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Organizations consist of individuals connected by their responsibilities,incentives, and reporting structure. These connections are aptly represented bya network, hierarchical or other, which is often used to divide tasks. Aprimary goal of the organization as a whole is to maximize the net productiveoutput. Individuals in these networks trade off between their productive andmanaging efforts to perform these tasks and the trade-off is influenced bytheir positions and share of rewards in the network. Efforts of the agents hereare substitutable, e.g., the increase in the productive effort by an individualin effect reduces the same of some other individual in the network, who nowputs their efforts into management. The management effort of an agent improvesthe productivity of certain other agents in the network.  In this paper, we carry out a detailed game-theoretic analysis ofindividual's equilibrium split of efforts into multiple components whenconnected over a network. We provide a design recipe of the reward sharingscheme that maximizes the net productive output. Our results show that underthe strategic behavior of the agents, it may not always be possible to achievethe optimal output using an idea from game theory called the price of anarchy.

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