties of connectivity characteristics of a network. For aggregation characteristics, it is shown how, in contrast to often held beliefs, certain classes of nonlinear functions used for aggregation in network models enable equilibrium analysis of the emerging dynamics within the network like linear functions do. For connectivity characteristics, it is shown by introducing a form of stratification how specifically for acyclic networks the equilibrium values of all nodes can be directly computed (by any functions used for aggregation) from those of the (independent) nodes without incoming connections. Moreover, by introducing a form of stratification for the network's strongly connected components, it is also shown for any type of (cyclic) connectivity, similar 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. Focusing on them in particular, 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 such nonlinear cases as well. Finally, it is shown and analysed in some depth how these function transformations can be described by the more general notion of function conjugate relation, which is also often used for coordinate transformations.