Game Theoretic Analysis of Production-Management Effort Distribution in Organizational Networks (1302.3045v4)

Abstract: 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.