An Interaction Value Perspective on Firms of Differing Size

We present a general model of a network of interacting individuals, each of whom derives a known, real-valued benefit from each possible dyadic interaction. The model views interactions as knowledge-transfer exchanges that add value to the organization. We use this model to derive interaction patterns within an organization. We assume that the value of dyadic interaction benefits is distributed as a randomly permuted geometric series. Moreover, interactions only add value when a large enough waiting period is observed between interaction attempts. We show that an organization optimized for knowledge transfer has a distribution of interaction frequencies which correlates well with observations. Organizations of differing sizes can have similar optimal structures as long they have similar normalized levels of interdependence between interactions, and distribution of interaction benefit values. This research has implications for the design of communication infrastructure in a growing organization, as well as for the predictive value of modeling organizations at different scales.