Principal-agent VCG contracts

R Lavi, Elisheva Shamash

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We study a complete information game with multiple principals and multiple common agents. Each agent takes an action that can affect the payoffs of all principals. Prat and Rustichini (2003) who introduce this model assume classic contracts: each principal offers monetary transfers to each agent conditional on the action taken by the agent. We define VCG contracts in which the monetary transfers to each agent additionally depend on all principals' offers, and study its effect on the existence of efficient pure subgame perfect equilibrium outcomes. Using a necessary and sufficient condition for the existence of a pure subgame perfect equilibrium (pure SPE) with VCG contracts, which we develop, we show that the class of instances that admit an efficient pure SPE with VCG contracts strictly contains the class of instances that admit an efficient pure SPE with classic contracts. In addition, the difference between the former class and the class of instances that admit a ‘weakly truthful’ SPE with classic contracts has positive measure. Although VCG contracts broaden the existence of pure subgame perfect equilibria, we show that the worst case welfare loss in a pure SPE outcome, over all games with any fixed M≥2 number of principals, is the same for both VCG contracts and classic contracts.

Original languageEnglish
Article number105443
Number of pages26
JournalJournal of Economic Theory
Early online date21 Mar 2022
Publication statusPublished - 30 Apr 2022

Bibliographical note

Funding Information:
A one-page abstract of a preliminary version of this paper has appeared in the proceedings of the 2019 ACM Conference on Economics and Computation ( Lavi and Shamash, 2019 ). This research was supported by the ISF-NSFC joint research program (grant No. 2560/17 ).


  • Contractible contracts
  • Games played through agents
  • Principal-agent
  • VCG

ASJC Scopus subject areas

  • Economics and Econometrics


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