Date: 29 Jul 2005

Decision-making by hierarchies of discordant agents

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Abstract

We study the following decision-making scenario: A linear program is solved by a set of agents arranged hierarchically in a tree, where each agent decides the level of certain variables, and has a distinct objective function, known to all agents. Authority is reflected in two ways: Agents higher in the tree set their variables first; and agents that are siblings in the tree resolve their game by focusing on the Nash equilibrium that is optimum for the agent above them. We give a necessary and sufficient condition for such a hierarchy to be efficient (i.e., to have perfect coordination, to ultimately optimize the objective of the firm). We study problems related to designing a hierarchy (assigning decision makers to positions in the tree) in order to achieve efficiency or otherwise optimize coordination.

This specificity of tasks that seems to be required for the derivation of meaningful results in this field may reflect the fact that managerial and organizational principles are not of general applicability, but very much industry-specific.