Game Theoretic Analysis of Production-Management Effort Distribution in Organizational Networks

In any organization, a primary goal of the designer is to maximize the net productive output. Every organization has a network (either hierarchical or other) that is used to divide the tasks. It is observed that the individuals in these networks trade off between their productive and managing efforts to do these tasks and the trade-off is caused by their positions and share of rewards in the network. Efforts of the agents here are substitutable, e.g., the increase in the productive effort by an individual in effect reduces the same of some other individual in the network, who now puts their efforts into management. The management effort of an agent improves the productivity of certain other agents in the network. In this paper, we provide a detailed analysis of the Nash equilibrium efforts of the individuals connected over a network and a design recipe of the reward sharing scheme that maximizes the net productive output. Our results show that under the strategic behavior of the agents, it may not always be possible to achieve the optimal output and we provide bounds on the achievability in such scenarios.