Multidimensional Networks: Creating a New Framework of Organization Structure for Complex Strategies
Firms today typically face and must coordinate multiple dimensions of competition. This paper extends the conventional notion of organization structure and recaptures it as an aggregation of differentiated networks specialized for multiple dimensions of strategic attention. Graph-theoretic languages commonly used for network representations are not sufficient to capture such aggregations. In this study, we develop an extension of directed graphs called modal graphs to represent and analyze the multidimensional complexity of organization structure. In modal graphs, elementary building blocks are coordination clauses, each of which is qualified by a strategic focus called a modality, a concept adapted from sentential modalities in modal logic. Individual networks of the firm's structure are then given by compositions of related coordination clauses. While modal graphs enable massively networked structures, it is still desirable to designate a dominant dimension as the conventional reporting hierarchy. We identify a class of modal graphs and develop soundness and completeness results for desirable reporting hierarchies with respect to this class. Namely, we construct a procedure and show that the procedure identifies only desirable reporting hierarchies (soundness) and all the desirable reporting hierarchies (completeness).