On Profit Sharing and Hierarchies in Organizations

We study the effect of hierarchies on the performance of an organization that exhibits both profit sharing and information sharing. We adopt a server-queue model of effort and intraorganizational competition and quantify the performance of an organization in terms of the overall efficiency and risk in meeting target production levels. On the one hand, we show that profit sharing leads to free riding at the Nash equilibrium and reduces overall effort. Introducing a form of information asymmetry, we then quantitatively establish the trade-off between free riding and the positive effects of information sharing in hierarchies. We formulate an optimal hierarchy design problem that captures both effects, and provide a simple algorithm that gives near optimal designs. We provide an analysis of the productive value of optimized hierarchies, considering their ability to attain target production levels with low risk.