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

TL;DR

This paper models how individuals in organizational networks allocate their efforts between production and management, analyzing strategic behaviors and designing reward schemes to optimize overall productivity.

Contribution

It provides a game-theoretic framework for effort distribution in networks and offers a design recipe for reward sharing to maximize net output.

Findings

Strategic effort allocation can lead to suboptimal productivity.

Reward schemes can be designed to improve overall output.

Price of anarchy may limit achieving optimal productivity.

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.