  Organizations consist of individuals connected by their responsibilities,
incentives, and reporting structure. These connections are aptly represented by
a network, hierarchical or other, which is often used to divide tasks. A
primary goal of the organization as a whole is to maximize the net productive
output. Individuals in these networks trade off between their productive and
managing efforts to perform these tasks and the trade-off is influenced 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 carry out a detailed game-theoretic analysis of
individual's equilibrium split of efforts into multiple components when
connected over a network. We provide 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 using an idea from game theory called the price of anarchy.
