Supervisory efficiency and collusion in a multiple-agent hierarchy

Xiaogang Che*, Yangguang Huang, Le Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)425-442
Number of pages18
JournalGames and Economic Behavior
Early online date17 Sep 2021
Publication statusPublished - Nov 2021


  • three-level hierarchy
  • collusion
  • supervisory efficiency
  • multiple agents
  • optimal contract


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