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Supervisory Efficiency and Collusion in a Multiple-Agent Hierarchy

Che, X., Huang, Y. and Zhang, L. (2021). Supervisory Efficiency and Collusion in a Multiple-Agent Hierarchy. Games and Economic Behavior,


We analyze a principal-supervisor-two-agent hierarchy with inefficient supervision. The supervisor may collect an incorrect signal on the agents’ effort levels. When reporting to the principal, the supervisor may collude with one or both agents to manipulate the signal in exchange for a bribe. In the hierarchy, we identify a new trade-off between inefficient supervision and supervisor-agent collusion: Due to the incorrect supervisory signal, truthfully reporting the supervisory signal under collusion proofness may mistakenly punish the agents. As a result, allowing a certain type of collusion helps correct the incorrect signal and provides a higher incentive for the agents to work. We characterize the optimal no-supervision, collusion-proof, and collusive-supervision contracts, and show that the collusive-supervision contract dominates the others when supervisory efficiency is at an intermediate level.

Publication Type: Article
Additional Information: © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Publisher Keywords: three-level hierarchy, collusion, supervisory efficiency, multiple agents, optimal contract
Subjects: H Social Sciences > HB Economic Theory
Departments: School of Arts & Social Sciences > Economics
Date available in CRO: 10 Sep 2021 07:39
Date deposited: 10 September 2021
Date of acceptance: 9 September 2021
[img] Text - Accepted Version
This document is not freely accessible due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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