Optimal Organization Size in a Stochastic Environment with Externalities

In this study, we explore the relationships among group size, the extent of interactions with other groups, and group performance in a stochastic environment. We have developed a modeling framework which allows the connections among the individual members constituting a group and the connections between groups (externalities) to be tuned independently. The search for improved group configurations is modeled as a random walk on a space of possible configurations whereby agents in a group periodically have the opportunity to accept or reject random changes in their characteristics. By controlling which groups have externalities with which other groups, we can manipulate the topology of the problem---the web of interactions within and between groups. We present numerical results showing that optimal group size relates to the magnitude of externalities and the length of the search period. Our main result suggests that for short search periods, large organizations perform best, while for longer time horizons, the advantage accrues to small sized groups with a small number of (but not no) externalities. However, over these long time horizons, as the extent of externalities increases, modest increases in group size enhances performance. Under all circumstances, organizations that perform best border on a regime of chaotic behavior. The results have applications at both the micro-scale for the size and structure of production units and at the macro-level for understanding the relationships between groups and communities in a hierarchy of market networks. <p> <p> Submitted to Organization Science.